Question

1. Which reaction has the faster rate;

      a. a reaction with Ea = 30.0 kJ/mol, or one wth Ea = 25.0 kJ/mol?

      b. A 1st order reaction with a rate constant, k, = 3.5 x 10^-3, s-1, or one with k = 6.2 x 10^-4 s-1 ? Explain.

2. a reaction has a rate constant, k = 4.62 x 10^-3 s-1 at 300 K and k = 6.54 x 10^-3 at 320 K. Determine Ea for this reaction.

3. Using your value for Ea from question 2, calculate k for this reaction at 340 K

Answer 1

According to arrhenius equation K = A * e ^(-Ea/RT)

K = rate constant

A = exponential factor

Ea = activation energy

R = universal gas constant

T = temperature

then K1 = A * e ^(-Ea1/RT) and K2 = A * e ^(-Ea2/RT)

so K1/K2 = A * e ^(-Ea1/RT)/A * e ^(-Ea2/RT)

ln(K1/K2) = -ln(Ea1/RT)/(-ln(Ea2/RT))

under same conditions of T

ln(K1/K2) = ln(Ea1/Ea2)

K1/K2 = Ea1/Ea2

Rate = K*[concentraton of reactnts]

Hence rate constant is proportional to Activation enrgy and rate reaction is proportional to activation energy.

Higher the activation energy faster the rate of reaction.

so Ea = 30 kJ/mol is faster reaction.

similarly k = 3.5 * 10^-3 is higher value so the rate of the reaction is faster.

2)

log(K1/K2) = Ea/(2.303*R)*((1/T2)-(1/T1))

log((4.62*10^-3)/(6.54*10^-3)) = Ea/(2.303*8.314)*((1/320)-(1/300))

Ea = 13871.94 J

3)

log(K1/K3) = Ea/(2.303*R)*((1/T3)-(1/T1))

log((4.62*10^-3)/K3) = (13871.94)/(2.303*8.314)*((1/340)-(1/300))

K3 = 8.89 * 10^-3 s^-1