To determine the value of the rate constant, we can use the Arrhenius equation. 

We can plug in the given values for T1 and T2 (must be in Kelvin), the activation energy (must be in J/mol), R (must use 8.314 J/mol K), and k1.  One important thing to note is that you must correctly pair k1/T1 and k2/T2.

ln (k2/0.315) = (260000 J/mol / 8.314 J/molK)(1/800 - 1/850)

ln (k2/0.315) = 2.30

To get rid of the ln, we need to take both sides to the power of e which will cancel out the ln.

k2/0.315 = e^2.30

k2/0.315 = 9.97

k2 = 3.14

You can go back and check this value by plugging in the temperatures and the k values, then solving for the activation energy.