What is the value of universal gas constant in Nernst equation when the potential is given in volts?

Options

A. ` 8.314 J mol ^(-1) K^(-1)`
B. `0.0821 I, " atm " mol^(-1) K^(-1)`
C. `8.205 m^(3) " atm " mol ^(-1) K^(-1)`
D. `1.987 " cal " mol ^(-1)K^(-1)`

Answer

To find the value of the universal gas constant (R) in the Nernst equation when the potential is given in volts, we can follow these steps:

### Step 1: Understand the Nernst Equation
The Nernst equation relates the reduction potential of a half-cell at non-standard conditions to the standard electrode potential, temperature, and the reaction quotient. The equation is given by:

\[ E = E^\circ - \frac{RT}{nF} \ln Q \]

Where:
- \( E \) = cell potential
- \( E^\circ \) = standard cell potential
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin
- \( n \) = number of moles of electrons exchanged
- \( F \) = Faraday's constant
- \( Q \) = reaction quotient

### Step 2: Identify the Units of R
The universal gas constant \( R \) is expressed in units of energy per temperature per mole. In the context of the Nernst equation, where the potential is given in volts (V), we need to ensure that \( R \) is in compatible units.

### Step 3: Convert R to the Appropriate Units
Since we are working with volts, we need to express \( R \) in joules per mole per Kelvin (J/(mol·K)). The standard value of the universal gas constant is:

\[ R = 8.314 \, \text{J/(mol·K)} \]

### Step 4: Conclusion
Thus, when the potential is given in volts, the value of the universal gas constant \( R \) in the Nernst equation is:

\[ R = 8.314 \, \text{J/(mol·K)} \]

### Final Answer
The value of the universal gas constant in the Nernst equation when the potential is given in volts is **8.314 J/(mol·K)**.

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