Question

The rate constant of a reaction at temperature 200 $K$ is10 times less than the rate constant at 400 $K$ . What is theactivation energy $\left(E_a\right)$ of the reaction $(R=$ gas constant)?

• A. 1842.4$R$
• B. 921.2$R$
• C. 460.6$R$
• D. 230.3$R$

Answer 1

Answer: (B)

921.2$R$

C₁ = rate constant at temperature 200 k

C₂ = rate constant at temperature 400 k

Given that

C₁ = C₂ /10

T₁ = lower temperature = 200 k

T₂ = higher temperature = 400 k

Q = activation energy

R = gas constant

The relation between activation energy , temperature and rate constants is given as

ln( C₂/C₁ ) = (Q/R) [(1/T₂) - (1/T₁)]

inserting the above values in the equation

ln( C₂/(C₂ /10) ) = - (Q/R) [(1/400) - (1/200)]

ln(10) ) = - (Q/R) [(1/400) - (1/200)]

2.303 = - (Q/R) [(1/400) - (1/200)]

Q/R = 921

Q = 921 R