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For a first order homogenous gaseous reaction, $\mathrm{\mathrm{P} \rightarrow 2 \mathrm{Q}+\mathrm{R},}$ then initial pressure was $\mathrm{Pi}$ while total pressure after time ' $\mathrm{t}$ ' was $\mathrm{Pt}$ . The write expression for the rate constants $\mathrm{k}$ in terms of $\mathrm{\mathrm{Pi}, \mathrm{Pt}\: and \: \mathrm{t}}$ is :

Option: 1
$\mathrm{ \mathrm{kt}=2.303 \log \left(2 \mathrm{P}_{\mathrm{i}} / 3 \mathrm{Pi}-\mathrm{P}_{\mathrm{t}}\right)}$

Option: 2
$\mathrm{\mathrm{kt}=2.303 \log \left(2 \mathrm{P}_{\mathrm{i}} / 2 \mathrm{P}_{\mathrm{i}} \cdot \mathrm{P}_{\mathrm{t}}\right)}$

Option: 3
$\mathrm{kt =2.303 \log \left(\mathrm{P}_{\mathrm{i}} / \mathrm{P}_{\mathrm{i}}-\mathrm{P}_{\mathrm{t}}\right)}$

Option: 4
None of these

Answers (1)

best_answer

$\mathrm{P \rightarrow 2 \theta+R}$

$\mathrm{ \text { At } t=0 }$

$\mathrm{ \text { At time t } }$

P	Q	R
$\mathrm{ P_i }$	$\mathrm0$	$\mathrm0$
$\mathrm{P_i-x}$	$\mathrm{2x}$	$\mathrm{x}$

$\mathrm{p_{total } =p_i-x+2 x+x }$

$\mathrm{x =\frac{p_t-p_i}{2} }$

$\mathrm{ p_i-x=\frac{1}{2}\left\{3 p_i-p_t\right\} }$

$\mathrm{\therefore \quad k=\frac{2 \cdot 303}{t} \log \left\{\frac{2 p_i}{3 p_i-p_t}\right\}}$

Hence option 1 is correct.

Posted by

Rishabh

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