Chemistry 102: Kinetics: Arrhenius Equation

Question

The rate constant for the reaction below was determined to be 3.241×10^-5  s^–1 at 800 K. The activation energy of the reaction is 265  kJ/mol. What would be the value of the rate constant at 9.50×10²  K?

N2​O(g)N2​(g)+O(g

Answer 1

Using the Arrhenius equation: ln k2/k1 = Ea/R(1/t1 - 1/t2) this equation allows you to calculate a new rate constant as the temperature changes. We know the rate of reaction will vary with temperature and thus so will the K values

K are are rate constants, Ea is the activation energy and R is a constant at 8.31 J/mol.K

The units have to match with regards to the Ea (activation energy) which is given in KJ/mol whereas the R constant is 8.31J/mol.K

converting the Ea to J you get 265000 J/mol

step 1) set the equation up using the knowns

ln K2/3.241x10-5 s-1 = 265000 J/mol/8.31 J/mol.K(1/8.0x10^2K - 1/9.5x10^2K)

step 2) consolidate terms on the right side of the equation = 6.282 so then you have:

ln K2/3.241x10-5. = 6.282

to eliminate the ln (natural log) on the left - multiply both sides of the equation by the antilogarithm (e^x)

step 3) now that you cleared the ln from the left side of the equation and found the value of e^6.282 to obtain 5.349x10^2 your equation looks like this:

K2/3.241x10-5 = 5.349x10^2 now solve for K2

K2 = 1.7x10-2 s-1

If you need further help just let me know.

Thanks

Answer 2

The value of the rate constant at 9.50*10² K would be 1.75*10^-2 s^-1.

We can solve this using the Arrhenius Equation: ln(k₂/k₁) = -E_a/R(1/T₂-1/T₁).

We can set the first variable k₁ equal to 3.241*10^-5 s^-1 and the variable T₁ as 800K.

That leaves the variable k₂ to be set at "x" as this is the rate constant we are finding the value of and T₂ as 9.50*10²K.

Finally, E_a represents activation energy at the value of 265000 J/mol (notice we must convert the value from kJ) and the R constant is 8.314 J/mol*K.

We can plug all these values into the equation to reach the above answer!