Question

4. A study of the rate of dimerization of C4H6 gave the data shown in the table: 2C4H6-C8H12 3200 6200 Time (s) 0 [C.Hol 1.00 (M) 1600 5.04 4800 2.53 3.37 x 2.08. 10-2 10-3 10-3 10-3 10-3 (a) Determine the average rate of dimerization (this reaction is a type of reaction classified as a dimerization) between 0s and 1600 s

Answer 1

The reaction here is:
2C₄H₆ ---> C₈H₁₂  

a)

We know that, Concentration of C₄H₆ at t=0s = 1.00 x 10^-2 M = 10.0 x 10^-3 M
And Concentration of C₄H₆ at t=1600s = 5.04 x 10^-3 M

Therefore, amount ot C₄H₆ consumed in 1600s = (Concentration of C₄H₆ at t=0s) - (Concentration of C₄H₆ at t=1600s )
=  10.0 x 10^-3 M - 5.04 x 10^-3 M
= 4.96 x 10^-3 M

As per the stoichiometry of reaction: 2 moles of C₄H₆ are consumed to form 1 mole of C₈H₁₂ .
Hence 1 moles of C₄H₆ will be consumed to form 0.5  mole of C₈H₁₂ .

amount ot C₄H₆ consumed in 1600s = 4.96 x 10^-3 M
So, amount ot C₈H₁₂ formed in 1600s = 0.5 x amount ot C₄H₆ consumed in 1600s
= 0.5 x 4.96 x 10^-3 M
= 2.48 x 10^-3 M

Now,

Average rate of dimerization between 0s and 1600s = Total amount of dimer formed(C₈H₁₂) / Total time
=  2.48 x 10^-3 M / 1600 s
= 1.55 x 10^-6 M /s

Answer = 1.55 x 10^-6 M /s