Question

For the reaction \[\ce{2X -> X2}\], rate of reaction becomes three times when the concentration of X is increased by 27 times. What is the order of reaction?

For the reaction \[\ce{2A -> A2}\], rate of reaction becomes three times when the concentration of A is increased by 27 times. What is the order of reaction?

Answer 1

Given:

Reaction: \[\ce{2X -> X2}\]

When [X] is increased 27 times, the rate increases 3 times

Need to find the order of reaction (n)

Rate ∝ [X]ⁿ

Let the ratio of new to original rate be

\(\frac{\mathrm{New~Rate}}{\text{Original Rate}}=\left(\frac{[X]_{\mathrm{new}}}{[X]_{\mathrm{original}}}\right)^n\)

⇒ \[\ce{\frac{3}{1} = (27)^n}\]

3 = 27ⁿ

= (3³)ⁿ

= 3³ⁿ

⇒ 3¹ = 3³ⁿ

⇒ 1 = 3n

\[\ce{n = \frac{1}{3}}\]

∴ Order of reaction = \[\ce{\frac{1}{3}}\]

Answer 2

Given:

Reaction: \[\ce{2A -> A2}\]

When [A] is increased 27 times, the rate increases 3 times

Need to find the order of reaction (n)

Rate ∝ [A]ⁿ

Let the ratio of new to original rate be

\(\frac{\mathrm{New~Rate}}{\text{Original Rate}}=\left(\frac{[A]_{\mathrm{new}}}{[A]_{\mathrm{original}}}\right)^n\)

⇒ \[\ce{\frac{3}{1} = (27)^n}\]

3 = 27ⁿ

= (3³)ⁿ

= 3³ⁿ

⇒ 3¹ = 3³ⁿ

⇒ 1 = 3n

\[\ce{n = \frac{1}{3}}\]

∴ Order of reaction = \[\ce{\frac{1}{3}}\]