Question

The soft drink industry is a major consumer of both nutritive (sugars) and non-nutritive sweeteners. The ‘diet’ soft drinks are formulated to have the same sweetness intensity as the ‘regular’ soft drinks. We will determine if the other characteristics of the ‘regular’ and ‘diet’ soft drinks are the same. Through this discussion, we will better understand the chemistry of water and properties of solutions. Background: Regular cola contains 39 g sugar in a 12-oz. serving (355 mL). We will assume that the sugar is sucrose (MW 342). Diet cola contains aspartame and acesulfame K as alternatives for sucrose. Each of these non-nutritive sweeteners is about 200 times sweeter than sucrose. For this example, we will assume that the only sweetener is aspartame. A 12-oz serving of diet cola would contain 0.195 g of aspartame (MW 294).

1. Compare the boiling points of ‘regular’ and ‘diet’ cola. In your response, discuss the effect of solutes on boiling point.

2. Compare the freezing points of ‘regular’ and ‘diet’ cola, if the two colas are frozen at the same temperature (e.g. -20C).

Answer 1

A solution is a homogenous mixture of two substances. A solute is a small amount of substance dissolved in the solution. A solvent is a major ingredient of a solution in which the solute is dissolved.

Concentration of a solution is the ratio of solvent to solute, expressed as molality 'm'.

molality = moles of solute / kg of solvent

Both regular and diet cola are solutions made of water and a solute like sucrose or aspartame.

1. The boiling point of a liquid or any solution is the temperature at which it turns to vapour. The boiling point of water is 100⁰C or 212⁰F. This value depends on the purity of the water itself.

Adding solutes or impurities to the water will increase it's boiling point, depending on amount of solute and concentration of the solution.

The difference in boiling point of the solvent versus the boiling point of the solution is known as delta T.

delta T = m x K_b

K_b is the molal boiling point elevation constant. It is a constant value of 0.51 ⁰C Kg/mol for water.

Boiling point of regular cola: 355ml of regular cola contains 39g of sucrose with MW 342.

Kg of water in regular cola = 355 / 1000 = 0.355 kg (1ml of water = 1g of water)

moles of sucrose = 39/342 = 0.114

m = 0.114 / 0.355 = 0.321 mol/Kg

delta T = 0.321 x 0.51 = 0.164 ⁰C

Boiling point of regular cola is 0.164 ⁰C higher than water, i.e., 100.164 ⁰C.

Boiling point of diet cola: 355ml of diet cola contains 0.195g of aspartame with MW 294.

Kg of water in diet cola = 355 / 1000 = 0.355 kg (1ml of water = 1g of water)

moles of aspartame = 0.195 / 294 = 0.001

m = 0.001 / 0.355 = 0.003 mol/Kg

delta T = 0.003 x 0.51 = 0.001 ⁰C

Boiling point of diet cola is 0.001⁰C higher than water, i.e., 100.001⁰C.

2. The freezing point of a liquid or any solution is the temperature at which it turns to solid. The freezing point of water is 0⁰C or 212⁰F. This value depends on the purity of the water itself.

Adding solutes or impurities to the water will decrease it's freezing point, depending on amount of solute and concentration of the solution.

The difference in freezing point of the solvent versus the freezing point of the solution is known as delta T.

delta T = m x K

K is the molal freezing point depression constant. It is a constant value of 1.86 ⁰C Kg/mol for water.

Freezing point of regular cola: 355ml of regular cola contains 39g of sucrose with MW 342.

Kg of water in regular cola = 355 / 1000 = 0.355 kg (1ml of water = 1g of water)

moles of sucrose = 39/342 = 0.114

m = 0.114 / 0.355 = 0.321 mol/Kg

delta T = 0.321 x 1.86 = 0.164 ⁰C

Freezing point of regular cola is 0.6 ⁰C lower than water, i.e., -0.6 ⁰C.

Freezing point of diet cola: 355ml of diet cola contains 0.195g of aspartame with MW 294.

Kg of water in diet cola = 355 / 1000 = 0.355 kg (1ml of water = 1g of water)

moles of aspartame = 0.195 / 294 = 0.001

m = 0.001 / 0.355 = 0.003 mol/Kg

delta T = 0.003 x 1.86 = 0.001 ⁰C

Freezing point of diet cola is 0.006⁰C lower than water, i.e., -0.006⁰C.