For the decomposition of dinitrogen oxide, the rate constant is 0.043 L/mol-min at 665 oC and 12.5 L/mol-min at 828 oC. What is the activation energy of the decomposition reaction?
ln K = -Ea/RT
100
To find the activation energy of the decomposition reaction, we can use the Arrhenius equation:
k = A * e^(-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
We are given two sets of data:
- At 665 °C (938 K), the rate constant is 0.043 L/mol-min.
- At 828 °C (1101 K), the rate constant is 12.5 L/mol-min.
We can use both sets of data to set up a system of equations:
0.043 = A * e^(-Ea/(8.314 * 938))
12.5 = A * e^(-Ea/(8.314 * 1101))
First, we can divide the first equation by the second equation to get rid of A:
0.043/12.5 = e^(-Ea/(8.314 * 938))/e^(-Ea/(8.314 * 1101))
Next, simplify the left side:
0.00344 = e^(-Ea/(8.314 * 938 - 1101))
Then, take the natural logarithm of both sides to eliminate the exponential:
ln(0.00344) = -Ea/(8.314 * 938 - 1101)
Now, solve for Ea:
Ea = -ln(0.00344) * (8.314 * 938 - 1101)
Calculating this expression will give you the activation energy for the decomposition reaction.