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The osmotic pressure of $0.1 \mathrm{M}$ monobasic acid of $\mathrm{pH} 3$ at $27^{\circ} \mathrm{C}$ is
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Verified Answer
The correct answer is:
$2.42 \mathrm{~atm}$
$\because$ Osmotic pressure $(\pi)=i \cdot C R T$
Also, according Arrhenius principle,
$\mathrm{pH}=\ldots-\log \mathrm{H}^{+}$
Given, $\mathrm{pH}=3$
$3=-\log \left[\mathrm{H}^{+}\right]$or $\left\lfloor\mathrm{H}^{+}\right]=0.001$
Assume $\mathrm{H} X$ is a monobasic acid.
Then,
$\mathrm{H} X=\mathrm{H}^{+}+X^{-}$
Relation between $\left[\mathrm{H}^{+}\right]$and degree of dissociation.
$\begin{aligned} {\left[\mathrm{H}^{+}\right] } & =C \cdot \alpha \\ \alpha & =\frac{0.001}{0.1}=0.01 \\ i & =1.01\end{aligned}$
Now, according to van't Hoff theory
$i=1+\alpha=1+0.01=1.01$
$\because$ Osmotic pressure $(\pi)=i C R T$
$\pi=1.01 \times 0.1 \times R T \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$
$\left[R=0.08 \mathrm{~L}\right.$ atm K ${ }^{-1} \mathrm{~mol}^{-1}, T=27+273=300 \mathrm{~K} \mid$
$\pi=1.01 \times 0.1 \times 0.08 \times 300=2.42 \mathrm{~atm}$
Hence, (a) is the correct answer.
Also, according Arrhenius principle,
$\mathrm{pH}=\ldots-\log \mathrm{H}^{+}$
Given, $\mathrm{pH}=3$
$3=-\log \left[\mathrm{H}^{+}\right]$or $\left\lfloor\mathrm{H}^{+}\right]=0.001$
Assume $\mathrm{H} X$ is a monobasic acid.
Then,
$\mathrm{H} X=\mathrm{H}^{+}+X^{-}$
Relation between $\left[\mathrm{H}^{+}\right]$and degree of dissociation.
$\begin{aligned} {\left[\mathrm{H}^{+}\right] } & =C \cdot \alpha \\ \alpha & =\frac{0.001}{0.1}=0.01 \\ i & =1.01\end{aligned}$
Now, according to van't Hoff theory
$i=1+\alpha=1+0.01=1.01$
$\because$ Osmotic pressure $(\pi)=i C R T$
$\pi=1.01 \times 0.1 \times R T \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$
$\left[R=0.08 \mathrm{~L}\right.$ atm K ${ }^{-1} \mathrm{~mol}^{-1}, T=27+273=300 \mathrm{~K} \mid$
$\pi=1.01 \times 0.1 \times 0.08 \times 300=2.42 \mathrm{~atm}$
Hence, (a) is the correct answer.
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