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(1)/(2)=(ln~2)/(k)`

so the rate constant (k) :

`\tt k=(ln~2)/(38.6)=0.018`

The rate after 1 hour=60 min :

`\tt A=A_o.e^(-0.018* 60)\\\\A=A_o.e^(-1.08)`