Find the value of the equilibrium constant and standard Gibb's free energy change at 25 °C for the following cell; (5 M)
Understand the Problem
The question is asking to find the value of the equilibrium constant and the standard Gibbs free energy change for a specific electrochemical cell at a temperature of 25 °C. This involves understanding concepts from thermodynamics and electrochemistry.
Answer
The relationship for standard Gibbs free energy and equilibrium constant is given by $\Delta G^\circ = -RT \ln K$.
Answer for screen readers
The value of the equilibrium constant $K$ and the standard Gibbs free energy change $\Delta G^\circ$ at 25 °C can be calculated using the formula:
$$ \Delta G^\circ = - (8.314)(298) \ln K $$
(Exact values can't be provided without $K$.)
Steps to Solve
- Identify the relevant equations
To find the equilibrium constant $K$ and the standard Gibbs free energy change $\Delta G^\circ$, we can use the following equations:
- The relationship between Gibbs free energy change and the equilibrium constant is given by: $$ \Delta G^\circ = -RT \ln K $$
Where:
- $R = 8.314 , \text{J/(mol K)}$ (the gas constant)
- $T = 298 , \text{K}$ (temperature in Kelvin at 25 °C)
- Calculate the standard Gibbs free energy change
Next, we need to plug in the values:
- $R = 8.314 , \text{J/(mol K)}$
- $T = 298 , \text{K}$
Assuming we know $K$, we can calculate $\Delta G^\circ$ as: $$ \Delta G^\circ = - (8.314) (298) \ln K $$
- Find the equilibrium constant
If the cell reaction (which is not provided) relates to a particular equilibrium constant, you would typically find $K$ using the concentration of reactants and products at equilibrium. Recognizing that we have a concentration of 5 M for reactants/products would be necessary for this evaluation.
Assuming the cell reaction gives us a $K$ value (the value must be specified or determined based on the information provided), we can now evaluate the negative logarithm function as described earlier.
The value of the equilibrium constant $K$ and the standard Gibbs free energy change $\Delta G^\circ$ at 25 °C can be calculated using the formula:
$$ \Delta G^\circ = - (8.314)(298) \ln K $$
(Exact values can't be provided without $K$.)
More Information
The relationship between Gibbs free energy and equilibrium constant indicates that a lower Gibbs free energy corresponds to a more favorable reaction, implying a larger equilibrium constant.
Tips
- Assuming a specific value for $K$ without given information about the specific cell reaction.
- Not converting temperature to Kelvin properly.
- Mixing up the signs when calculating $\Delta G^\circ$.
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