In the text, the equation ΔG=ΔG^∘+R T ln(Q) was derived for gaseous reactions where the quantiti

step 1 So what we're doing here is continuing on with thermodynamics. And our equation of importance he

In the text, the equation ΔG=ΔG^∘+R T ln(Q) was derived for...

In the text, the equation $$\Delta G=\Delta G^{\circ}+R T \ln (Q)$$ was derived for gaseous reactions where the quantities in $Q$ were expressed in units of pressure. We also can use units of $\mathrm{mol} / \mathrm{L}$ for the quantities in $Q$, specifically for aqueous reactions. With this in mind, consider the reaction $$\mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)$$ for which $K_{\mathrm{a}}=7.2 \times 10^{-4}$ at $25^{\circ} \mathrm{C}$. Calculate $\Delta G$ for the reaction under the following conditions at $25^{\circ} \mathrm{C}$. a. $[\mathrm{HF}]=\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=1.0 \mathrm{M}$ b. $[\mathrm{HF}]=0.98 M,\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=2.7 \times 10^{-2} M$ c. $[\mathrm{HF}]=\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=1.0 \times 10^{-5} \mathrm{M}$ d. $[\mathrm{HF}]=\left[\mathrm{F}^{-}\right]=0.27 M,\left[\mathrm{H}^{+}\right]=7.2 \times 10^{-4} M$ e. $[\mathrm{HF}]=0.52 M,\left[\mathrm{~F}^{-}\right]=0.67 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-3} M$ Based on the calculated $\Delta G$ values, in what direction will the reaction shift to reach equilibrium for each of the five sets of conditions?

In the text, the equation
$$\Delta G=\Delta G^{\circ}+R T \ln (Q)$$
was derived for gaseous reactions where the quantities in $Q$ were expressed in units of pressure. We also can use units of $\mathrm{mol} / \mathrm{L}$ for the quantities in $Q$, specifically for aqueous reactions. With this in mind, consider the reaction
$$\mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)$$
for which $K_{\mathrm{a}}=7.2 \times 10^{-4}$ at $25^{\circ} \mathrm{C}$. Calculate $\Delta G$ for the reaction under the following conditions at $25^{\circ} \mathrm{C}$.
a. $[\mathrm{HF}]=\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=1.0 \mathrm{M}$
b. $[\mathrm{HF}]=0.98 M,\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=2.7 \times 10^{-2} M$
c. $[\mathrm{HF}]=\left[\mathrm{H}^{+}\right]=\left[\mathrm{F}^{-}\right]=1.0 \times 10^{-5} \mathrm{M}$
d. $[\mathrm{HF}]=\left[\mathrm{F}^{-}\right]=0.27 M,\left[\mathrm{H}^{+}\right]=7.2 \times 10^{-4} M$
e. $[\mathrm{HF}]=0.52 M,\left[\mathrm{~F}^{-}\right]=0.67 M,\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-3} M$
Based on the calculated $\Delta G$ values, in what direction will the reaction shift to reach equilibrium for each of the five sets of conditions?

Key Concepts

Equilibrium_Constant

The equilibrium constant (K) quantifies the ratio of the concentrations (or pressures) of products to reactants when a reaction is at equilibrium. It is a key parameter that reflects the position of equilibrium and is fundamental in predicting the extent of a reaction under standard conditions.

Reaction_Quotient

The reaction quotient (Q) is a dimensionless number that expresses the current ratio of the concentrations (or pressures) of products to reactants in a reaction, each raised to the power of their stoichiometric coefficients. Q is used in the relationship ?G = ?G° + RT ln(Q) to determine the instantaneous free energy change, comparing the actual state of the system to equilibrium.

Reaction_Direction

The sign of ?G in relation to the magnitude of Q versus K is used to predict the direction in which a reaction will shift to reach equilibrium. When Q is less than K, the reaction will proceed in the forward direction (producing more products) to reach equilibrium, and when Q is greater than K, the reaction will shift in the reverse direction (favoring the reactants).

Gibbs_Free_Energy

Gibbs free energy (?G) is a thermodynamic potential that indicates the maximum reversible work obtainable from a chemical reaction at constant temperature and pressure. It determines the spontaneity of a reaction—if ?G is negative, the reaction proceeds spontaneously in the forward direction, whereas a positive ?G indicates a non-spontaneous process under those conditions.

Standard_Gibbs_Free_Energy

The standard Gibbs free energy change (?G°) is measured under standard state conditions, which provides a reference point for reactions. This value allows us to compare the thermodynamic favorability of different reactions by standardizing the concentration or pressure of reactants and products.

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