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 the solubility of dissolved gases in the liquid to decrease according to Henry's Law. As the temperature of the liquid increases, Henry's law constant increases for most gases, which implies that the solubility of the gas decreases. Consequently, the gas is driven off from the liquid, with more gas being released at higher temperatures.

Step-by-step solution

Understand Henry's Law

Henry's law states that the concentration of a dissolved gas in a liquid is directly proportional to the partial pressure of that gas above the liquid surface. Mathematically, Henry's law can be represented as: C = k_H * P_gas Where C is the concentration of the dissolved gas in the liquid, k_H is Henry's law constant (which depends on the specific gas and liquid, and the temperature), and P_gas is the partial pressure of the gas above the liquid.

Show the effect of temperature on Henry's law constant

The value of the Henry's law constant (k_H) depends on the temperature of the solution. Generally, k_H increases with increasing temperature for most gases. Consequently, the solubility of the gas in the liquid decreases with an increase in temperature. This means that, at higher temperatures, the gas dissolves to a lesser extent in the liquid. We can express the relationship between Henry's law constant and temperature using the van 't Hoff equation: ln(k_H2 / k_H1) = -ΔH/R * (1/T2 - 1/T1) Where ΔH is the enthalpy change associated with the dissolution process, R is the universal gas constant, T1 and T2 are the initial and final temperatures, and k_H1 and k_H2 are the initial and final Henry's law constants, respectively.

Apply the temperature change

When a liquid is heated, its temperature increases. According to the van 't Hoff equation mentioned in Step 2, the increase in temperature leads to a decrease in solubility (an increase in k_H) for most gases. Consequently, when the temperature of the liquid increases, the concentration of the dissolved gas decreases (as the solubility of the gas reduces according to Henry's law), which results in the gas being driven off from the liquid. For example, let's assume that we are heating a liquid solution from an initial temperature T1 to a final temperature T2, and we observe an increase in k_H from k_H1 to k_H2 and consequently a decrease in gas solubility. This implies that more gas will be released from the liquid as the temperature increases.

Conclusion

In conclusion, using Henry's law, we can show that the dissolved gases in a liquid can be driven off by heating the liquid. As the temperature of the liquid increases, Henry's law constant increases for most gases, which implies that the solubility of the gas decreases. As a result, the gas is driven off from the liquid, with more gas being released at higher temperatures.

Key concepts

Gas Solubility

Gas solubility refers to the ability of a gas to dissolve in a liquid. Understanding how gases dissolve helps us explore their behavior in various conditions. Henry's Law provides the foundation for understanding gas solubility, stating that the concentration of a dissolved gas in a liquid is directly proportional to the partial pressure of that gas above the liquid's surface. This relationship can be mathematically expressed as: \[C = k_H \times P_{gas}\] where:

• \( C \) is the concentration of the dissolved gas
• \( k_H \) is Henry’s law constant, which varies with temperature and specific gas-liquid pairs
• \( P_{gas} \) is the partial pressure of the gas

Hence, by changing the pressure, we can influence how much gas dissolves in the liquid. At higher pressures, more gas dissolves, whereas at lower pressures, less gas remains dissolved.

Temperature Effect

The effect of temperature on gas solubility is significant and often counterintuitive. As the temperature of a liquid increases, the solubility of most gases in the liquid decreases. This is due to the increase of Henry's law constant \( k_H \) with temperature. This means more gas tends to escape from the liquid as it gets warmer. When you heat a liquid, say water, the increase in temperature leads to higher kinetic energy of gas molecules. This increased energy makes it easier for gas molecules to escape the liquid phase. Therefore, you see bubbles or fizzing as the gas leaves the solution. The concept links directly to everyday experiences, like why soda goes flat faster when left out at room temperature compared to when it is refrigerated.Thus, practically, if you want to keep gas dissolved in a liquid, cooling it will enhance its solubility.

van 't Hoff Equation

The van 't Hoff equation gives us a deeper insight into the temperature dependency of Henry's law constant. It helps quantify how \( k_H \) changes with temperature using the equation:\[\ln \left(\frac{k_{H2}}{k_{H1}}\right) = -\frac{\Delta H}{R} \left( \frac{1}{T2} - \frac{1}{T1} \right)\]where:

• \( \Delta H \) is the enthalpy change of the dissolution process
• \( R \) is the universal gas constant
• \( T1 \) and \( T2 \) are initial and final temperatures
• \( k_{H1} \) and \( k_{H2} \) are initial and final Henry's law constants

This mathematical expression shows that the change in solubility constant is not random but follows a predictable path depending on fixed thermodynamic variables. It highlights that if \( \Delta H \) is positive, as it often is for gases dissolving in liquids, then \( k_H \) will increase as the liquid is heated, reinforcing that gases become less soluble as temperature rises. Therefore, understanding this equation allows scientists and engineers to predict and manipulate conditions for desired solubility in industrial and laboratory settings.