# Concentration Measures

## Concentration Terms

### Percent Concentration

• Mass percent
• ppt = parts/thousand (1mg/L of water); ppb = parts/billion (1 microgram/L of water)
• Volume percent

### Molarity = moles of solute dissolved in 1 L of solution.

The most commonly used concentration term in chemistry = moles of solute dissolved in 1 L of solution.

### FYI

Example: Make up a 1.00000 L solution of 0.25 M NaCl (note that water is the "default" solvent).

First weigh out o.25 moles of NaCl

= (0.25 mole)(22.99 g + 35.45 g)/mole = 14.61 g

Example: What is the concentration of a solution made by dissolving 10.00 g of KI in enough water to make
1.00000 L?

First need to find the number of moles of KI:

(10.00 g) / ({39.10 g+ 126.9 g}/mole) = 6.135 x 10-2 mole

Thus the concentration will be 6.135 x 10-2 M

### Mole fraction = moles of solute dissolved in total moles of solution = na /n

Example: What is the mole fraction of a solution of 10.0 moles of glycerol dissolved in 15.0 moles of water?

(10 mol) / (10 mol + 15 mol) = 10/25 = 0.400

# Colligative properties

Colligative properties (properties which depend only on the number or concentration, not on the type, of particles). [Exchange across surfaces model]

Colligative properties are only strictly followed for ideal solutions. That is, other forces are at work in real solutions, so will get deviations. As a result colligative properties are followed most closely for dilute solutions (e.g. <0.1 M) where solute-solute interactions are minimal.

Be able to solve problems for:

### Vapor pressure lowering

Raoult's Law: P = XP°, where P = vapor pressure of substance in solution, P° = the vapor pressure of the pure substance and X = its mole fraction. Recall that mole fraction is the number of moles of substance divided by the total number of moles of all substances in the solution (moles solute/(moles solute + moles solvent)) In other words the vapor pressure of a substance in solution is proportional to the molecular fraction or molecular percentage of that substance in the solution.

Example: What is the vapor pressure of water in 80 proof alcohol (XH2O = 0.79) at 25° C (vapor pressure = 23.76 mmHg).

P = XP°

X = [60g/18.01 g/mol] / [60g/18.01 g/mol + 40g/(2x12.01 + 6x1.008 + 16.00)g/mol

P = 0.79 (23.76 mmHg) = 18.77 mmHg = 19 mmHg

### Boiling point elevation

Tb = kbm, where m = molality = moles solute/kg solvent, and kb is a constant specific to the solvent.

Which of the following solutions will have the highest boiling point: 3 m glucose or 1 m aluminum chloride?

First need to look at concentration of particles.

glucose is covalent, so 1 m particles,

aluminum chloride is ionic with 1 mole aluminum ions and 3 moles of chlroide ions for each mole of AlCl3 = 4 m particles,

Therefore the 1 m aluminum choride solution will have the higher bp.

### Freezing point depression

Tf = -kfm, where m = molality = moles solute/kg solvent, and kf is a constant specific to the solvent.

Which of the following solutions will have the lowest melting point: 2 m sugar (sucrose) or 0.8 m calcium chloride?

First need to look at concentration of particles.

sugar is covalent, so 2 m particles,

calcium chloride is ionic with 1 mole calcium ions and 3 moles of chloride ions for each mole of CaCl2 = 2.4 m particles,

Therefore the 0.8 m calcium chloride solution will have the higher bp.

### Osmotic pressure ()

V = nRT; or, dividing both sides by V, = MRT, where M = molarity.

Example: What are the osmotic pressures of 1.00 M sugar and 1 M aluminum chloride solutions at 25°C?

sugar= MRT = (1 mol/L)(0.0821 L*atm/mol*K)(298 K) = 24.5 atm

AlCl3= MRT = (1 mol/L)(4 mol ion/mol)(0.0821 L*atm/mol*K)(298 K) = 97.9 atm

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