When copper reacts with nitric acid, a mixture of NO(g) and NO2(g) is evolved. The volume ratio

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When copper reacts with nitric acid, a mixture of NO(g) and...

When copper reacts with nitric acid, a mixture of $\mathrm{NO}(\mathrm{g})$ and $\mathrm{NO}_{2}(g)$ is evolved. The volume ratio of the two product gases depends on the concentration of the nitric acid according to the equilibrium $2 \mathrm{H}^{+}(a q)+2 \mathrm{NO}_{3}^{-}(a q)+\mathrm{NO}(g) \rightleftharpoons 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$ Consider the following standard reduction potentials at $25^{\circ} \mathrm{C}$ : $3 \mathrm{e}^{-}+4 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$ $$\begin{array}{r}\mathscr{E}^{\circ}=0.957 \mathrm{~V}\end{array}$$ $\mathrm{e}^{-}+2 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$ $${8}^{\circ}=0.775 \mathrm{~V}$$ a. Calculate the equilibrium constant for the above reaction. b. What concentration of nitric acid will produce a NO and $\mathrm{NO}_{2}$ mixture with only $0.20 \% \mathrm{NO}_{2}$ (by moles) at $25^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ ? Assume that no other gases are present and that the change in acid concentration can be neglected.

When copper reacts with nitric acid, a mixture of $\mathrm{NO}(\mathrm{g})$ and $\mathrm{NO}_{2}(g)$ is evolved. The volume ratio of the two product gases depends on the concentration of the nitric acid according to the equilibrium
$2 \mathrm{H}^{+}(a q)+2 \mathrm{NO}_{3}^{-}(a q)+\mathrm{NO}(g) \rightleftharpoons 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$
Consider the following standard reduction potentials at $25^{\circ} \mathrm{C}$ :
$3 \mathrm{e}^{-}+4 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
$$\begin{array}{r}\mathscr{E}^{\circ}=0.957 \mathrm{~V}\end{array}$$
$\mathrm{e}^{-}+2 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
$${8}^{\circ}=0.775 \mathrm{~V}$$
a. Calculate the equilibrium constant for the above reaction.
b. What concentration of nitric acid will produce a NO and $\mathrm{NO}_{2}$ mixture with only $0.20 \% \mathrm{NO}_{2}$ (by moles) at $25^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ ? Assume that no other gases are present and that the change in acid concentration can be neglected.

Key Concepts

Standard Reduction Potentials

Standard reduction potentials quantify the inherent tendency of a species to gain electrons under standard conditions. They are essential in determining the driving force for redox reactions. By comparing the potentials of two half-reactions, one can establish the overall cell potential and predict whether a redox reaction will be spontaneous under standard conditions.

Gibbs Free Energy and Equilibrium Constants

The relationship between Gibbs free energy change (?G°) and the equilibrium constant (K) is a cornerstone of chemical thermodynamics. The equation ?G° = -RT ln K connects the thermodynamic favorability of a reaction to its equilibrium position, allowing the calculation of K from standard free energy changes or, equivalently, from standard cell potentials in electrochemical systems.

Nernst Equation

The Nernst equation provides a quantitative link between the electrode potential of a redox reaction and the reaction quotient (Q), taking into account the effect of non-standard conditions such as concentrations and partial pressures. It is particularly useful for determining how the potential changes as a reaction system approaches equilibrium, where the cell potential becomes zero.

Gas Phase Equilibrium and Partial Pressures

In reactions that involve gaseous species, the concept of gas phase equilibrium is critical. The partial pressures of gases in a mixture are related to their mole fractions by Dalton’s Law, and these pressures play a significant role in the equilibrium expression for the reaction. Understanding how to relate gas composition to pressure is key when determining the conditions needed to achieve a desired mixture of gases.

Redox Reaction Stoichiometry

Accurately balancing redox reactions is fundamental to understanding electron transfer processes. The stoichiometric coefficients in the half-reactions determine the number of electrons transferred, which is crucial when combining potentials and calculating overall reaction spontaneity and equilibrium constants. This concept ensures that both mass and charge are conserved in the reaction analysis.

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