(b) At 320°C the rate constant is 2.2 × 10^-5 s^-1. What is the half-life at this temperature?

검증된 단계별 안내

Identify the type of reaction. Since the rate constant is given in s^-1, this suggests a first-order reaction.

Recall the formula for the half-life of a first-order reaction:

t

_1/2=0.693k, where

k

is the rate constant.

Substitute the given rate constant value into the formula:

t

_1/2=0.6932.2×10-5.

Perform the division to calculate the half-life: divide 0.693 by the rate constant value.

The result from the division will give you the half-life of the reaction at 320°C.

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주요 개념

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

Rate Constant

The rate constant (k) is a proportionality factor in the rate equation of a chemical reaction, indicating the speed of the reaction at a given temperature. It is specific to the reaction and varies with temperature, reflecting how the frequency of effective collisions between reactants changes. In this case, the rate constant is given as 2.2 × 10-5 s-1, which is essential for calculating the half-life.

Half-Life

Half-life 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 inversely proportional to the rate constant, allowing for straightforward calculations. The formula for half-life (t1/2) in first-order kinetics is t1/2 = 0.693/k, where k is the rate constant.

First-Order Kinetics

First-order kinetics describes a reaction where the rate is directly proportional to the concentration of one reactant. This means that as the concentration decreases, the rate of reaction also decreases. The relationship between the rate constant and half-life in first-order reactions simplifies calculations, making it easier to determine how long it takes for a substance to reduce to half its amount.

(b) At 320°C the rate constant is 2.2 × 10-5 s-1. What is the half-life at this temperature?