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Question

The following are experiments performed at 85.37°C:

Exp’t # [F2]initial [Cl2]initial [Br2]initial Rate initial (M/second)

1. 0.363 0.294 0.312 7.476 x 10^-3

2. 0.121 0.294 0.312 2.492 x 10^-3

3. 0.363 0.147 0.312 3.738 x 10^-3

4. 0.363 0.147 0.624 7.476 x 10^-3

5. 0.121 0.147 0.624 2.492 x 10^-3

1.) What is the correct rate law expression for this reaction including a value of “k” with correct units?

2.) If Experiment #2 is repeated at 97.64°C, the initial rate is 1.839 x 10^-2 M/second. What is the activation energy for this reaction?

Answer 1

1). To write the correct rate law, we must first determine the order of the reaction with respect to each reactant, F_2, Cl₂ and Br₂. To do this, we will find experiments in which only one of these changes and see the effect on rate.

For F₂ we compare experiment #2 to expt. #1 where [F₂] is tripled while [Cl₂] and [Br₂] remain constant. The rate also tripled, so the reaction is FIRST ORDER IN F₂

For Cl₂ we compare expt.# 3 to expt.#1 where [Cl₂] is doubled while [F₂] and [Br₂] remain constant. The rate also doubles, so the reaction is FIRST ORDER IN Cl₂

For Br₂ we compare expt # 3 to expt #4 where [Br₂] is doubles while [F₂] and [Cl₂] remain constant. The rate also doubles, so the reaction is FIRST ORDER IN Br₂

Now we can write the rate law as

rate = k[F₂][Cl₂]Br₂] and to complete the rate law with the correct value of k, we use any experiment to solve for k, as follows:

Using expt #1, we have 7.476 x 10^-3 M/s = k(0.363 M)(0.294 M)(0.312 M)

k = 7.476 x 10^-3 M/s ÷ 0.03330 M³

k = 0.2245 M^-2s^-1

So, the final rate law is ...

rate = 0.2245 M^-2s^-1 [F₂][Cl₂][Br₂]

2). To find the activation energy of the reaction from the given data, we can use the Arrhenius equation:

ln (k2/k1) = -Ea/R (1/T2 - 1/T1)

But to do so, we must find the value of the rate constant (k2) at the new temperature of 97.64ºC.

rate = k2[F₂][Cl₂][Br₂]

1.839x10^-2 M/s = k2(0.121 M)(0.294 M)(0.312 M)

k2 = 1.657 M^-2s^-1

From the Arrhenius equation:

ln (k2/k1) = -Ea/R (1/T2 - 1/T1)

k1 = 0.2245

k2 = 1.657

Ea = ?

R = 8.314 J/molK

T1 = 85.37C + 273.15 = 358.52K

T2 = 97.64C + 273.15 = 370.79K

ln(1.657/0.2245) = (1/370.79 - 1/358.52)

1.9989 = -Ea / 8.314 (2.697x10^-3 - 2.789x10^-3) = -Ea / 8.314 (-9.2x10^-5)

1.9989 = 9.2x10^-5 Ea / 8.314

Ea = 180,640 J/mol = 180.6 kJ/mol