The decomposition of phosphine, a very toxic gas, forms...

The decomposition of phosphine, a very toxic gas, forms phosphorus and hydrogen in the following reaction: $$4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g)$$ (a) Express the rate of the reaction with respect to each of the reactants and products. (b) If the instantaneous rate of the reaction with respect to $\mathrm{PH}_{3}$ is $0.34 \mathrm{M} \mathrm{s}^{-1}$, what is the instantaneous rate of the reaction?

The decomposition of phosphine, a very toxic gas, forms phosphorus and hydrogen in the following reaction:
$$4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g)$$
(a) Express the rate of the reaction with respect to each of the reactants and products.
(b) If the instantaneous rate of the reaction with respect to $\mathrm{PH}_{3}$ is $0.34 \mathrm{M} \mathrm{s}^{-1}$, what is the instantaneous rate of the reaction?

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Key Concepts

Instantaneous Reaction Rate

The instantaneous reaction rate refers to the rate calculated at a specific moment in time or concentration. It is determined by taking the derivative of the concentration with respect to time at that particular moment, allowing for the evaluation of how fast the reaction is proceeding at that instant.

Rate of Reaction

The rate of reaction is a measure of how quickly the concentration of a reactant or product changes over time in a chemical reaction. It is typically expressed by taking the time derivative of the concentration, and in a balanced chemical equation, the rate is normalized by the corresponding stoichiometric coefficient. This standardization allows the rate to be compared across different species in the reaction.

Stoichiometric Coefficients in Rate Expressions

Stoichiometric coefficients are used to balance chemical equations and indicate the relative amounts of reactants and products involved in the reaction. When expressing the rate of reaction, these coefficients are used to adjust the changes in concentration of each species so that the intrinsic speed of the reaction can be uniformly described regardless of which species is being monitored.

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