Question

In an adsorption experiment, a graph between log$\left(\frac{x}{m}\right)$ versus log $p$ is found to be linear with slope of ${45}^o$. The intercept on log$\left(\frac{x}{m}\right)$ axis was found to $0.3010$. The amount of the gas adsorbed per gram of charcoal under the pressure of $0.5$ atm will be:

• A. $1.0$
• B. $2.0$
• C. $0.50$
• D. $0.25$

Answer 1

Answer: (A)

$1.0$

We know

$\frac{x}{m}=k{p}^{1/n}$

or, $log\frac{x}{m}logk+\frac{1}{n}logp$

$\therefore$ Plot of $log\frac{x}{m}vs\cdot logp$ is linear

with slope $=\frac{1}{n}$ and intercept $=logk$

Hence, $\frac{1}{n}=\tan \theta =\tan {45}^o=1$ i.e., $n=1$

and $logk=0.3010$ or $k=$ antilog $\left(0.3010\right)=2$

At $p=0.5$ atm, $\frac{x}{m}=k{p}^{1/n}=2\times (0.5{)}^1=1.0$.