From WolfWikis

Concentrations

One lump or two?

A very British question. It refers to the number of lumps of sugar to be added to the milk that is soon to be safely scalded to sterility by adding boiling hot tea. (Raw milk used to carry tuberculosis).

There is an American equivalent: sweet or unsweet, but it is a bit less precise in inquiring after someone's preferred sucrose concentration and varies in its meaning from North to South.

Concentrations are best measured in amounts per amounts, like lumps of sugar per cup of scalded milk.

There are a host of ways to do that:

• grams of trans fat per serving
• pounds of sulfur per barrel of oil
• number of eggs per pound of flour

Notice that concentrations are compound units (ratios actually) but they have a meaning of their own. Sugar concentration for example relates directly to sweetness.

Molarity

In CH 101 we concentrate on one particular measure:

• molarity: moles per liter: [mol/l]. (This unit is often shown as a capital M.)

To be more precise molarity is defined as the number of moles of solute per liter of solution.

Some nomenclature:

• The lumps of sugar that dissolve would be called the solute
• The scalded milk into which they dissolve is known as the solvent.
• The resulting beverage -admittedly an acquired taste- is called the solution

The solute is not necessarily a solid. E.g. the cops may well measure someone's alcohol concentration to determine how much alcohol there is in the blood. Both alcohol and blood are liquids. Gases can also be solutes. E.g. we need a certain oxygen concentration in the blood, otherwise we die.

Molarity is often indicated with square brackets around the chemical formula of the solute, e.g [O₂] for the oxygen concentration expressed in molarity.

Notice also that we are dealing with mixtures, but tacitly assume that one component (the 'solute') is in the minority. Just turn around the sentence to see that. Ever asked someone how much blood they have in their alcohol?

(Unfortunately that may not be an inappropriate question for everybody...)

But seriously: for say 50:50 mixtures molarity is not a very good measure to work with. Just think of what is the solute and what the solvent in that case. Molarities work best for dilute solutions. People often choose other measures than molarity in non-dilute cases.^[1]

Conversions

Like molar masses, molarities are ratios as the word per already indicated:

molar mass: [g/mol]: grams per mole.

molarity: [mol/l]: moles per liter.

Much like we have seen in the case of molar masses, we'd better keep track of our units (double bookkeeping!) to make sure we do not divide when we should multiply or vice versa....

We can easily add prefixes as long as we do that on top and on bottom simultaneously:

[mol/l] = [mmol/ml] = [μmol/μl] = [nmol/nl] etc.

If we do not write the prefix in both numerator and denominator we have to include factors of 1000 (10³):

1 [mol/l] = 1000 [mmol/l] = 10³ [mmol/l]

1 [mol/l] = 0.0001 [mol/ml] = 10^-3 [mol/ml]

Because 1 ml equals 1 cm³ we can also write:

[mol/l] = [mmol/ml] = [mmol/cm³]

One common conversion is to combine molar mass and molarity:

molar mass: [g/mol]

molarity: [mol/l]

Multiplying gives: [g/mol]*[mol/l] = [g/l], e.g. grams of sugar per liter of tea.

If we want to go the other direction we must divide by the molar mass to get molarity back:

[g/l] / [g/mol] = [g/l] * [mol/g] = [mol/l]

Please do not try to memorize when to do what. Experience tells that that leads to many mistakes. Instead train yourself in doing the symbolic bookkeeping. Write out the units and cancel the ones that can be canceled. See if you get the unit you want. Once you master that, mistakes are pretty much impossible to make.

Exercises

Exercise 1

• How many grams of alcohol (CH₃CH₂OH) must we add to 1 liter of water to obtain a solution of 1 [mmol/l]?

Exercise 2

• The concentration of oxygen [O₂] in a blood sample of 300ml is 0.0023 [mol/l]. How many grams of oxygen does the sample contain?

Exercise 3: dilution

• To 500 ml of a solution with a molarity of 0.1 [mol/l] is added more solvent until the volume is 2 l. What is the resulting concentration?

Exercise 4: adding solutions

• 40 ml of an aqueous solution of 1-propanol with a concentration of [C₃H₈O] = 0.021 [mol/l] is added to 60 ml of a 1-propanol solution with [C₃H₈O] = 0.0105 [mol/l]. The solutions are thoroughly mixed. What is [C₃H₈O] in the resulting solution?

Exercise 5: adding solutions

• 40 ml of an aqueous solution of 1-propanol with a concentration of [C₃H₈O] = 0.021 [mol/l] is added to 60 ml of a butanol solution with [C₄H₁₀O] = 0.0105 [mol/l]. The solutions are thoroughly mixed. What is [C₃H₈O] and [C₄H₁₀O] in the resulting solution?

Execise 6: evaporation

• 100 ml of a solution with a concentration of 0.1 [mol/l] is exposed to evaporation until the volume is only 75 ml. The solvent is volatile, the solute is not. What is the resulting concentration?

Exercise 7

Myoglobin and its active center

• Myoglobin is a protein found in the muscle tissues of many vertebrates. Its molar mass is 16,700 Daltons. The globular protein is soluble in water and contains an active center consisting of a heme molecule in the center of which is a single iron atom. What is the iron concentration in 5 ml of a solution containing 5 g of myoglobin? What is the mass of the iron present in this solution?

Notes

1. ↑ Another reason why molarity does not work very well for non-dilute cases is that it is defined as moles of solute per liter of solution not: solvent. For dilute solutions there is not much of a difference between those two and we happily ignore the difference in CH 101. In non-dilute solutions you have to be more careful, because volumes are not strictly additive.