Question

Consider a solution of CO$_2$(g) dissolved in water in a closed container. Which one of the following plots correctly represents variation of $\log$ (partial pressure of CO$_2$ in vapour phase above water) [y-axis] with $\log$ (mole fraction of CO$_2$ in water) [x-axis] at
 $25^\circ$C? 

• A. A
• B. B
• C. C
• D. D

Hint:

Henry’s law gives a direct proportionality between partial pressure and mole fraction, resulting in a straight-line graph on a log–log plot.

Answer 1

The Correct Option is A

The problem involves understanding the relationship between the partial pressure of CO₂ in the vapour phase and its mole fraction in water. According to Henry's Law, the partial pressure of a gas above a liquid is directly proportional to the mole fraction of the gas dissolved in the liquid. Mathematically, this can be expressed as:

\(P = k_H \cdot x\)

where:

• \(P\) is the partial pressure of the gas.
• \(k_H\) is Henry’s Law constant.
• \(x\) is the mole fraction of the gas in the liquid.

Taking the logarithm of both sides, we get:

\(\log(P) = \log(k_H) + \log(x)\)

This equation shows that a plot of \(\log(P)\) versus \(\log(x)\) should be a straight line with a slope of 1, because logarithms allow multiplication to be expressed as addition.

Thus, the correct plot is a straight line with a positive slope passing through the origin, as depicted in option A.