Question

Using Henry's law, show that the dissolved gases in a liquid can be driven off by heating the liquid.

Short answer

Answer: Heating a liquid causes an increase in the vapor pressure of the gas above the liquid due to the Clausius-Clapeyron equation. Since Henry's law states that the concentration of dissolved gas is proportional to the partial pressure of the gas, this increase in vapor pressure will in turn cause a decrease in the concentration of dissolved gas in the liquid. This leads to the dissolved gases being driven off as the temperature of the liquid increases.

Step-by-step solution

Understanding Henry's law

Henry's law states that the concentration of a gas dissolved in a liquid (C) is proportional to the partial pressure of the gas (P) above the liquid. Mathematically, it is represented as: C = kP where k is the Henry's law constant which is specific to each gas-liquid pair and depends on temperature.

Relation between temperature and vapor pressure

As the temperature of a liquid increases, the vapor pressure of the gas above the liquid also increases due to increased kinetic energy of the gas molecules. This relationship can be expressed using the Clausius-Clapeyron equation: \ln(\frac{P_2}{P_1}) = -\frac{L}{R}(\frac{1}{T_2}-\frac{1}{T_1}) where P_1 and P_2 are the vapor pressures at temperatures T_1 and T_2, L is the latent heat of vaporization, and R is the gas constant.

Heating the liquid and its effect on dissolved gases

As the temperature of the liquid increases (from T_1 to T_2), the vapor pressure of the gas above it (from P_1 to P_2) also increases due to the Clausius-Clapeyron equation. Since the concentration of the gas dissolved in the liquid (C) is proportional to the partial pressure of the gas (P) as per Henry's law, increasing the vapor pressure will also result in a decrease in the concentration of the dissolved gas. This implies that as the temperature of the liquid increases, the dissolved gases will be driven off. To conclude, using Henry's law in conjunction with the Clausius-Clapeyron equation, we showed that by increasing the temperature of a liquid, the concentration of the dissolved gases will decrease, resulting in the gases being driven out of the liquid.