Problem 80 - Chemistry: An Atoms-Focused Approach

Question

The values of \(k_{\mathrm{H}}\) for \(\mathrm{NO}\) and \(\mathrm{CO}\) gas in water at \(20^{\circ} \mathrm{C}\) are \(1.4 \times 10^{-3} \mathrm{M} / \mathrm{atm}\) and \(7.4 \times 10^{-3} \mathrm{M} / \mathrm{atm},\) respectively. Why is CO more soluble in water?

Step-by-Step Solution

Answer

Answer: CO is less soluble in water compared to NO because it has a higher Henry's law constant. The higher the Henry's law constant, the lower the solubility of the gas in the liquid. In this case, since \(k_{H}(\mathrm{CO}) > k_{H}(\mathrm{NO})\), CO is less soluble than NO in water at 20°C.

Step 1: Henry's law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid, under constant temperature. Mathematically, it can be expressed as: \(C = k_H \cdot P\) where, \(C\) = concentration of the gas in the liquid (in mol/L or M) \(k_H\) = Henry's law constant (in M/atm) \(P\) = partial pressure of the gas above the liquid (in atm) #Step 2: Interpret the given values of Henry's law constants#

We are given the values of Henry's law constants for NO and CO gas in water at 20°C: \(k_{H}(\mathrm{NO}) = 1.4 \times 10^{-3} \frac{\mathrm{M}}{\mathrm{atm}}\) \(k_{H}(\mathrm{CO}) = 7.4 \times 10^{-3} \frac{\mathrm{M}}{\mathrm{atm}}\) From these values, we can see that the Henry's law constant for CO is greater than the constant for NO. #Step 3: Relate the Henry's Law constant to solubility#

Step 2: According to Henry's law, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. However, if we compare two different gases, like NO and CO in this case, we need to compare their Henry's law constants. The lower the value of \(k_H\), the higher the solubility of the gas in the liquid. This is because the gas dissolves more easily in the liquid, requiring less pressure to achieve equilibrium. Vice versa, a higher value of \(k_H\) represents a lower solubility. #Step 4: Compare the solubility of NO and CO in water#

As we can see from the given values of Henry's law constants: \(k_{H}(\mathrm{CO}) > k_{H}(\mathrm{NO})\) This means that CO has a lower value for its solubility in water when compared with NO, indicating that CO is less soluble than NO in water. This is contrary to what the question asked, so it is important to double-check the information given in the problem statement and make sure it is correct.

Key Concepts

Solubility of Gases

The solubility of gases in liquids is an intriguing concept that plays a crucial role in various scientific and everyday processes. When we talk about the solubility of a gas, we refer to how much of the gas can dissolve in a liquid at a given temperature and pressure. There are several factors that can influence this:

• The nature of the gas and the liquid involved
• Temperature of the solution
• Pressure of the gas above the liquid

A fundamental principle behind the solubility of gases is Henry's Law. This law states that the amount of gas dissolved in a liquid at a constant temperature is directly proportional to the partial pressure of the gas in contact with the liquid. This means if you increase the pressure, more gas will dissolve. But it isn't just about pressure; the interaction between the molecules of the gas and liquid also determines how easily a gas dissolves.

Henry's Law Constant

The Henry's law constant ( k_H ) is a unique value for each gas-liquid pair, further emphasizing how different gases behave differently when in solution. This constant helps us understand the solubility characteristic of a gas in a particular solvent at a specific temperature. It is measured in units like M/atm and essentially tells us how much gas will dissolve in a liquid at a given pressure:

• A smaller k_H indicates higher solubility because less pressure is needed to dissolve the gas.
• A larger k_H means lower solubility, requiring more pressure to dissolve the gas to the same extent.

In the exercise's context, k_H provides critical insights into why CO is more soluble than NO in water. With k_H values given, it was expected that CO had lower solubility compared to NO, based solely on the constant, unless other factors play a significant role.

Gas-Liquid Equilibrium

Gas-liquid equilibrium is the state where a gas is dissolving in a liquid at the same rate as it is leaving the liquid into the gas phase. At this equilibrium, the concentration of the gas in the liquid remains constant over time. Understanding the equilibrium involves:

• The interaction of gas molecules with the liquid
• Temperature of the system, as it affects both gas solubility and vapor pressure
• The partial pressure of the gas in equilibrium with its concentration in the liquid

At equilibrium, changing the partial pressure or temperature can disrupt the balance, causing more or less gas to dissolve. In practical scenarios, this concept helps in processes like carbonation of beverages or the dissolving of gases from the atmosphere into oceans. Here, Henry’s Law plays a key role in predicting how gases will behave, thereby guiding decisions in scientific applications and industry.