A particular first-order reaction has a rate constant of 1.35 × at 25.0°C.What is the magnitude of k at 75.0°C if

Question

A particular first-order reaction has a rate constant of 1.35 ×   at 25.0°C.What is the magnitude of k at 75.0°C if

Quizplus · Accepted Answer

The Arrhenius equation relates the rate constant of a reaction to the activation energy (Ea) and the temperature in Kelvin (T):
k = A * exp(-Ea/RT)
where R is the gas constant (8.314 J/mol K).

To solve for the rate constant at 75.0°C, we need to convert the temperatures to Kelvin:
T1 = 25.0°C + 273.15 = 298.15 K
T2 = 75.0°C + 273.15 = 348.15 K

We are given that k1 = 1.35 × 10^11 s^-1, so we can solve for the pre-exponential factor A:
A = k1 * exp(Ea/RT1)

Next, we can use the same equation to solve for k2 using A and Ea from the first step:
k2 = A * exp(-Ea/RT2)

To eliminate A, we can divide the two equations to get:
k2/k1 = exp((Ea/R) * (1/T1 - 1/T2))

Solving for k2, we get:
k2 = k1 * exp((Ea/R) * (1/T1 - 1/T2))

Plugging in the given values and solving:
k2 = 1.35 × 10^11 s^-1 * exp((Ea/8.314) * (1/298.15 - 1/348.15))
k2 = 1.92 × 10^14 s^-1

Therefore, the best choice is B, 1.92 × 10^14 s^-1.

A Particular First-Order Reaction Has a Rate Constant of 1