In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration.[1] A concentration can be any kind of chemical mixture, but most frequently solutes and solvents in solutions. The molar (amount) concentration has variants such as normal concentration and osmotic concentration.

Qualitative description

Dilution-concentration simple example
These glasses containing red dye demonstrate qualitative changes in concentration. The solutions on the left are more dilute, compared to the more concentrated solutions on the right.

Often in informal, non-technical language, concentration is described in a qualitative way, through the use of adjectives such as "dilute" for solutions of relatively low concentration and "concentrated" for solutions of relatively high concentration. To concentrate a solution, one must add more solute (for example, alcohol), or reduce the amount of solvent (for example, water). By contrast, to dilute a solution, one must add more solvent, or reduce the amount of solute. Unless two substances are fully miscible there exists a concentration at which no further solute will dissolve in a solution. At this point, the solution is said to be saturated. If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, when supersaturation may occur. Instead, phase separation will occur, leading to coexisting phases, either completely separated or mixed as a suspension. The point of saturation depends on many variables such as ambient temperature and the precise chemical nature of the solvent and solute.

Concentrations are often called levels, reflecting the mental schema of levels on the vertical axis of a graph, which can be high or low (for example, "high serum levels of bilirubin" are concentrations of bilirubin in the blood serum that are greater than normal).

Quantitative notation

There are four quantities that describe concentration:

Mass concentration

The mass concentration is defined as the mass of a constituent divided by the volume of the mixture :

The SI unit is kg/m3 (equal to g/L).

Molar concentration

The molar concentration is defined as the amount of a constituent (in moles) divided by the volume of the mixture :

The SI unit is mol/m3. However, more commonly the unit mol/L (= mol/dm3) is used.

Number concentration

The number concentration is defined as the number of entities of a constituent in a mixture divided by the volume of the mixture :

The SI unit is 1/m3.

Volume concentration

The volume concentration (not to be confused with volume fraction[2]) is defined as the volume of a constituent divided by the volume of the mixture :

Being dimensionless, it is expressed as a number, e.g., 0.18 or 18%; its unit is 1.

There seems to be no standard notation in the English literature. The letter used here is normative in German literature (see Volumenkonzentration).

Related quantities

Several other quantities can be used to describe the composition of a mixture. Note that these should not be called concentrations.[1]


Normality is defined as the molar concentration divided by an equivalence factor . Since the definition of the equivalence factor depends on context (which reaction is being studied), IUPAC and NIST discourage the use of normality.


(Not to be confused with Molarity)

The molality of a solution is defined as the amount of a constituent (in moles) divided by the mass of the solvent (not the mass of the solution):

The SI unit for molality is mol/kg.

Mole fraction

The mole fraction is defined as the amount of a constituent (in moles) divided by the total amount of all constituents in a mixture :

The SI unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole fractions.

Mole ratio

The mole ratio is defined as the amount of a constituent divided by the total amount of all other constituents in a mixture:

If is much smaller than , the mole ratio is almost identical to the mole fraction.

The SI unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole ratios.

Mass fraction

The mass fraction is the fraction of one substance with mass to the mass of the total mixture , defined as:

The SI unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass fractions.

Mass ratio

The mass ratio is defined as the mass of a constituent divided by the total mass of all other constituents in a mixture:

If is much smaller than , the mass ratio is almost identical to the mass fraction.

The SI unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass ratios.

Dependence on volume

Concentration depends on the variation of the volume of the solution with temperature due mainly to thermal expansion.

Table of concentrations and related quantities

Concentration type Symbol Definition SI unit other unit(s)
mass concentration or kg/m3 g/100mL (= g/dL)
molar concentration mol/m3 M (= mol/L)
number concentration 1/m3 1/cm3
volume concentration m3/m3
Related quantities Symbol Definition SI unit other unit(s)
normality mol/m3 N (= mol/L)
molality mol/kg
mole fraction mol/mol ppm, ppb, ppt
mole ratio mol/mol ppm, ppb, ppt
mass fraction kg/kg ppm, ppb, ppt
mass ratio kg/kg ppm, ppb, ppt

See also


  1. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "concentration". doi:10.1351/goldbook.C01222
  2. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "volume fraction". doi:10.1351/goldbook.V06643
Anne Frank

Annelies Marie "Anne" Frank (German: [anəˈliːs maˈʁiː ˈfʁaŋk], Dutch: [ɑnəˈlis maːˈri ˈfrɑŋk]); 12 June 1929 – February or March 1945) was a German-born Dutch-Jewish diarist. One of the most discussed Jewish victims of the Holocaust, she gained fame posthumously with the publication of The Diary of a Young Girl (originally Het Achterhuis in Dutch; English: The Secret Annex), in which she documents her life in hiding from 1942 to 1944, during the German occupation of the Netherlands in World War II. It is one of the world's best known books and has been the basis for several plays and films.

Born in Frankfurt, Germany, she lived most of her life in or near Amsterdam, Netherlands, having moved there with her family at the age of four and a half when the Nazis gained control over Germany. Born a German national, she lost her citizenship in 1941 and thus became stateless. By May 1940, the Franks were trapped in Amsterdam by the German occupation of the Netherlands. As persecutions of the Jewish population increased in July 1942, the Franks went into hiding in some concealed rooms behind a bookcase in the building where Anne's father, Otto Frank, worked. From then until the family's arrest by the Gestapo in August 1944, she kept a diary she had received as a birthday present, and wrote in it regularly. Following their arrest, the Franks were transported to concentration camps. In October or November 1944, Anne and her sister, Margot, were transferred from Auschwitz to Bergen-Belsen concentration camp, where they died (probably of typhus) a few months later. They were originally estimated by the Red Cross to have died in March, with Dutch authorities setting 31 March as their official date of death, but research by the Anne Frank House in 2015 suggests it is more likely that they died in February.Otto, the only survivor of the Franks, returned to Amsterdam after the war to find that her diary had been saved by his secretary, Miep Gies, and his efforts led to its publication in 1947. It was translated from its original Dutch version and first published in English in 1952 as The Diary of a Young Girl, and has since been translated into over 60 languages.

Auschwitz concentration camp

The Auschwitz concentration camp (Konzentrationslager Auschwitz) was a complex of over 40 concentration and extermination camps built and operated by Nazi Germany in occupied Poland during World War II and the Holocaust. It consisted of Auschwitz I, the main camp (Stammlager) and administrative headquarters in Oświęcim; Auschwitz II–Birkenau, a combined concentration and extermination camp three kilometers away in Brzezinka; Auschwitz III–Monowitz, a labor camp created to staff an IG Farben synthetic-rubber factory; and dozens of other subcamps.After Germany invaded Poland in September 1939, sparking World War II, the Germans converted Auschwitz I, a former army barracks, to hold Polish political prisoners. The first prisoners, German criminals brought to the camp as functionaries, arrived in May 1940, and the first gassing of prisoners took place in block 11 of Auschwitz I in September 1941. Auschwitz II–Birkenau went on to become a major site of the Nazis' Final Solution to the Jewish Question. From early 1942 until late 1944, transport trains delivered Jews from all over German-occupied Europe to the camp's gas chambers. Of the estimated 1.3 million people sent to Auschwitz, at least 1.1 million died, around 90 percent of them Jews. Approximately one in six Jews killed in the Holocaust died at the camp. Others deported to Auschwitz included 150,000 non-Jewish Poles, 23,000 Roma, 15,000 Soviet prisoners of war, 400 Jehovah's Witnesses, tens of thousands of others of diverse nationalities, and an unknown number of gay men. Many of those not killed in the gas chambers died because of starvation, forced labor, infectious diseases, individual executions, and medical experiments.

In the course of the war, the camp was staffed by 7,000 members of the German Schutzstaffel (SS), approximately 12 percent of whom were later convicted of war crimes; several, including camp commandant Rudolf Höss, were executed. The Allies did not act on early reports of atrocities at the camp, and their failure to bomb the camp or its railways remains controversial. At least 802 prisoners tried to escape from Auschwitz, 144 successfully, and on 7 October 1944 two Sonderkommando units, consisting of prisoners assigned to staff the gas chambers, launched a brief, unsuccessful uprising.

As Soviet troops approached Auschwitz in January 1945, most of its population was sent west on a death march. The remaining prisoners were liberated on 27 January 1945, a day commemorated as International Holocaust Remembrance Day. In the following decades, survivors such as Primo Levi, Viktor Frankl, and Elie Wiesel wrote memoirs of their experiences in Auschwitz, and the camp became a dominant symbol of the Holocaust. In 1947 Poland founded the Auschwitz-Birkenau Memorial and Museum on the site of Auschwitz I and II, and in 1979 it was named a World Heritage Site by UNESCO.

Bergen-Belsen concentration camp

Bergen-Belsen [ˈbɛʁɡn̩.bɛlsn̩], or Belsen, was a Nazi concentration camp in what is today Lower Saxony in northern Germany, southwest of the town of Bergen near Celle. Originally established as a prisoner of war camp, in 1943, parts of it became a concentration camp. Initially this was an "exchange camp", where Jewish hostages were held with the intention of exchanging them for German prisoners of war held overseas. The camp was later expanded to accommodate Jews from other concentration camps.

After 1945 the name was applied to the displaced persons camp established nearby, but it is most commonly associated with the concentration camp. From 1941 to 1945, almost 20,000 Soviet prisoners of war and a further 50,000 inmates died there. Overcrowding, lack of food and poor sanitary conditions caused outbreaks of typhus, tuberculosis, typhoid fever and dysentery, leading to the deaths of more than 35,000 people in the first few months of 1945, shortly before and after the liberation.

The camp was liberated on April 15, 1945, by the British 11th Armoured Division. The soldiers discovered approximately 60,000 prisoners inside, most of them half-starved and seriously ill, and another 13,000 corpses, including those of Anne and Margot Frank, lying around the camp unburied. The horrors of the camp, documented on film and in pictures, made the name "Belsen" emblematic of Nazi crimes in general for public opinion in many countries in the immediate post-1945 period. Today, there is a memorial with an exhibition hall at the site.

Buchenwald concentration camp

Buchenwald (German pronunciation: [ˈbuːxənvalt]; literally beech forest) was a Nazi concentration camp established on Ettersberg hill near Weimar, Germany, in July 1937. It was one of the first and the largest of the concentration camps within Germany's 1937 borders. Many actual or suspected communists were among the first internees.

Prisoners from all over Europe and the Soviet Union—Jews, Poles and other Slavs, the mentally ill and physically disabled, political prisoners, Romani people, Freemasons, criminals, homosexuals, and prisoners of war—worked primarily as forced labor in local armaments factories. The insufficient food and poor conditions, as well as deliberate executions, led to 56,000 deaths at Buchenwald of the 250,000 prisoners who passed through the camp. The camp gained notoriety when it was liberated by the United States Army in 1945; Allied commander Dwight D. Eisenhower visited one of its subcamps.

From 1945 to 1950, the camp was used by the Soviet occupation authorities as an internment camp, NKVD special camp Nr. 2. Today the remains of Buchenwald serve as a memorial and permanent exhibition and museum.

Dachau concentration camp

Dachau concentration camp (; German: Konzentrationslager (KZ) Dachau, IPA: [ˈdaxaʊ]) was the first of the Nazi concentration camps opened in 1933, intended to hold political prisoners. It is located on the grounds of an abandoned munitions factory northeast of the medieval town of Dachau, about 16 km (10 mi) northwest of Munich in the state of Bavaria, in southern Germany. Opened by Heinrich Himmler, its purpose was enlarged to include forced labor, and eventually, the imprisonment of Jews, German and Austrian criminals, and eventually foreign nationals from countries that Germany occupied or invaded. The Dachau camp system grew to include nearly 100 sub-camps, which were mostly work camps or Arbeitskommandos, and were located throughout southern Germany and Austria. The camps were liberated by U.S. forces on 29 April 1945.

Prisoners lived in constant fear of brutal treatment and terror detention including standing cells, floggings, the so-called tree or pole hanging, and standing at attention for extremely long periods. There were 32,000 documented deaths at the camp, and thousands that are undocumented.Approximately 10,000 of the 30,000 prisoners were sick at the time of liberation.In the postwar years the Dachau facility served to hold SS soldiers awaiting trial. After 1948, it held ethnic Germans who had been expelled from eastern Europe and were awaiting resettlement, and also was used for a time as a United States military base during the occupation. It was finally closed in 1960.

There are several religious memorials within the Memorial Site, which is open to the public.


Diffusion is net movement of ions and molecules from a region of higher concentration (or high chemical potential) to a region of lower concentration (or low chemical potential). Diffusion is driven by a gradient in chemical potential of the diffusing species.

A gradient is the change in the value of a quantity e.g. concentration, pressure, or temperature with the change in another variable, usually distance. A change in concentration over a distance is called a concentration gradient, a change in pressure over a distance is called a pressure gradient, and a change in temperature over a distance is called a temperature gradient.

The word diffusion derives from the Latin word, diffundere, which means "to spread way out.”

A distinguishing feature of diffusion is that it depends on particle random walk, and results in mixing or mass transport without requiring directed bulk motion. Bulk motion, or bulk flow, is the characteristic of advection.

The term convection is used to describe the combination of both transport phenomena.


Internment is the imprisonment of people, commonly in large groups, without charges or intent to file charges, and thus no trial. The term is especially used for the confinement "of enemy citizens in wartime or of terrorism suspects". Thus, while it can simply mean imprisonment, it tends to refer to preventive confinement, rather than confinement after having been convicted of some crime. Use of these terms is subject to debate and political sensitivities.Interned persons may be held in prisons or in facilities known as internment camps. In certain contexts, these may also be known either officially or pejoratively, as concentration camps.

Internment also refers to a neutral country's practice of detaining belligerent armed forces and equipment on its territory during times of war under the Hague Convention of 1907.The Universal Declaration of Human Rights restricts the use of internment. Article 9 states that "No one shall be subjected to arbitrary arrest, detention or exile."

List of Nazi concentration camps

This article presents a partial list of the most prominent Nazi concentration camps and extermination camps set up across Europe before and during the course of World War II and the Holocaust. A more complete list drawn up in 1967 by the West German Ministry of Justice names about 1,200 camps and subcamps in countries occupied by Germany, while the Jewish Virtual Library writes: "It is estimated that the Germans established 15,000 camps in the occupied countries." Some of the data presented in this table originates from the monograph titled The War Against the Jews by Lucy Dawidowicz among similar others.In 1933–1939, before the onset of war, most prisoners consisted of German Communists, Socialists, Social Democrats, Roma, Jehovah's Witnesses, homosexuals, and persons accused of 'asocial' or socially 'deviant' behavior by the Germans. They were not utilized to sustain the German war effort.

Although the term 'concentration camp' is often used as a general term for all German camps during World War II, there were in fact several types of concentration camps in the German camp system. Holocaust scholars make a clear distinction between death camps and concentration camps which served a number of war related purposes including prison facilities, labor camps, prisoner of war camps, and transit camps among others.Concentration camps served primarily as detention and slave labor exploitation centers. An estimated 15 to 20 million people were imprisoned in 42,500 camps and ghettos, and often pressed into slavery during the subsequent years, according to research by the United States Holocaust Memorial Museum conducted more recently. The system of about 20,000 concentration camps in Germany and German-occupied Europe played a pivotal role in economically sustaining the German reign of terror. Most of them were destroyed by the Germans in an attempt to hide the evidence of war crimes and crimes against humanity; nevertheless tens of thousands of prisoners sent on death marches were liberated by the Allies afterward.Extermination camps were designed and built exclusively to kill prisoners on a massive scale, often immediately upon arrival. The extermination camps of Operation Reinhard such as Bełżec, Sobibór and Treblinka served as "death factories" in which German SS and police murdered nearly 2,700,000 Jews by asphyxiation with poison gas, shooting, and extreme work under starvation conditions.The concentration camps held large groups of prisoners without trial or judicial process. In modern historiography, the term refers to a place of systemic mistreatment, starvation, forced labour and murder.

Mauthausen-Gusen concentration camp complex

The Mauthausen–Gusen concentration camp complex consisted of the Mauthausen concentration camp on a hill above the market town of Mauthausen (roughly 20 kilometres (12 mi) east of Linz, Upper Austria) plus a group of nearly 100 further subcamps located throughout Austria and southern Germany. The three Gusen concentration camps in and around the village of St Georgen/Gusen, just a few kilometres from Mauthausen, held a significant proportion of prisoners within the camp complex, at times exceeding the number of prisoners at the Mauthausen main camp.

The Mauthausen main camp operated from the time of the Anschluss, when Austria was annexed to Nazi Germany in 8 August 1938, to 5 May 1945, at the end of the Second World War. Starting with the camp at Mauthausen, the number of subcamps expanded over time and by the summer of 1940 Mauthausen and its subcamps had become one of the largest labour camp complexes in the German-controlled part of Europe. As at other Nazi concentration camps, the inmates at Mauthausen and its subcamps were forced to work as slave labour, under conditions that caused many deaths. Mauthausen and its subcamps included quarries, munitions factories, mines, arms factories and plants assembling Me 262 fighter aircraft. In January 1945, the camps contained roughly 85,000 inmates. The death toll remains unknown, although most sources place it between 122,766 and 320,000 for the entire complex.

Mauthausen was one of the first massive concentration camp complexes in Nazi Germany, and the last to be liberated by the Allies. The two largest camps, Mauthausen and Gusen I, were classed as "Grade III" (Stufe III) concentration camps, which meant that they were intended to be the toughest camps for the "incorrigible political enemies of the Reich". Mauthausen never lost this Stufe III classification. In the offices of the Reich Main Security Office (Reichssicherheitshauptamt; RSHA) it was referred to by the nickname Knochenmühle – the bone-grinder (literally bone-mill). Unlike many other concentration camps, which were intended for all categories of prisoners, Mauthausen was mostly used for extermination through labour of the intelligentsia – educated people and members of the higher social classes in countries subjugated by the Nazi regime during World War II. The Mauthausen main camp is now a museum.

Median lethal dose

In toxicology, the median lethal dose, LD50 (abbreviation for "lethal dose, 50%"), LC50 (lethal concentration, 50%) or LCt50 is a measure of the lethal dose of a toxin, radiation, or pathogen. The value of LD50 for a substance is the dose required to kill half the members of a tested population after a specified test duration. LD50 figures are frequently used as a general indicator of a substance's acute toxicity. A lower LD50 is indicative of increased toxicity.

The test was created by J.W. Trevan in 1927. The term semilethal dose is occasionally used in the same sense, in particular with translations of foreign language text, but can also refer to a sublethal dose. LD50 is usually determined by tests on animals such as laboratory mice.

In 2011, the U.S. Food and Drug Administration approved alternative methods to LD50 for testing the cosmetic drug Botox without animal tests.

Michaelis–Menten kinetics

In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate (rate of formation of product, ) to , the concentration of a substrate S. Its formula is given by

This equation is called the Michaelis–Menten equation. Here, represents the maximum rate achieved by the system, at saturating substrate concentration. The Michaelis constant is the substrate concentration at which the reaction rate is half of . Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions.

Molar concentration

Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per litre, having the unit symbol mol/L. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M.

Nazi concentration camp badge

Nazi concentration camp badges, primarily triangles, were part of the system of identification in Nazi camps. They were used in the concentration camps in the Nazi-occupied countries to identify the reason the prisoners had been placed there. The triangles were made of fabric and were sewn on jackets and trousers of the prisoners. These mandatory badges of shame had specific meanings indicated by their colour and shape. Such emblems helped guards assign tasks to the detainees. For example, a guard at a glance could see if someone were a convicted criminal (green patch) and thus likely of a tough temperament suitable for kapo duty.

Someone with an escape suspect mark usually would not be assigned to work squads operating outside the camp fence. Someone wearing an F could be called upon to help translate guards' spoken instructions to a trainload of new arrivals from France. Some historical monuments quote the badge-imagery, with the use of a triangle being a sort of visual shorthand to symbolize all camp victims.

The modern-day use of a pink triangle emblem to symbolize gay rights is a response to the camp identification patches.

Nazi concentration camps

Nazi Germany maintained concentration camps (German: Konzentrationslager, KZ or KL) throughout the territories it controlled before and during the Second World War. The first Nazi camps were erected in Germany in March 1933 immediately after Hitler became Chancellor and his Nazi Party was given control of the police by Reich Interior Minister Wilhelm Frick and Prussian Acting Interior Minister Hermann Göring. Used to hold and torture political opponents and union organizers, the camps initially held around 45,000 prisoners. In 1933–1939, before the onset of war, most prisoners consisted of German Communists, Socialists, Social Democrats, Roma, Jehovah's Witnesses, homosexuals, and persons accused of 'asocial' or socially 'deviant' behavior by the Germans.Heinrich Himmler's Schutzstaffel (SS) took full control of the police and the concentration camps throughout Germany in 1934–35. The role of the camps expanded to hold so-called "undesirables" such as Jews, Romanis/Sintis, Serbs, Soviet POWs, Poles, disabled people, and clergymen. The number of people in the camps, which had fallen to 7,500, grew again to 21,000 by the start of World War II and peaked at 715,000 in January 1945.Beginning in 1934 the concentration camps were administered by the Concentration Camps Inspectorate (CCI), which in 1942 was merged into SS-Wirtschafts-Verwaltungshauptamt, and they were guarded by SS-Totenkopfverbände (SS-TV).

Holocaust scholars draw a distinction between concentration camps (described in this article) and extermination camps, which were established by Nazi Germany for the industrial-scale mass murder of Jews in the ghettos by way of gas chambers.


Osmosis () is the spontaneous net movement of solvent molecules through a selectively permeable membrane into a region of higher solute concentration, in the direction that tends to equalize the solute concentrations on the two sides. It may also be used to describe a physical process in which any solvent moves across a selectively permeable membrane (permeable to the solvent, but not the solute) separating two solutions of different concentrations. Osmosis can be made to do work. Osmotic pressure is defined as the external pressure required to be applied so that there is no net movement of solvent across the membrane. Osmotic pressure is a colligative property, meaning that the osmotic pressure depends on the molar concentration of the solute but not on its identity.

Osmosis is a vital process in biological systems, as biological membranes are semipermeable. In general, these membranes are impermeable to large and polar molecules, such as ions, proteins, and polysaccharides, while being permeable to non-polar or hydrophobic molecules like lipids as well as to small molecules like oxygen, carbon dioxide, nitrogen, and nitric oxide. Permeability depends on solubility, charge, or chemistry, as well as solute size. Water molecules travel through the plasma membrane, tonoplast membrane (vacuole) or protoplast by diffusing across the phospholipid bilayer via aquaporins (small transmembrane proteins similar to those responsible for facilitated diffusion and ion channels). Osmosis provides the primary means by which water is transported into and out of cells. The turgor pressure of a cell is largely maintained by osmosis across the cell membrane between the cell interior and its relatively hypotonic environment.


In chemistry, pH () is a scale used to specify how acidic or basic a water-based solution is. Acidic solutions have a lower pH, while basic solutions have a higher pH. At room temperature (25 °C), pure water is neither acidic nor basic and has a pH of 7.

The pH scale is logarithmic and approximates the negative of the base 10 logarithm of the molar concentration (measured in units of moles per liter) of hydrogen ions in a solution. More precisely it is the negative of the base 10 logarithm of the activity of the hydrogen ion. At 25 °C, solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. The neutral value of the pH depends on the temperature, being lower than 7 if the temperature increases. The pH value can be less than 0 for very strong acids, or greater than 14 for very strong bases.The pH scale is traceable to a set of standard solutions whose pH is established by international agreement. Primary pH standard values are determined using a concentration cell with transference, by measuring the potential difference between a hydrogen electrode and a standard electrode such as the silver chloride electrode. The pH of aqueous solutions can be measured with a glass electrode and a pH meter, or a color-changing indicator. Measurements of pH are important in chemistry, agronomy, medicine, water treatment, and many other applications.

Ravensbrück concentration camp

Ravensbrück (pronounced [ʁaːvənsˈbʁʏk]) was a German concentration camp exclusively for women from 1939 to 1945, located in northern Germany, 90 km (56 mi) north of Berlin at a site near the village of Ravensbrück (part of Fürstenberg/Havel). The largest single national group consisted of 40,000 Polish women. Others included 26,000 Jewish women from various countries: 18,800 Russian, 8,000 French, and 1,000 Dutch. More than 80 percent were political prisoners. Many slave labor prisoners were employed by Siemens & Halske. From 1942 to 1945, medical experiments to test the effectiveness of sulfonamides were undertaken.

In the spring of 1941, the SS established a small adjacent camp for male inmates, who built and managed the camp's gas chambers in 1944. Of some 130,000 female prisoners who passed through the Ravensbrück camp, about 50,000 of them perished, some 2,200 were killed in the gas chambers and 15,000 survived until liberation.

Sachsenhausen concentration camp

Sachsenhausen (German pronunciation: [zaksənˈhaʊzən]) or Sachsenhausen-Oranienburg was a Nazi concentration camp in Oranienburg, Germany, used primarily for political prisoners from 1936 to the end of the Third Reich in May 1945. After World War II, when Oranienburg was in the Soviet Occupation Zone, the structure was used as an NKVD special camp until 1950 (See NKVD special camp Nr. 7). The camp ground with the remaining buildings is now open to the public as a museum.

Theresienstadt Ghetto

Theresienstadt (Czech: Terezín [ˈtɛrɛziːn]) was a hybrid concentration camp and ghetto established by the SS during World War II in the fortress town Terezín, located in the Protectorate of Bohemia and Moravia (German-occupied Czech lands) in which tens of thousands of Jews were killed. Theresienstadt served two main purposes: it was simultaneously a waystation to the extermination camps, and a "retirement settlement" for elderly and prominent Jews to mislead their communities about the Final Solution. Its conditions were deliberately engineered to hasten the death of its prisoners, and the ghetto also served a propaganda role. Unlike other ghettos, the exploitation of forced labor was not economically significant.

The ghetto was established by a transport of Czech Jews in November 1941. The first German and Austrian Jews arrived in June 1942; Dutch and Danish Jews came beginning in 1943 and prisoners of a wide variety of nationalities were sent to Theresienstadt in the last months of the war. About 33,000 people died at Theresienstadt, mostly from malnutrition and disease. More than 88,000 people were held there for months or years before being deported to extermination camps and other killing sites; the Jewish self-administration's role in choosing those to be deported has attracted significant controversy. Including 4,000 of the deportees who survived, the total number of survivors was around 23,000.

Theresienstadt was known for its relatively rich cultural life, including concerts, lectures, and clandestine education for children. The fact that it was governed by a Jewish self-administration as well as the large number of "Prominent" Jews imprisoned there facilitated the flourishing of cultural life. This spiritual legacy has attracted the attention of scholars and sparked interest in the ghetto. In the postwar period, a few of the SS perpetrators and Czech guards were put on trial, but the ghetto was generally forgotten by the Soviet authorities for political reasons. The Terezín Ghetto Museum is visited by 250,000 people each year.

and related quantities

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