The overall reaction in the lead storage battery is Pb(s)+PbO2(s)+2 H^+(a q)+2 HSO4^-(a q) ⟶2 Pb

step 1 So for this problem, first thing that we need to do is use the same equation that we derived ear

The overall reaction in the lead storage battery is...

The overall reaction in the lead storage battery is $\mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{HSO}_{4}^{-}(a q) \longrightarrow$ $2 \mathrm{PbSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)$ a. For the cell reaction $\Delta H^{\circ}=-315.9 \mathrm{~kJ}$ and $\Delta S^{\circ}=263.5 \mathrm{~J} / \mathrm{K}$. Calculate $\mathscr{}^{\circ}$ at $-20 .{ }^{\circ} \mathrm{C}$. Assume $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not depend on temperature. b. Calculate 8 at $-20 .^{\circ} \mathrm{C}$ when $\left[\mathrm{HSO}_{4}^{-}\right]=\left[\mathrm{H}^{+}\right]=4.5 M$. c. Consider your answer to Exercise $67 .$ Why does it seem that batteries fail more often on cold days than on warm days?

The overall reaction in the lead storage battery is
$\mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+2 \mathrm{H}^{+}(a q)+2 \mathrm{HSO}_{4}^{-}(a q) \longrightarrow$
$2 \mathrm{PbSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)$
a. For the cell reaction $\Delta H^{\circ}=-315.9 \mathrm{~kJ}$ and $\Delta S^{\circ}=263.5 \mathrm{~J} / \mathrm{K}$.
Calculate $\mathscr{}^{\circ}$ at $-20 .{ }^{\circ} \mathrm{C}$. Assume $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not depend on temperature.
b. Calculate 8 at $-20 .^{\circ} \mathrm{C}$ when $\left[\mathrm{HSO}_{4}^{-}\right]=\left[\mathrm{H}^{+}\right]=4.5 M$.
c. Consider your answer to Exercise $67 .$ Why does it seem that batteries fail more often on cold days than on warm days?

Key Concepts

Gibbs Free Energy (?G)

Gibbs Free Energy is a thermodynamic function that combines enthalpy and entropy to determine the maximum reversible work obtainable from a process at constant temperature and pressure. It is expressed as ?G = ?H - T?S and indicates the spontaneity of a reaction; a negative ?G signifies a spontaneous process, while a positive ?G indicates non-spontaneity. This concept is central to understanding how temperature influences the feasibility of chemical reactions.

Enthalpy (?H) and Entropy (?S)

Enthalpy is a measure of the total heat content of a system, whereas entropy is a measure of the disorder or randomness within the system. In the context of a chemical reaction, the interplay between the exothermic or endothermic nature (enthalpy change) and the change in disorder (entropy change) determines the overall free energy change. These parameters are essential for predicting how reactions respond to changes in temperature.

Temperature Dependence in Thermodynamics

Temperature plays a crucial role in determining the spontaneity and equilibrium position of a chemical reaction. Since ?G is calculated using the equation ?G = ?H - T?S, variations in temperature can shift the balance between enthalpic and entropic contributions. This concept is particularly important when analyzing reactions under non-standard conditions or explaining performance differences in practical devices like batteries under different temperature environments.

Relationship Between Free Energy and Equilibrium Constant

The connection between Gibbs Free Energy and the equilibrium constant is given by the equation ?G° = -RT ln K, where R is the gas constant and T is the absolute temperature. This relationship allows for the calculation of the equilibrium constant from thermodynamic data and provides insights into how a reaction’s position of equilibrium shifts with temperature changes. It is a key concept in linking thermodynamics with chemical equilibria in both theoretical and practical applications such as energy storage devices.

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