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Question

The reaction, $$2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$$ is carried out in a $$1\ dm^{3}$$ vessel and $$2\ dm^{3}$$ vessel separately. The ratio of the reaction velocities will be:


A
1:8
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B
1:4
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C
4:1
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D
8:1
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Solution

The correct option is A $$8 : 1$$
Reaction velocity is the rate of reaction.

The concentration in $$2\ dm^3$$ vessel will be halved compared to when carried out in $$1\ dm^3$$.

The rate of reaction or velocity of reaction is,

$$r=k[SO_2]^2[O_2]$$

$$r_1=k[SO_2]^2[O_2]$$, 

$$r_2=k[\dfrac{[SO_2]}{2}]^2\dfrac{[O_2]}{2}=\dfrac{1}{8}k[SO_2]^2[O_2]$$

Hence, $$\dfrac {r_1}{r_2}=\dfrac{8}{1}$$

So, option $$D$$ is correct.

Chemistry

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