Question

For a certain reaction, the frequency factor A is 5.0 × 109 s−1 and the activation energy is 16.3 kJ/mol. What is the rate constant for the reaction at 79°C

Answer 1

Final answer:

Using the Arrhenius equation, the rate constant at 79°C is calculated to be approximately 1.915 × 10^7 s^-1 after converting temperature to Kelvin and inputting the given frequency factor and activation energy.

Step-by-step explanation:

To calculate the rate constant for the reaction at 79°C using the Arrhenius equation, we first need to convert the temperature from Celsius to Kelvin. The conversion is done by adding 273.15 to the Celsius temperature. Thus, 79°C is equal to 79 + 273.15 = 352.15 K.

Next, we use the Arrhenius equation k = Ae-Ea/RT. Here, A represents the frequency factor, Ea is the activation energy, R is the ideal gas constant, and T is the temperature in Kelvin.

Given that the activation energy is 16.3 kJ/mol, we need to convert it to joules per mole by multiplying by 1000, so we have 16300 J/mol. The ideal gas constant R is 8.314 J/mol/K. Substituting the known values into the equation gives:

k = 5.0 × 109 s−1 × e-(16300 J/mol)/(8.314 J/mol/K × 352.15 K)

Calculating the exponent first:

e-(16300 J/mol)/(8.314 J/mol/K × 352.15 K) = e-5.5612 ≈ 3.83 × 10-3

Now we can find the rate constant:

k = 5.0 × 109 s−1 × 3.83 × 10-3 = 1.915 × 107 s−1

Therefore, the rate constant at 79°C is approximately 1.915 × 107 s−1.

Answer 2

K(79°C) = 1.906 E7 s-1

Step-by-step explanation:

Arrhenius eq:

• K(T) = A e∧(- Ea/RT)

∴ A = 5.0 E9 s-1

∴ Ea = 16.3 KJ/mol

∴ R = 8.314 E-3 KJ/K.mol

∴ T = 79°C ≅ 352 K ⇒ K = ?

⇒ K(79°C) = (5.0 E9 s-1)e∧[ - (16.3KJ/mol)/(8.314 E-3 KJ/K.mol)(352 K)]

⇒ K(79°C) = (5.0 E9 s-1)e∧(- 5.5697)

⇒ K(79°C) = (5.0 E9 s-1)*(3.811 E-3)

⇒ K(79°C) = 1.906 E7 s-1