How Do You Calculate the Higher Temperature in a Chemical Kinetics Problem?

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To calculate the higher temperature in a chemical kinetics problem with an activation energy of 54.0 kJ/mol and a rate constant increase by a factor of 7.00, the Arrhenius equation can be applied. The equation ln(k) = -Ea/RT + ln(A) is central to the calculation. One participant notes the challenge of having two variables, the new temperature and the rate constant, complicating the solution. They suggest relating the original and new rate constants as K1 and 7.K1 to simplify the problem. This approach can help isolate the temperature variable and facilitate finding the higher temperature.
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1. A certain reaction has an activation energy of 54.0 kJ/mol. As the temperature is increased from 22degrees celsius to a higher temperature, the rate constant increases by a factor of 7.00. Calculate the higher temperature.

2. ln(k)=-Ea/RT + ln(A)



3. i don't think that i have enough information because when i plugged the values given and there are still two variables. Then i tried simultanious equations by solving for [A] and there are still two variables the new temp and the rate constant. So if anyone can help it would be very appreciated.
 
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The rate constant is just 7 times the original rate constant, so can't you relate the two together as K1 and 7.K1, and then if you solve for T2 you should be able to get the K1s and the As to cancel out.
 

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