Observe the following data given in the table. (\(K_H\) = Henry's law constant)
Gas
CO₂
Ar
HCHO
CH₄
\(K_H\) (k bar at 298 K)
1.67
40.3
\(1.83 \times 10^{-5}\)
0.413
The correct order of their solubility in water is
Show Hint
Remember the inverse relationship: \textbf{High \(K_H\)} = \textbf{Low Solubility}. A simple way to think about it is that a high \(K_H\) means a high pressure is needed to dissolve even a small amount of gas. Formaldehyde (HCHO) is extremely soluble in water (forming formalin), so it must have a very low \(K_H\), which is consistent with the data.
Step 1: Understanding the Concept:
Henry's Law describes the solubility of a gas in a liquid. It states that the partial pressure (\(p\)) of a gas in the vapor phase is directly proportional to the mole fraction (\(x\)) of the gas in the solution. The proportionality constant is the Henry's Law constant, \(K_H\). Step 2: Key Formula or Approach:
The mathematical form of Henry's Law is:
\[ p = K_H \cdot x \]
Here, \(x\) (mole fraction) is a measure of the gas's solubility. We can rearrange the formula to express solubility:
\[ x = \frac{p}{K_H} \]
This relationship shows that for a given partial pressure of a gas, its solubility (\(x\)) is inversely proportional to the Henry's Law constant (\(K_H\)). Therefore, a higher value of \(K_H\) corresponds to lower solubility. Step 3: Detailed Explanation:
To find the correct order of solubility, we need to arrange the gases in order of increasing \(K_H\) values. The order of decreasing solubility will be the reverse.
Let's list the given \(K_H\) values:
- \(K_H(\text{HCHO}) = 1.83 \times 10^{-5}\) kbar (smallest value)
- \(K_H(\text{CH}_4) = 0.413\) kbar
- \(K_H(\text{CO}_2) = 1.67\) kbar
- \(K_H(\text{Ar}) = 40.3\) kbar (largest value)
The order of increasing \(K_H\) is:
\[ \text{HCHO}<\text{CH}_4<\text{CO}_2<\text{Ar} \]
Since solubility is inversely proportional to \(K_H\), the order of decreasing solubility will be the reverse of the order above:
\[ \text{HCHO}>\text{CH}_4>\text{CO}_2>\text{Ar} \]
Step 4: Final Answer:
The correct order of solubility is HCHO>CH₄>CO₂>Ar. This matches option (C).
