The reaction for the decomposition of dinitrogen monoxide gas to form an oxygen radical is: N2O(g)==>N2(g)+O(g) . If the activation energy is 250 kJ/mol and the frequency factor is 8.0 x 1011 s-1, what is the rate constant for the first-order reaction at 1000 K?

k = A * exp ( -Ea / RT )

k = rate constant (s-1)
A = frequency factor or preexponential factor (s-1)
Ea = activation energy (J / mol)
R = gas constant (J / K*mol)
T = Temp (K)

k=8.0x10^11s-1(250kj/mol/8.314472*1000K)

did i set this up right?

Never mind i know i didn't what goes in the exp?

I use it in the form that follows:

ln(k2/k1) = Ea/R(1/T1 - 1/T2)
You must insert A appropriately.

i don't understand where k1 k2 t1 t2 come from... :(

Yes, you have set up the equation correctly. To calculate the rate constant (k) for the first-order reaction at 1000 K using the Arrhenius equation, you need to substitute the values of the frequency factor (A), activation energy (Ea), gas constant (R), and temperature (T) into the equation.

However, there is a small mistake in your conversion of the activation energy from kJ/mol to J/mol. The gas constant (R) is usually expressed in J/K*mol, so make sure to convert the activation energy to J/mol as well.

So, the corrected setup would be:

k = 8.0x10^11 s^-1 * exp(-250,000 J/mol / (8.314472 J/K*mol * 1000 K))

To solve this equation, you would need to calculate the exponential term separately and then multiply it by the frequency factor.

Let me know if you need any further assistance!