The activation energy for the decomposition reaction,
2 HI---> H2 + Hi
Is 186 kj/mol. The rate at 555 k is 3.2 x 10 -7L/mol. Sec. What is the rate at 645 k
To determine the rate at 645 K for the given decomposition reaction, you can use the Arrhenius equation. The Arrhenius equation is commonly used to calculate the temperature dependence of reaction rates. It is given as:
k = A * e^(-Ea / (R * T))
Where:
- k represents the rate constant
- A is the pre-exponential factor (also known as the frequency factor)
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin
First, convert the given activation energy from kilojoules per mole (kJ/mol) to joules per mole (J/mol) by multiplying by 1000 since 1 kJ = 1000 J:
Ea = 186 kJ/mol * 1000 J/kJ = 186000 J/mol
Next, calculate the rate constant (k) at 555 K using the given data:
k1 = 3.2 × 10^(-7) L/mol·s (*)
Now, to find the rate at 645 K, you can rearrange the Arrhenius equation:
k2 = A * e^(-Ea / (R * T2))
Since we want to compare the rates at both temperatures, we can set up a ratio between the two rate constants:
k2 / k1 = (A * e^(-Ea / (R * T2))) / k1
We know k1 and T1 (555 K), so we can rearrange the equation to solve for k2:
k2 = k1 * e^((Ea / (R * T1 - R * T2))) (**)
Now, plug in the values to calculate k2 at 645 K:
T1 = 555 K
T2 = 645 K
R = 8.314 J/(mol·K)
Ea = 186000 J/mol
k1 = 3.2 × 10^(-7) L/mol·s
Substitute these values into equation (**):
k2 = (3.2 × 10^(-7) L/mol·s) * e^((186000 J/mol / (8.314 J/(mol·K) * T1 - 8.314 J/(mol·K) * T2))
Finally, calculate the value of k2 using the above equation, and that will give you the rate at 645 K for the decomposition reaction.