The decomposition of phosphine, PH3, proceeds according to the equation 4 PH3(g) ⟶P4(g)+6 H2(g)

step 1 So this is a question that requires a little bit of intuition about the half -lives of a first -

The decomposition of phosphine, PH3, proceeds according to...

The decomposition of phosphine, $\mathrm{PH}_{3},$ proceeds according to the equation $$4 \mathrm{PH}_{3}(\mathrm{g}) \longrightarrow \mathrm{P}_{4}(\mathrm{g})+6 \mathrm{H}_{2}(\mathrm{g})$$ It is found that the reaction has the following rate equation: Rate $=k\left[\mathrm{PH}_{3}\right] .$ The half-life of $\mathrm{PH}_{3}$ is $37.9 \mathrm{s}$ at $120^{\circ} \mathrm{C}$ (a) How much time is required for three fourths of the $\mathrm{PH}_{3}$ to decompose? (b) What fraction of the original sample of $\mathrm{PH}_{3}$ remains after 1 min?

The decomposition of phosphine, $\mathrm{PH}_{3},$ proceeds according to the equation
$$4 \mathrm{PH}_{3}(\mathrm{g}) \longrightarrow \mathrm{P}_{4}(\mathrm{g})+6 \mathrm{H}_{2}(\mathrm{g})$$
It is found that the reaction has the following rate equation: Rate $=k\left[\mathrm{PH}_{3}\right] .$ The half-life of $\mathrm{PH}_{3}$ is $37.9 \mathrm{s}$ at $120^{\circ} \mathrm{C}$
(a) How much time is required for three fourths of the $\mathrm{PH}_{3}$ to decompose?
(b) What fraction of the original sample of $\mathrm{PH}_{3}$ remains after 1 min?

Key Concepts

First-Order Reaction Kinetics

This concept pertains to reactions in which the rate is directly proportional to the concentration of one reactant. In such reactions, the concentration decreases exponentially with time. Understanding first-order kinetics is essential for applying integrated rate laws and for predicting how long a reactant takes to decompose to a given extent.

Half-Life

Half-life is the time required for the concentration of a reactant in a first-order reaction to fall to half of its initial value. For first-order processes, the half-life is constant and independent of the initial concentration, and it is mathematically related to the rate constant by the formula t1/2 = ln(2)/k.

Integrated Rate Law

The integrated rate law for a first-order reaction describes how the reactant concentration decreases over time as an exponential function. It relates the initial concentration, the concentration at a later time, the rate constant, and the elapsed time, allowing for the determination of kinetic parameters or reaction progress.

Exponential Decay

Exponential decay is a characteristic of first-order kinetics where the reactant concentration decreases by a constant proportion in equal time intervals. This mathematical relationship underpins the calculation of how much of a substance remains after a given period and is integral to understanding reaction dynamics.

Transcript

Please give Ace some feedback