The rate constant k for a certain reaction is measured at two different temperatures:temperature k392.0°C ×1.71011470.0°C ×2.91011Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy Ea for this reaction.Round your answer to 2 significant digits.

The Arrhenius equation is given by:

k = A * exp(-Ea / R * T)

where: k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

Taking the natural logarithm of both sides gives:

ln(k) = ln(A) - Ea / (R * T)

We can rearrange this to:

Ea = -R * T * ln(k) + ln(A)

We have two sets of values for k and T, so we can set up two equations and subtract one from the other to eliminate ln(A):

Ea = -R * T1 * ln(k1) + ln(A) Ea = -R * T2 * ln(k2) + ln(A)

Subtracting these gives:

0 = -R * T1 * ln(k1) + R * T2 * ln(k2)

Rearranging gives:

R * (T1 * ln(k1) - T2 * ln(k2)) = 0

R * (ln(k1) / T1 - ln(k2) / T2) = 0

So:

Ea = -R * (ln(k1) / T1 - ln(k2) / T2)

We can plug in the given values for k1, k2, T1, and T2, and use R = 8.314 J/(mol*K) to find Ea.

Remember to convert the temperatures from Celsius to Kelvin by adding 273.15.

T1 = 392.0°C = 392.0 + 273.15 = 665.15 K T2 = 470.0°C = 470.0 + 273.15 = 743.15 K

k1 = 1.71 * 10^11 k2 = 2.91 * 10^11

So:

Ea = -8.314 * (ln(1.71 * 10^11) / 665.15 - ln(2.91 * 10^11) / 743.15)

Calculate the value to get the activation energy. Round your answer to 2 significant digits.