(a) The gas-phase decomposition of SO2Cl2, SO2Cl21g2 ¡SO21g2 + Cl21g2, is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 * 105 s. What is the rate constant at this temperature?

Key Concepts

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases. The rate law for a first-order reaction can be expressed as rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Half-Life of a Reaction

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For first-order reactions, the half-life is constant and independent of the initial concentration, calculated using the formula t1/2 = 0.693/k, where k is the rate constant. This relationship is crucial for determining the rate constant from the given half-life.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that quantifies the speed of a reaction at a given temperature. It is specific to each reaction and varies with temperature. For first-order reactions, the rate constant can be derived from the half-life using the equation k = 0.693/t1/2, allowing us to calculate k when the half-life is known.