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Chemistry Question on Rate of a Chemical Reaction

In the first order thermal decomposition of C2H5I(g)⟶C2H4(g)+HI(g)C _{2} H _{5} I (g) \longrightarrow C _{2} H _{4}(g)+ HI (g), the reactant in the beginning exerts a pressure of 22 bar in a closed vessel at 600 K600 \,K. If the partial pressure of the reactant is 0.10.1 bar after 10001000 minutes at the same temperature the rate constant in min⁡−1\min ^{-1} is (log⁡2=0.3010)(\log 2=0.3010)

A

6.0×10−46.0 \times 10^{-4}

B

6.0×10−36.0 \times 10^{- 3}

C

3.0×10−33 .0 \times 10^{- 3}

D

3.0×10−43.0 \times 10^{-4}

Answer

3.0×10−33 .0 \times 10^{- 3}

Explanation

Solution

Since, the reaction is first order,

k=2.303tlog⁡pp0−xk= \frac{2.303}{t} \log \frac{p}{p_{0}-x}

k=2.3031000log⁡22−1.9k =\frac{2.303}{1000} \log \frac{2}{2-1.9}

=23031000log⁡20=\frac{2303}{1000} \log 20

k=3×10−3min⁡−1k =3 \times 10^{-3} \min ^{-1}