At 293 K, HCl(g) is dissolved in cyclohexane. Identify the graph obtained for this solution (x-axis = mole fraction of HCl dissolved in cyclohexane; y-axis = partial pressure of HCl(g)).
Show Hint
Henry's law:
\[
p = K_Hx
\]
A graph of partial pressure (\(p\)) versus mole fraction (\(x\)) is always a straight line passing through the origin. Whenever you see a graph-based Henry's law question, look for a positive straight line through the origin.
Concept:
For a gas dissolved in a liquid, the relation between the partial pressure of the gas and its mole fraction in the solution is given by Henry's law.
\[
p = K_H x
\]
where
• \(p\) = partial pressure of the gas
• \(x\) = mole fraction of the dissolved gas
• \(K_H\) = Henry's law constant
This law is applicable to dilute solutions of gases in liquids.
Step 1: Identify the solute and solvent.
Here,
\[
\text{HCl(g)}
\]
is the solute and cyclohexane is the solvent.
At constant temperature (\(293~K\)), the dissolved gas follows Henry's law.
Therefore,
\[
p \propto x
\]
This means that as the mole fraction of dissolved HCl increases, its partial pressure also increases proportionally.
Step 2: Interpret the mathematical form of Henry's law.
The equation
\[
p = K_Hx
\]
is of the form
\[
y = mx
\]
which represents a straight line.
Since there is no constant term, the line passes through the origin.
Thus:
\[
x=0 \quad \Rightarrow \quad p=0
\]
Hence the graph must start from the origin and rise linearly with increasing mole fraction.
Step 3: Compare with the given graphs.
Among the four graphs:
• Graph 1 does not pass through the origin.
• Graph 2 has a negative slope.
• Graph 3 is a straight line passing through the origin.
• Graph 4 is independent of mole fraction.
Only Graph 3 satisfies
\[
p = K_Hx
\]
Therefore Graph 3 is the correct representation.
Step 4: Final answer.
\[
\boxed{\text{Graph 3}}
\]
