Hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst \(\left(\mathrm{MnO}_{2}ight)\). The activation energy of the uncatalyzed reaction is \(70.0 \mathrm{~kJ} / \mathrm{mol}\). When the catalyst is added, the activation energy at \(20 .^{\circ} \mathrm{C}\) is 42.0 \(\mathrm{kJ} / \mathrm{mol}\). Theoretically, to what temperature \(\left({ }^{\circ} \mathrm{C}ight)\) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at \(20 .{ }^{\circ} \mathrm{C}\) ? Assume the frequency factor \(A\) is constant and assume the initial concentrations are the same.