For first-order reactions, the half-life is inversely proportional to the rate constant (t1/2 = 0.693/k).

An increase in activation energy decreases the rate constant according to the Arrhenius equation, k = Ae^(-Ea/RT), where an increase in Ea results in a smaller k.

According to the Arrhenius equation, an increase in temperature results in an increase in the rate constant, k, as it provides more energy to overcome the activation energy barrier.

For a first-order reaction, the half-life (t1/2) is given by t1/2 = 0.693/k. Rearranging gives k = 0.693/t1/2 = 0.693/10 min = 0.0693 min^-1.

For first-order reactions, the half-life is independent of concentration but depends on the rate constant, which increases with temperature. Typically, the half-life will decrease, but the exact value requires the Arrhenius equation.

The rate-determining step is the slowest step in a reaction mechanism and thus controls the overall rate of the reaction.

According to the rate laws, increasing the concentration of reactants generally increases the rate of reaction, as it leads to more frequent collisions.

For a zero-order reaction, the integrated rate law is [A] = [A]0 - kt, indicating that the concentration decreases linearly with time.

The rate law is determined by the stoichiometry of the rate-determining step. For second order in A and first order in B, the rate law is Rate = k[A]^2[B].

According to the Arrhenius equation, the rate constant increases with temperature due to the exponential dependence on the negative activation energy divided by temperature.