Cell Potential Under Nonstandard Conditions - AP Chemistry
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Calculate $\Delta G$ if $n=2$ and $E=0.25\ \text{V}$ (use $F=96485\ \text{C mol}^{-1}$).
Calculate $\Delta G$ if $n=2$ and $E=0.25\ \text{V}$ (use $F=96485\ \text{C mol}^{-1}$).
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$\Delta G=-4.82\times 10^4\ \text{J mol}^{-1}$. $\Delta G=-(2)(96485)(0.25)=-48242.5$ J/mol.
$\Delta G=-4.82\times 10^4\ \text{J mol}^{-1}$. $\Delta G=-(2)(96485)(0.25)=-48242.5$ J/mol.
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Calculate $E^\circ$ at $25^\circ\text{C}$ if $K=1.0\times 10^6$ and $n=2$.
Calculate $E^\circ$ at $25^\circ\text{C}$ if $K=1.0\times 10^6$ and $n=2$.
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$E^\circ=0.178\ \text{V}$. $E^\circ=\frac{0.0592}{2}\log(10^6)=0.0296\times 6$.
$E^\circ=0.178\ \text{V}$. $E^\circ=\frac{0.0592}{2}\log(10^6)=0.0296\times 6$.
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Calculate $K$ at $25^\circ\text{C}$ if $E^\circ=0.30\ \text{V}$ and $n=2$.
Calculate $K$ at $25^\circ\text{C}$ if $E^\circ=0.30\ \text{V}$ and $n=2$.
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$K=1.4\times 10^{10}$. $0.30=\frac{0.0592}{2}\log K$; $\log K=10.14$.
$K=1.4\times 10^{10}$. $0.30=\frac{0.0592}{2}\log K$; $\log K=10.14$.
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Find $Q$ at $25^\circ\text{C}$ if $E^\circ=0.50\ \text{V}$, $E=0.44\ \text{V}$, and $n=2$.
Find $Q$ at $25^\circ\text{C}$ if $E^\circ=0.50\ \text{V}$, $E=0.44\ \text{V}$, and $n=2$.
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$Q=4.0\times 10^2$. $0.44=0.50-\frac{0.0592}{2}\log Q$; solve for $Q$.
$Q=4.0\times 10^2$. $0.44=0.50-\frac{0.0592}{2}\log Q$; solve for $Q$.
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Calculate $E$ at $25^\circ\text{C}$ if $E^\circ=0.80\ \text{V}$, $n=1$, and $Q=10^2$.
Calculate $E$ at $25^\circ\text{C}$ if $E^\circ=0.80\ \text{V}$, $n=1$, and $Q=10^2$.
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$E=0.68\ \text{V}$. $E=0.80-0.0592\log(100)=0.80-0.118$.
$E=0.68\ \text{V}$. $E=0.80-0.0592\log(100)=0.80-0.118$.
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Calculate $E$ at $25^\circ\text{C}$ if $E^\circ=1.10\ \text{V}$, $n=2$, and $Q=10^{-4}$.
Calculate $E$ at $25^\circ\text{C}$ if $E^\circ=1.10\ \text{V}$, $n=2$, and $Q=10^{-4}$.
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$E=1.22\ \text{V}$. $E=1.10-\frac{0.0592}{2}\log(10^{-4})=1.10+0.118$.
$E=1.22\ \text{V}$. $E=1.10-\frac{0.0592}{2}\log(10^{-4})=1.10+0.118$.
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What is $n$ in the Nernst equation, and how is it determined from the reaction?
What is $n$ in the Nernst equation, and how is it determined from the reaction?
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$n$ is moles of electrons transferred in the balanced redox reaction. Count electrons in half-reactions after balancing.
$n$ is moles of electrons transferred in the balanced redox reaction. Count electrons in half-reactions after balancing.
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What is the relationship between $E$ and $E^\circ$ when $Q=1$?
What is the relationship between $E$ and $E^\circ$ when $Q=1$?
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$E=E^\circ$. Standard conditions: all activities equal 1.
$E=E^\circ$. Standard conditions: all activities equal 1.
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What is the sign of the Nernst correction when $Q<1$ (relative to $E^\circ$)?
What is the sign of the Nernst correction when $Q<1$ (relative to $E^\circ$)?
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$E>E^\circ$. Reactants favored, so potential increases from standard.
$E>E^\circ$. Reactants favored, so potential increases from standard.
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What is the sign of the Nernst correction when $Q>1$ (relative to $E^\circ$)?
What is the sign of the Nernst correction when $Q>1$ (relative to $E^\circ$)?
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$E<E^\circ$. Products favored, so potential decreases from standard.
$E<E^\circ$. Products favored, so potential decreases from standard.
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State the relationship between cell potential and Gibbs free energy under any conditions.
State the relationship between cell potential and Gibbs free energy under any conditions.
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$\Delta G=-nFE$. Negative sign shows spontaneous reactions have $E>0$.
$\Delta G=-nFE$. Negative sign shows spontaneous reactions have $E>0$.
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Identify which species are omitted from $Q$: pure solids, pure liquids, aqueous ions, or gases.
Identify which species are omitted from $Q$: pure solids, pure liquids, aqueous ions, or gases.
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Pure solids and pure liquids are omitted from $Q$. Only dissolved species and gases affect cell potential.
Pure solids and pure liquids are omitted from $Q$. Only dissolved species and gases affect cell potential.
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What does $Q$ represent in the Nernst equation for an electrochemical cell?
What does $Q$ represent in the Nernst equation for an electrochemical cell?
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Reaction quotient from activities in the balanced net ionic equation. Ratio of products to reactants raised to stoichiometric powers.
Reaction quotient from activities in the balanced net ionic equation. Ratio of products to reactants raised to stoichiometric powers.
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State the relationship between standard cell potential and standard Gibbs free energy.
State the relationship between standard cell potential and standard Gibbs free energy.
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$\Delta G^\circ=-nFE^\circ$. Links thermodynamics to electrochemistry at standard state.
$\Delta G^\circ=-nFE^\circ$. Links thermodynamics to electrochemistry at standard state.
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State the relationship between $E^\circ$ and the equilibrium constant $K$ at $25^\circ\text{C}$.
State the relationship between $E^\circ$ and the equilibrium constant $K$ at $25^\circ\text{C}$.
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$E^\circ=\frac{0.0592}{n}\log K$. Derived from $\Delta G^\circ=-RT\ln K=-nFE^\circ$.
$E^\circ=\frac{0.0592}{n}\log K$. Derived from $\Delta G^\circ=-RT\ln K=-nFE^\circ$.
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What is the cell potential at equilibrium, and what is the corresponding value of $Q$?
What is the cell potential at equilibrium, and what is the corresponding value of $Q$?
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$E=0$ and $Q=K$. No driving force at equilibrium; $\Delta G=0$.
$E=0$ and $Q=K$. No driving force at equilibrium; $\Delta G=0$.
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Identify the direction of spontaneity when $E>0$ for the cell reaction as written.
Identify the direction of spontaneity when $E>0$ for the cell reaction as written.
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Spontaneous as written. Positive $E$ means $\Delta G<0$.
Spontaneous as written. Positive $E$ means $\Delta G<0$.
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Identify the direction of spontaneity when $E<0$ for the cell reaction as written.
Identify the direction of spontaneity when $E<0$ for the cell reaction as written.
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Nonspontaneous as written; spontaneous in reverse. Negative $E$ means $\Delta G>0$ forward.
Nonspontaneous as written; spontaneous in reverse. Negative $E$ means $\Delta G>0$ forward.
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State the Nernst equation at $25^\circ\text{C}$ using base-10 logarithms.
State the Nernst equation at $25^\circ\text{C}$ using base-10 logarithms.
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$E=E^\circ-\frac{0.0592}{n}\log Q$. Simplified form at 298 K using $\log$ instead of $\ln$.
$E=E^\circ-\frac{0.0592}{n}\log Q$. Simplified form at 298 K using $\log$ instead of $\ln$.
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State the formula for the cell potential under nonstandard conditions (Nernst equation).
State the formula for the cell potential under nonstandard conditions (Nernst equation).
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$E=E^\circ-\frac{RT}{nF}\ln Q$. Modifies standard potential by concentration effects via $\ln Q$ term.
$E=E^\circ-\frac{RT}{nF}\ln Q$. Modifies standard potential by concentration effects via $\ln Q$ term.
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Identify the condition on $Q$ when $E=0$ for a cell at equilibrium.
Identify the condition on $Q$ when $E=0$ for a cell at equilibrium.
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$Q=K$. At equilibrium, $E=0$ and reaction quotient equals equilibrium constant.
$Q=K$. At equilibrium, $E=0$ and reaction quotient equals equilibrium constant.
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State the relationship between $E^\circ$ and the equilibrium constant $K$ at $25^\circ\text{C}$.
State the relationship between $E^\circ$ and the equilibrium constant $K$ at $25^\circ\text{C}$.
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$E^\circ=\frac{0.0592}{n}\log K$. Derived from $E=0$ when $Q=K$ in Nernst equation.
$E^\circ=\frac{0.0592}{n}\log K$. Derived from $E=0$ when $Q=K$ in Nernst equation.
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State the general relationship between $\Delta G$ and cell potential $E$.
State the general relationship between $\Delta G$ and cell potential $E$.
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$\Delta G=-nFE$. Relates electrical work to thermodynamic spontaneity.
$\Delta G=-nFE$. Relates electrical work to thermodynamic spontaneity.
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State the relationship between $\Delta G^\circ$ and the equilibrium constant $K$.
State the relationship between $\Delta G^\circ$ and the equilibrium constant $K$.
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$\Delta G^\circ=-RT\ln K$. Fundamental thermodynamic relationship at equilibrium.
$\Delta G^\circ=-RT\ln K$. Fundamental thermodynamic relationship at equilibrium.
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Identify how $E$ changes when $Q$ increases (with $E^\circ$, $T$, and $n$ constant).
Identify how $E$ changes when $Q$ increases (with $E^\circ$, $T$, and $n$ constant).
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$E$ decreases. Larger $Q$ means more products, driving reverse reaction.
$E$ decreases. Larger $Q$ means more products, driving reverse reaction.
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Calculate $\log K$ at $25^\circ\text{C}$ if $E^\circ=0.30\ \text{V}$ and $n=3$.
Calculate $\log K$ at $25^\circ\text{C}$ if $E^\circ=0.30\ \text{V}$ and $n=3$.
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$\log K\approx15.2$. $0.30=\frac{0.0592}{3}\log K$; $\log K=\frac{0.90}{0.0592}\approx15.2$.
$\log K\approx15.2$. $0.30=\frac{0.0592}{3}\log K$; $\log K=\frac{0.90}{0.0592}\approx15.2$.
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State the formula for cell potential under nonstandard conditions (Nernst equation).
State the formula for cell potential under nonstandard conditions (Nernst equation).
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$E=E^\circ-\frac{RT}{nF}\ln Q$. Modified by reaction quotient $Q$ and temperature; $n$ is electrons transferred.
$E=E^\circ-\frac{RT}{nF}\ln Q$. Modified by reaction quotient $Q$ and temperature; $n$ is electrons transferred.
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State the Nernst equation at $25^\circ\text{C}$ using base-10 logarithms.
State the Nernst equation at $25^\circ\text{C}$ using base-10 logarithms.
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$E=E^\circ-\frac{0.0592}{n}\log Q$. Simplified form at 298 K using $\frac{2.303RT}{F}=0.0592$ V.
$E=E^\circ-\frac{0.0592}{n}\log Q$. Simplified form at 298 K using $\frac{2.303RT}{F}=0.0592$ V.
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What does $Q$ represent in the Nernst equation for an electrochemical cell?
What does $Q$ represent in the Nernst equation for an electrochemical cell?
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Reaction quotient, products over reactants using activities. Measures reaction progress; equals $K$ at equilibrium.
Reaction quotient, products over reactants using activities. Measures reaction progress; equals $K$ at equilibrium.
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What does $n$ represent in the Nernst equation for a galvanic cell?
What does $n$ represent in the Nernst equation for a galvanic cell?
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Moles of electrons transferred in the balanced redox reaction. Count electrons in half-reaction balancing.
Moles of electrons transferred in the balanced redox reaction. Count electrons in half-reaction balancing.
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