Consider an elementary reaction
A( g)+B( g) → C( g)+D( g)
If the volume of reaction mixture is suddenly reduced to 1/3 of its initial volume, the reaction rate will become ' x′ times of the original reaction rate. The value of x is :

Solution

Chemistry ma’am · 3 steps

Squeeze the volume to one-third and each concentration triples; the rate feels both of them.

1. Write the rate law. For an elementary reaction the rate law comes straight from the equation. One A and one B collide, so rate = k[A][B], first order in each and second order overall.
2. Effect on concentration. Concentration is moles divided by volume. The moles do not change in a sudden compression, so making the volume 1/3 makes both [A] and [B] three times larger.

   rate' = k(3[A])(3[B]) = 9 k[A][B] = 9 × rate

3. So. The new rate is 9 times the original rate, so x = 9, option (b).

The idea to keep. When the volume changes by a factor n, every gas concentration changes by 1/n. Raise that to the overall order to get the new rate: here 3² = 9.

Answer from the NTA final answer key. Solution by PrepWiser.