First-order reactions are chemical reactions where the reaction rate depends linearly on the concentration of only one reactant. This means that as the concentration of the reactant decreases, the rate of the reaction decreases proportionally. These reactions are characterized by a constant half-life, which is the time it takes for half of the reactant to be consumed. Understanding first-order kinetics is crucial in fields ranging from chemical engineering to environmental science.
The integrated rate law for a first-order reaction is given by: $\ln[A]_t - \ln[A]_0 = -kt$, where $[A]_t$ is the concentration of reactant A at time t, $[A]_0$ is the initial concentration of reactant A, and k is the rate constant.
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Rate Constant | a. Time required for half of the reactant to be consumed |
| 2. Half-Life | b. Substance that increases the rate of a reaction without being consumed |
| 3. Catalyst | c. A reaction whose rate depends on the concentration of one reactant |
| 4. First-Order Reaction | d. A measure of how quickly a reaction proceeds |
| 5. Reaction Rate | e. The proportionality constant relating reaction rate to reactant concentration |
Complete the following paragraph with the correct terms:
In a first-order reaction, the __________ decreases exponentially with time. The __________ is constant, meaning it takes the same amount of time for the concentration to halve, regardless of the starting concentration. The __________ is a measure of how fast the reaction proceeds and is denoted by 'k'. The integrated rate law helps to determine the concentration of reactant at any given __________. If a __________ is used, the reaction rate will increase.
Explain how understanding first-order kinetics can be useful in determining the shelf life of a medication. Provide a detailed explanation.
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