Question

6. At 180 °C, the decomposition of a gaseous compound XO2 is a first order reaction
with the half-life 38.6 min. The initial pressure of XO2 is 372.5 kPa.
a) What is the rate of decomposition of XO2 after 1 hour?

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Answer 1

The rate of decomposition of XO2 after 1 hour : $\tt A=A_o.e^{-1.08}$

Further explanation

Given

the half-life 38.6 min

time of decomposition = 1 hour

Required

the rate of decomposition

Solution

First-order reaction :

$\tt A=A_o.e^{-kt}$

the half life=t1/2 :

$\tt t\frac{1}{2}=\dfrac{ln~2}{k}$

so the rate constant (k) :

$\tt k=\dfrac{ln~2}{38.6}=0.018$

The rate after 1 hour=60 min :

$\tt A=A_o.e^{-0.018\times 60}\\\\A=A_o.e^{-1.08}$