A certain first order reaction has a rate constant of 5.68 x 10–3 s–1 at 139°C and a rate constant of 8.99 x 10–1 s–1 at a temperature of 215°C.

Question

A certain first order reaction has a rate constant of 5.68 x 10–3 s–1 at 139°C and a rate constant of 8.99 x 10–1 s–1 at a temperature of 215°C.

Ea = 111 kJ mol–

q1) What is the value of the rate constant at 275°C?

q2) At what temperature does the rate constant have a value of 7.87 x 10–4 s–1?

I don't require the answer as i have it just the working out, i can't get to the answer for some reason.

Answer 1

Have you used the Arrhenius equation? Show your work; perhaps we can find the error.

Answer 2

lnK = -Ea/R (1/T) + lnA

lnK = -111000/8.314 (1/548.15) + lnA

so i've tried different things however given im provided with two rate constants and two temperatures im not sure which to use and also i don't have an A value. At first i tried to input one set of data and then find A corresponding and then find K but it doesnt work.

I tried to find A first and then find K but im not getting the right answer in the end
which is supposed to be 18.2s.

Answer 3

To find the value of the rate constant at 275°C, we can use the Arrhenius equation:

k2 = Ae^(-Ea/RT)

Where:
k2 is the unknown rate constant at 275°C
A is the pre-exponential factor (constant)
Ea is the activation energy
R is the gas constant (8.314 J mol^(-1) K^(-1))
T is the temperature in Kelvin

Given values:
k1 = 5.68 x 10^(-3) s^(-1) at 139°C (412 K)
k2 = ? (to be found) at 275°C (548 K)
Ea = 111 kJ mol^(-1) (convert to Joules: 111 x 10^(3))

Now, let's solve for k2 using the Arrhenius equation:

ln(k2) = ln(A) - (Ea/RT)

ln(k2) = ln(A) - (Ea/(R*T))

ln(k2) = ln(k1) - (Ea/(R*T1))

ln(k2) = ln(5.68 x 10^(-3)) - ((111 x 10^(3))/(8.314 * 412))

Now, calculate ln(k2) using the provided equation.

To find the temperature at which the rate constant is 7.87 x 10^(-4) s^(-1), we use the same Arrhenius equation:

k2 = Ae^(-Ea/RT)

Given values:
k2 = 7.87 x 10^(-4) s^(-1) (to be found)
A = ?
Ea = 111 kJ mol^(-1) (convert to Joules: 111 x 10^(3))
R = 8.314 J mol^(-1) K^(-1)
T = ? (to be found)

We can rearrange the equation and solve for T:

T = Ea / (R * ln(k2 / A))

Plug in the given values to calculate T.

Answer 4

To solve these questions, we can use the Arrhenius equation, which relates the rate constant (k) to the temperature and the activation energy (Ea). The Arrhenius equation is given by:

k = A * exp(-Ea/RT)

Where:
- k is the rate constant,
- A is the pre-exponential factor,
- Ea is the activation energy,
- R is the gas constant (8.314 J/(mol·K)),
- T is the temperature in Kelvin (K).

Now, let's proceed to solve the questions step by step.

q1) What is the value of the rate constant at 275°C?

First, we need to convert the temperature to Kelvin. The conversion is given by:

T(K) = T(°C) + 273.15

So, T = 275 + 273.15 = 548.15 K

Now, we can use the given data to set up two equations using the Arrhenius equation.

At 139°C:
5.68 x 10^(-3) = A * exp(-111000 / (8.314 * (139 + 273.15)))

At 215°C:
8.99 x 10^(-1) = A * exp(-111000 / (8.314 * (215 + 273.15)))

We can solve these equations simultaneously to find the values of A. Once we have A, we can plug it into the Arrhenius equation for the desired temperature.

q2) At what temperature does the rate constant have a value of 7.87 x 10⁻⁴ s⁻¹?

We want to find T when k = 7.87 x 10⁻⁴ s⁻¹.

Using the Arrhenius equation, we can rearrange it to solve for T:

T = -Ea / (R * ln(k / A))

Plug in the given values of Ea, R, k, and the previously calculated value of A to find the temperature.

By following these steps, you should be able to solve these questions.