Cyclopropane, C3 H6, is converted to its isomer propylene, CH2=CHCH3, when heated. The rate law

step 1 For this question, we have cyclopropane that is being converted into its isomer propylene. The r

Cyclopropane, C3 H6, is converted to its isomer propylene,...

Cyclopropane, $\mathrm{C}_{3} \mathrm{H}_{6}$, is converted to its isomer propylene, $\mathrm{CH}_{2}=\mathrm{CHCH}_{3}$, when heated. The rate law is first order in cyclopropane, and the rate constant is $6.0 \times 10^{-4} / \mathrm{s}$ at $500^{\circ} \mathrm{C}$. If the initial concentration of cyclopropane is $0.0226 \mathrm{~mol} / \mathrm{L}$, what is the concentration after $899 \mathrm{~s}$ ?

Key Concepts

Chemical Kinetics

Chemical kinetics is the study of reaction rates and the steps by which reactions occur. It involves analyzing how different conditions such as concentration, temperature, and catalysts affect the speed of a chemical reaction, providing insight into reaction mechanisms and allowing predictions about reaction behavior.

First Order Reactions

A first order reaction is one in which the rate of reaction is directly proportional to the concentration of a single reactant. In such reactions, the rate decreases exponentially with time, and the reaction is characterized by a constant rate that is independent of the concentration of any other species.

Integrated Rate Law for First Order Reactions

The integrated rate law for first order reactions relates the concentration of a reactant at any time to its initial concentration and the rate constant. It is expressed as [A] = [A]_0 · e^(–kt), where [A] is the concentration at time t, [A]_0 is the initial concentration, k is the rate constant, and t is the time elapsed. This formula is key for calculating concentrations over time in first order processes.

Reaction Rate Constant

The reaction rate constant, often denoted by k, is a proportionality factor in the rate law that quantifies the speed of a reaction. Its value is specific to a particular reaction at a given temperature and determines how quickly reactants are converted to products. In the context of first order reactions, the rate constant directly influences the exponential decay of the reactant concentration over time.

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