The graph drawn between $\log \left(\frac{x}{m}\right)$ and $\log (p)$ is shown below with intercept…

The graph drawn between $\log \left(\frac{x}{m}\right)$ and $\log (p)$ is shown below with intercept $\mathrm{OA}$. What is the value of $\left(\frac{\mathrm{x}}{\mathrm{m}}\right)$ at a pressure of $0.3 \mathrm{~atm}$ ? $(\log 2=0.30, \log 3=0.477)$
  1. $0.6$
  2. $0.5$
  3. $0.4$
  4. $0.7$

Solution

$\log \left(\frac{x}{m}\right)=\log K+\left(\frac{1}{n}\right) \log P(y=c+m x)$ $\begin{aligned} & \text { Slope }=c=\frac{1}{n}=\tan 45^{\circ}=1 \\ & \log P=\log (0.3)=-0.523 \\ & \log K=0.03 \\ & \text { (given) } \\ & \text { Thus, } \log \left(\frac{\mathrm{x}}{\mathrm{m}}\right)=0.30+(1)(-0.523)=-0.223 \\ & \Rightarrow \frac{\mathrm{x}}{\mathrm{m}}=0.6 \\ & \end{aligned}$

Asked in: AP EAMCET 2023 (16 May Shift 2)

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