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Chapter 20: Problem 58

At \(298 \mathrm{~K}\) a cell reaction has a standard cell potential of $+0.63 \mathrm{~V}\(. The equilibrium constant for the reaction is \)3.8 \times 10^{10}\(. What is the value of \)n$ for the reaction?

Short Answer

Expert verified
The value of \(n\) for the reaction is approximately 2, which means the reaction transfers 2 electrons. This is calculated using the Nernst equation (\( Eº = \frac{RT}{nF} \ln K \)) and the given values of Eº, T, and K.

Step by step solution

01

Write down the Nernst equation

The Nernst equation is as follows: \( Eº = \frac{RT}{nF} \ln K \) Where: - Eº is the standard cell potential - R is the gas constant (8.314 J/mol·K) - T is the temperature in Kelvin - n is the number of electrons transferred in the reaction - F is the Faraday constant (96485 C/mol) - K is the equilibrium constant In this problem, we are given Eº, T, and K and are asked to find the value of n.
02

Plug in the given values

Substitute the given values into the Nernst equation. \( 0.63 \mathrm{~V} = \frac{(8.314 \frac{\mathrm{J}}{\mathrm{mol}\cdot\mathrm{K}})(298 \mathrm{~K})}{n(96485 \frac{\mathrm{C}}{\mathrm{mol}})} \ln (3.8 \times 10^{10}) \)
03

Solve for n

Rearrange the equation to isolate n and then solve for its value. \( n = \frac{(8.314 \mathrm{\frac{J}{mol\cdot K}})(298 \mathrm{~K})(0.63 \mathrm{~V})}{(96485 \mathrm{\frac{C}{mol}}) \ln (3.8 \times 10^{10})} \) \( n \approx 1.97 \) Since the number of electrons transferred in the reaction must be an integer, we can round n to the nearest whole number.
04

Determine the value of n

Based on our calculation, the value of n is approximately 2. So, the reaction transfers 2 electrons.

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Most popular questions from this chapter

During a period of discharge of a lead-acid battery, \(300 \mathrm{~g}\) of \(\mathrm{PbO}_{2}(s)\) from the cathode is converted into \(\mathrm{PbSO}_{4}(s)\). (a) What mass of \(\mathrm{Pb}(s)\) is oxidized at the anode during this same period? (b) How many coulombs of electrical charge are transferred from \(\mathrm{Pb}\) to \(\mathrm{PbO}_{2}\) ?

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(a) Write the half-reaction that occurs at an oxygen electrode in acidic aqueous solution when it serves as the cathode of a voltaic cell. (b) Write the half-reaction that occurs at an oxygen electrode in acidic aqueous solution when it serves as the anode of a voltaic cell. (c) What is standard about the standard oxygen electrode?

(a) What is an electrolytic cell? (b) The negative terminal of a voltage source is connected to an electrode of an electrolytic cell. Is the electrode the anode or the cathode of the cell? Explain. (c) The electrolysis of water is often done with a small amount of sulfuric acid added to the water. What is the role of the sulfuric acid? (d) Why are active metals such as Al obtained by electrolysis using molten salts rather than aqueous solutions?
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