The activation energy of a certain reaction is 30.3 kJ/mol. At 20 C, the rate constant is 0.0130 s^{-1}. At what temperature would this reaction go twice as fast?

Can't you use Arrhenius' equation for this. Look it up. You have Ea. you have T1. You have k1 and k2. That leaves T2 as the only unknown.