Answer:
1
Step-by-step explanation:
To determine the value of K (equilibrium constant) at 25 °C, we can use the Nernst equation, which relates the cell potential (E) to the equilibrium constant (K) and the standard cell potential (EºCell). The Nernst equation is given by:
E = EºCell - (RT / nF) * ln(K)
Where:
E = cell potential
EºCell = standard cell potential
R = gas constant (8.314 J/(mol·K))
T = temperature in Kelvin (25 °C = 298 K)
n = number of electrons transferred in the balanced redox equation
F = Faraday's constant (96,485 C/mol)
ln = natural logarithm
In this case, the given standard cell potential (EºCell) is -0.37 V.
The balanced redox equation for the cell reaction is:
Pt + Cr²+ -> Pt + Cr³+
Since there is no change in the oxidation state of Pt, no electrons are transferred in the reaction (n = 0).
Substituting the known values into the Nernst equation, we have:
E = -0.37 V - (8.314 J/(mol·K) * 298 K / (0 * 96,485 C/mol)) * ln(K)
E = -0.37 V
Since n = 0, the term (RT / nF) * ln(K) becomes 0, and we are left with:
-0.37 V = -0.37 V - 0
This implies that the value of K is 1, since any number raised to the power of 0 is equal to 1.
Therefore, the value of K at 25 °C for the given cell is 1.