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Question

For a first order reaction A(g)2B(g)+C(g) at constant volume and 300 K, the total pressure at the beginning (t= 0) and at time t are P0 and Pt, respectively. Initially, only A is present with concentration [A0], and t13 is the time required for the partial pressure of A to reach 13rd of its initial vlaue. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

A
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B
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C
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D
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Solution

The correct option is D
at t=0A(g)2B(g) +C(g)p000(p0p)2pp
pt=p0p+2p+p=p0+2p
p=(ptp0)2
t=1Kln2p03p0pt
kt=ln2p0ln(3p0pt)
ln(3p0pt)=ln2p0kt
This is analogous to y=mx+c
So, slope (m) = -k i.e. negative slope.
c=ln(2p0)

Again,
kt13=lnp0p03
t13=ln3k

Here rate constant doest not depend on concentration of A, since we are considering in gas phase. So in the plot of rate constant vs [A]o we will get a parallel line of X-axis.

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