Hypofluorous acid, HOF, is very unstable, decomposing in a...

Hypofluorous acid, HOF, is very unstable, decomposing in a first-order reaction to give HF and $\mathrm{O}_{2}$, with a halflife of only 30 min at room temperature: $$\mathrm{HOF}(\mathrm{g}) \longrightarrow \mathrm{HF}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$ If the partial pressure of HOF in a $1.00-\mathrm{L}$. flask is initially $1.00 \times 10^{2} \mathrm{mm} \mathrm{Hg}$ at $25^{\circ} \mathrm{C},$ what is the total pressure in the flask and the partial pressure of HOF after exactly 30 min? After 45 min?

Hypofluorous acid, HOF, is very unstable, decomposing in a first-order reaction to give HF and $\mathrm{O}_{2}$, with a halflife of only 30 min at room temperature:
$$\mathrm{HOF}(\mathrm{g}) \longrightarrow \mathrm{HF}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$
If the partial pressure of HOF in a $1.00-\mathrm{L}$. flask is initially $1.00 \times 10^{2} \mathrm{mm} \mathrm{Hg}$ at $25^{\circ} \mathrm{C},$ what is the total pressure in the flask and the partial pressure of HOF after exactly 30 min? After 45 min?

Key Concepts

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships among the reactants and products in a chemical reaction. It is crucial for determining how changes in the amount or pressure of one species affect the others, based on the balanced chemical equation.

Rate Constant

The rate constant, denoted by k, quantifies the speed of a chemical reaction. For first-order reactions, it is directly related to the half-life by the formula k = ln(2)/t?/?. This constant is essential for calculating the amount of reactant remaining at any given time.

Partial Pressure

In the context of gases, partial pressure is the pressure exerted by an individual component in a mixture of gases. It is especially useful in reaction kinetics for gases, since the change in partial pressures of the reactants and products can be monitored over time, and the total pressure is the sum of the partial pressures of all components.

First-order Reaction Kinetics

First-order kinetics describe reactions where the rate depends linearly on the concentration (or pressure, in the case of gases) of one reactant. This means that as the reactant decays, its rate of reaction decreases proportionally with its concentration. The mathematical representation of this behavior is typically an exponential decay function.

Half-life

The half-life of a reaction is the time required for the concentration (or partial pressure) of a reactant to decrease to one-half of its initial value. In first-order reactions, this half-life is constant and independent of the starting concentration, which simplifies predictions about reactant decay over time.

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