(a) The gas-phase decomposition of SO₂Cl₂, SO₂Cl₂(g) → SO₂(g) + Cl₂(g), 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?

검증된 단계별 안내

Step 1: Understand the problem. We are given that the reaction is first order and we are given the half-life. We need to find the rate constant (k).

Step 2: Recall the formula for the rate constant in a first order reaction. The formula is k = ln(2) / t1/2, where t1/2 is the half-life of the reaction.

Step 3: Substitute the given half-life into the formula. The half-life is given as 2.3 * 10^5 s.

Step 4: Calculate the rate constant. Remember that ln(2) is approximately 0.693.

Step 5: The rate constant k is then the result of the calculation from step 4. This is the final answer.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

(a) The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2(g) + Cl2(g), 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?