Answer to Question #106479 in General Chemistry for Beverlie

Question

1. The dimerization of ClO is second order in ClO.
2ClO(g) ⇌ Cl2O2
Time (s) [ClO] (molecules/cm3)
0 2.08 x 105
1 8.64 x 104
2 5.46 x 104
3 3.99 x 104
a) Use the following data to determine the value of k at 350 K. answer in cm3/molecules•s
b) Use the data above to determine the value the half-life at 350 K. answer in s

Answer 1

The rate constant for the given reaction is calculated as shown below.

a) If the reaction refers to second-order reactions (С01 = С02), then the rate constant:

k=1/t(1/c-1/c₀)

k=1/1(1/8,64 х 10⁴-1/2.08 x 10⁵) =1(1/8,64 х 10⁴-1/20.8 x 10⁴)=(20.8x 10⁴-8,64 х 10⁴)/20.8x 10⁴х8,64 х 10⁴=12.16х 10⁴/179.712х 10⁴=0.0676х 10⁴ cm3/molecules•s 

k=1/2(1/5.46 x 10⁴-1/ 2.08 x 10⁵)=1/2(20.8x 10⁴-5,46х 10⁴)/20.8x 10⁴х4,46х10⁴)=1/215.34х 10⁴/113.568х 10⁴=1/2 х 0.1350х 10⁴/molecules•s=0.0676 х 10⁴/molecules•s

k=1/3(1/3.99 x 10⁴-1/ 2.08 x 10⁵)=1/3(20.8x 10⁴-3.99х 10⁴)/20.8x 10⁴х3.99х10⁴)=1/316.81х 10⁴/82.992х 10⁴ =1/3 0.2025 х 10⁴/molecules•s=0.0676х 10⁴ cm3/molecules•s

b) t_1/2=1/k х 1/c0=1/0.0676х 104 cm3/molecules•sх 1/20.8 x 104cm3/molecules•s)=1/1.40608x104=0.71x10^-4s