Posted by Brunette on Sunday, October 14, 2012 at 10:42pm.

Values of the rate constant for the decomposition of N2O5 at four different temperatures are as follows:

T(K) k(s^-1)
658....2.14*10^5
673....3.23*10^5
688....4.81*10^5
703....7.03*10^5

The activation energy is 1.02*10^2 kJ/mol. Calculate the value of the rate constant at 300 K
chemistry - DrBob222, Sunday, October 14, 2012 at 11:23pm
Can't you use the Arrhenius equation?
Use two T values with corresponding k values. One T will be 300 and k at that T will be the unknown.
chemistry - Brunette, Monday, October 15, 2012 at 6:36pm
I keep trying that and it is saying that I have the wrong answer. here is my work:

slope: -1.19*10^4 y-intercept= 30.439

Ea: -(-1.19*10^4 K) *(8.314J/moK)= 9.89*10^4 J/mol

A= e^30.439= 1.65*10^13

(1.65*10^13) e^-(9.89*10^4J/mol/8.314*300 K)= 9.98*10^-5

I keep getting different answers, and each time they are saying it is wrong. Can you tell me where I am going wrong? And am I supposed to convert the Ea into joules/mole?

Yes, Ea goes in with units of J.

You don't need a graph.
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
Pick a k1 with T1, then k2 with 300 K for T2 and solve for k2. R is 8.314.

Oh! Thank you! I forgot to pick a second temperature.

To calculate the value of the rate constant at 300 K using the Arrhenius equation, you need to follow these steps:

1. First, choose two T values with corresponding k values from the given data. In this case, let's choose 673 K and 688 K:

T1 = 673 K
k1 = 3.23 * 10^5 s^-1

T2 = 688 K
k2 = 4.81 * 10^5 s^-1

2. Next, calculate the activation energy (Ea) in joules/mole:

Ea = 1.02 * 10^2 kJ/mol * (1000 J/kJ) = 1.02 * 10^5 J/mol

Yes, you are correct in converting Ea into joules/mole.

3. Now you can find the pre-exponential factor (A) using the Arrhenius equation:

A = k1 / e^(-Ea / (R * T1))

A = (3.23 * 10^5 s^-1) / e^(-1.02 * 10^5 J/mol / (8.314 J/mol*K * 673 K))

A = 1.146 * 10^12 s^-1

4. Finally, calculate the value of the rate constant (k) at 300 K:

k = A * e^(-Ea / (R * T))

k = (1.146 * 10^12 s^-1) * e^(-1.02 * 10^5 J/mol / (8.314 J/mol*K * 300 K))

k ≈ 3.07 * 10^-4 s^-1

So, the value of the rate constant at 300 K is approximately 3.07 * 10^-4 s^-1.

To calculate the value of the rate constant (k) at 300 K using the Arrhenius equation, you can follow these steps:

1. Identify two temperature values (T1 and T2) with their respective rate constants (k1 and k2).

2. Use the Arrhenius equation:
k = A * e^(-Ea/RT)

Where:
k = rate constant
A = pre-exponential factor or frequency factor
Ea = activation energy
R = gas constant (8.314 J/mol·K)
T = temperature (in Kelvin)

3. Plug in the values into the equation. You need to choose two values that are closest to 300 K. In this case, you can choose T1 = 288 K and T2 = 303 K.

From the given data:
T1 = 288 K, k1 = 7.03 × 10^5 s^-1
T2 = 303 K, k2 = 4.81 × 10^5 s^-1

4. Convert the activation energy (Ea) from kJ/mol to J/mol. Given Ea = 1.02 × 10^2 kJ/mol, convert it to J/mol by multiplying by 1000:
Ea = 1.02 × 10^2 kJ/mol × 1000 J/kJ = 1.02 × 10^5 J/mol

5. Plug in the values into the Arrhenius equation and solve for k at 300 K:
k = A * e^(-Ea/RT)
k1 = A * e^(-Ea/RT1)
k2 = A * e^(-Ea/RT2)

Divide equation 2 by equation 1 to cancel out the pre-exponential factor:
k2/k1 = e^(Ea/R) * (e^(-Ea/T2)) / (e^(-Ea/T1))
k2/k1 = e^(Ea/R) * e^(-Ea/T2 + Ea/T1)
k2/k1 = e^(Ea/R) * e^(-Ea(1/T2 - 1/T1))

Rearrange the equation to solve for k at 300 K (k300):
k300 = k1 * e^(Ea/R) * e^(-Ea(1/T2 - 1/T1)), where T1 = 288 K, T2 = 303 K

6. Substitute the values into the equation and calculate k300:
k300 = 7.03 × 10^5 s^-1 * e^(1.02 × 10^5 J/mol / (8.314 J/mol·K)) * e^(-1.02 × 10^5 J/mol (1/300 K - 1/288 K))

7. Calculate k300 to get the value of the rate constant at 300 K.