Given that the initial rate constant is 0.0190s^-1 at an initial temperature of 20 degrees Celsius, what would the rate constant be at a temperature of 170 degrees Celsius?
Activation energy is 32.4kJ/mol
To calculate the rate constant at a temperature of 170 degrees Celsius, we can use the Arrhenius equation:
k2 = k1 * exp((Ea/R) * ((1/T2) - (1/T1)))
where:
k2 = rate constant at temperature T2
k1 = initial rate constant at temperature T1
Ea = activation energy
R = gas constant (8.314 J/(mol*K))
T2 = final temperature (in Kelvin)
T1 = initial temperature (in Kelvin)
First, we need to convert the temperatures from Celsius to Kelvin:
T1 = 20 + 273.15 = 293.15 K
T2 = 170 + 273.15 = 443.15 K
Now, we can calculate the rate constant at 170 degrees Celsius:
k2 = 0.0190 * exp((32.4 * 1000)/(8.314 * ((1/443.15) - (1/293.15))))
Using the given values and performing the calculation:
k2 = 0.0190 * exp((32.4 * 1000)/(8.314 * ((0.002688) - (0.003411))))
k2 ≈ 0.0190 * exp(15683.54)
k2 ≈ 0.0190 * 2.61 x 10^6
k2 ≈ 49.59 s^-1
Therefore, the rate constant at a temperature of 170 degrees Celsius is approximately 49.59 s^-1.
To determine the rate constant at a different temperature, we can use the Arrhenius equation. The Arrhenius equation relates the rate constant (k) to the temperature (T) and the activation energy (Ea):
k = A * e^(-Ea / (R * T))
In this equation:
- k is the rate constant
- A is the pre-exponential factor or the frequency factor
- Ea is the activation energy
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (20°C = 293 K and 170°C = 443 K)
First, we need to calculate the pre-exponential factor (A) using the initial rate constant and temperature given. The equation for calculating A is:
A = k / e^(-Ea / (R * T))
Plugging in the values from the problem:
A = (0.0190 s^-1) / e^(-32.4 kJ/mol / (8.314 J/(mol·K) * 293 K))
Calculate A using a calculator or software that can handle scientific notation.
Once we have the value of A, we can use it in the Arrhenius equation to find the rate constant at a different temperature (170°C = 443 K):
k_new = A * e^(-Ea / (R * T_new))
Plug in the values:
k_new = A * e^(-32.4 kJ/mol / (8.314 J/(mol·K) * 443 K))
Calculate k_new using a calculator or software that can handle scientific notation. The result will give you the rate constant at a temperature of 170°C.