Phosphine, PH3, decomposes into phosphorus, P4, and hydrogen at 680^∘ C, as described in Problem

step 1 We know that the order of the reaction is going to be first order, although it is not specified,

Phosphine, PH3, decomposes into phosphorus, P4, and hydrogen...

Phosphine, $\mathrm{PH}_{3},$ decomposes into phosphorus, $\mathrm{P}_{4},$ and hydrogen at $680^{\circ} \mathrm{C}$, as described in Problem $13.60 .$ If the initial concentration of phosphine is $1.1 \times 10^{-6} \mathrm{~g} \mathrm{~L}^{-1}$, and after $180 \mathrm{~s}$ the concentration has dropped to $0.30 \times$ $10^{-6} \mathrm{~g} \mathrm{~L}^{-1}$, what is the rate constant for this process in $\mathrm{s}^{-1}$?

Key Concepts

Chemical Kinetics

Chemical kinetics is the study of reaction rates and the steps by which reactions occur. It involves understanding how various factors such as concentration, temperature, and the presence of catalysts affect the speed of reactions. This subject also includes quantitative analysis of how quickly reactants are consumed and products are formed.

Reaction Order

The reaction order describes how the rate of a chemical reaction is influenced by the concentration of the reactants. In kinetic studies, acknowledging the order (for example, first order, second order, etc.) is crucial as it determines the mathematical relationship between concentration and time, guiding which integrated rate law to use.

Integrated Rate Law

An integrated rate law is an equation that relates the concentration of reactants to time and the rate constant. It allows one to calculate changes in reactant concentration over time for a given reaction order. For a first-order reaction, the integrated rate law is commonly expressed as ln([A]?/[A]) = kt, providing a direct method to obtain the rate constant from concentration data.

Rate Constant

The rate constant is a proportionality factor in the rate law that quantifies the speed of a reaction under given conditions. It is specific to a particular reaction at a given temperature and can be determined using the integrated rate law by comparing initial and subsequent concentrations over time. Its units depend on the order of the reaction, with first-order reactions having units of s?¹.

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