Question

Suppose coal-fired power plants used water in scrubbers to remove \(\mathrm{SO}_{2}\) from smokestack gases (see Chemical Connections, Section 6.6). (a) If the partial pressure of \(\mathrm{SO}_{2}\) in the stack gases is \(2.0 \times 10^{-3} \mathrm{~atm},\) what is the solubility of \(\mathrm{SO}_{2}\) in the scrubber liquid \(\left(k_{\mathrm{H}}\right.\) for \(\mathrm{SO}_{2}\) in water is \(1.23 \mathrm{~mol} / \mathrm{L} \cdot\) atm at \(\left.200 .{ }^{\circ} \mathrm{C}\right) ?\) (b) From your answer to part (a), why are basic solutions, such as limewater slurries \(\left[\mathrm{Ca}(\mathrm{OH})_{2}\right],\) used in scrubbers?

Short answer

Solubility is \2.46 \times 10^{-3}\ mol/L. Basic solutions remove \(\text{SO}_2\) to maintain low concentration.

Step-by-step solution

- Identify Known Variables

Given data includes the partial pressure of \(\text{SO}_2\), which is \(2.0 \times 10^{-3}\) atm, and the Henry's law constant, \k_{\text{H}}\ for \(\text{SO}_2\) in water, which is \(1.23 \text{ mol/L} \cdot \text{ atm}\).

- Apply Henry's Law to Find Solubility

Use Henry's law to find the solubility of \(\text{SO}_2\) in water. Henry's Law is given by \C = k_{\text{H}} \cdot P_{\text{gas}}\, where \C\ is the concentration (solubility) of the gas, \k_{\text{H}}\ is the Henry's law constant, and \P_{\text{gas}}\ is the partial pressure of the gas. Plug in the values: \[ C = (1.23 \text{ mol} / \text{L} \cdot \text{ atm}) \cdot (2.0 \times 10^{-3} \text{ atm}) = 2.46 \times 10^{-3} \text{ mol/L} \]

- Understand the Role of Limewater Slurries

Limewater slurries \[ \text{Ca(OH)}_2 \] are used in scrubbers because they are basic solutions that react with \( \text{SO}_2 \) to form solid calcium sulfite \[ \text{CaSO}_3 \]. This reaction removes \( \text{SO}_2 \) from the water, maintaining its low concentration and allowing more \( \text{SO}_2 \) to dissolve.

Key concepts

Henry's Law

Henry's Law explains the relationship between the partial pressure of a gas and its solubility in a liquid. This law can be expressed with the formula: \[ C = k_{\text{H}} \times P_{\text{gas}} \] where \( C \) is the solubility (concentration) of the gas in the liquid, \( k_{\text{H}} \) is the Henry's law constant, and \( P_{\text{gas}} \) is the partial pressure of the gas. In the given exercise, we used Henry’s Law to determine the solubility of \( \text{SO}_2 \) in water. With \( k_{\text{H}} = 1.23 \text{ mol/L} \times \text{ atm} \) and \( P_{\text{gas}} = 2.0 \times 10^{-3} \text{ atm} \), we calculated the solubility as: \[ C = (1.23 \text{ mol/L} \times \text{ atm}) \times (2.0 \times 10^{-3} \text{ atm}) = 2.46 \times 10^{-3} \text{ mol/L} \] This means that under a partial pressure of \( 2.0 \times 10^{-3} \text{ atm} \), \( \text{SO}_2 \) will dissolve in water to a concentration of \( 2.46 \times 10^{-3} \text{ mol/L} \).

Partial Pressure

The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume of the mixture. It is a crucial factor in determining the solubility of gases in liquids through Henry's Law. In our exercise, the partial pressure of \( \text{SO}_2 \) in the smokestack gases was given as \( 2.0 \times 10^{-3} \text{ atm} \). This value is relatively low, indicating that only a small amount of \( \text{SO}_2 \) is present in the mixture of gases coming from the power plant. By knowing the partial pressure, we can use Henry's Law to find the solubility of \( \text{SO}_2 \) in water, as we calculated earlier.

Limewater Slurries

Limewater slurries are basic solutions made from calcium hydroxide \( \text{Ca(OH)}_2 \). They are used in scrubbers to remove \( \text{SO}_2 \) from smokestack gases. The basicity of limewater slurries plays a crucial role in this process. When \( \text{SO}_2 \) dissolves in water, it forms sulfurous acid \( \text{H}_2\text{SO}_3 \), which is acidic. The basic limewater reacts with this acid to form calcium sulfite \( \text{CaSO}_3 \), a solid compound: \[ \text{Ca(OH)}_2 + \text{SO}_2 \rightarrow \text{CaSO}_3 + \text{H}_2\text{O} \] This reaction removes \( \text{SO}_2 \) from the water, keeping the concentration of \( \text{SO}_2 \) low. As a result, it allows more \( \text{SO}_2 \) to dissolve, effectively cleaning the smokestack gases. Limewater slurries are efficient in reducing \( \text{SO}_2 \) emissions from power plants, protecting the environment from sulfur dioxide pollution.