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Consider the cell Pt |Cr²+ (aq, 1.0 M), Cr3+ (aq, 2.2 mM) || Pb2+ (aq, 1.3M)| Pb. EºCell -0.37. What is the value of K at 25 °C

User Icarumbas
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1 Answer

2 votes

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.

User Dickson
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