COMEDK 2024 Shift 2 Paper

To determine the order of reaction, we will use the method of initial rates. The rate law for the decomposition of the compound XY can be expressed as:
Rate =k[XY]n
where:
k is the rate constant
[XY] is the concentration of the XY compound
n is the order of the reaction with respect to XY
We have three sets of data points:
‌‌ At ‌[XY]=0.4‌mol∕L,‌ Rate ‌=5.5×10−7‌mol∕L∕ s
‌‌ At ‌[XY]=0.8‌mol∕L,‌ Rate ‌=22.0×10−7‌mol∕L∕ s
‌‌ At ‌[XY]=1.2‌mol∕L,‌ Rate ‌=49.5×10−7‌mol∕L∕ s
We can analyze how the rate changes with the concentration. By comparing the rate when the concentration is doubled, you can find the order of reaction:
Step 1: Compare the first two data points:
‌

‌ Rate ‌2

‌ Rate ‌1

=(‌

22.0×10−7

5.5×10−7

)=(‌

0.8

0.4

)n
This simplifies to:
‌‌

22.0

5.5

=(2)n
‌4=2n
Taking logs on both sides, we get:
log‌4=n‌log‌2
Since log‌4=2‌log‌2, we have:
2=n
Step 2: Confirm our answer with third data point, comparing with the first again:
‌ Rate ‌3=(‌

49.5×10−7

5.5×10−7

)=(‌

1.2

0.4

)n
This simplifies to:
‌‌

49.5

5.5

=(3)n
‌9=3n
Taking logs on both sides, we get:
log‌9=n‌log‌3
Since log‌9=2‌log‌3, we again find:
2=n
Since the calculated value for n is 2 , the order of reaction with respect to the decomposition of XY is
Option B: 2