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Chapter 20: Problem 119

A student designs an ammeter (device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the device for 90 min, \(32.5 \mathrm{~mL}\) of water-saturated \(\mathrm{H}_{2}(g)\) is collected. The temperature of the system is \(20^{\circ} \mathrm{C},\) and the atmospheric pressure is \(101.3 \mathrm{kPa}\). What is the magnitude of the average current in amperes?

Short Answer

Expert verified
To find the magnitude of the average current, we first determine the moles of hydrogen gas produced using the ideal gas law: \(n=\frac{PV}{RT}\). Then, we find the number of electrons transferred during the electrolysis process using the balanced chemical equation. The total charge transferred is obtained by multiplying the number of electrons transferred by the Faraday constant. Finally, the average current is calculated by dividing the total charge transferred by the time duration (in seconds). Using the given information, we can find the average current through the device in amperes.

Step by step solution

01

Find the moles of hydrogen gas produced

To determine the moles of hydrogen produced, we'll use the ideal gas law: \[PV=nRT\] where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. We have \(P = 101.3\ \mathrm{kPa}\), \(V = 32.5\ \mathrm{mL} = 0.0325\ \mathrm{L}\), and \(T = 20^\circ \mathrm{C} + 273.15 = 293.15\ \mathrm{K}\). Also, the gas constant is \(R = 8.314\ \mathrm{J\cdot K^{-1}\cdot mol^{-1}}\). Now, we can solve for n: \[n=\frac{PV}{RT}\]
02

Convert pressure to required unit

The pressure is given in kPa, but we need it in the unit of atm for the ideal gas law. We can use the conversion factor \(1\ \mathrm{atm} = 101.325\ \mathrm{kPa}\) to get the pressure in atm: \[P_\mathrm{atm} = \frac{101.3\ \mathrm{kPa}}{101.325\ \mathrm{kPa/atm}}\]
03

Plug in values and solve for moles of hydrogen gas

Now let's calculate the moles of hydrogen gas using the modified ideal gas law formula: \[n=\frac{P_\mathrm{atm}\cdot V}{R\cdot T}\]
04

Calculate the number of electrons transferred

The electrolysis of water produces hydrogen gas, so the balanced reaction is: \[\mathrm{2H_2O\to 2H_2 + O_2}\] For every 1 mole of hydrogen gas produced, 2 moles of electrons are transferred. Hence, we need to find the number of electrons transferred during the entire process. \[\mathrm{Electrons\:transferred} = 2\cdot n\]
05

Calculate the total charge transferred

We can calculate the total charge transferred using the Faraday constant, which is \(96485\ \mathrm{C/mol}\) (Coulombs per mole of electrons): \[\mathrm{Total\:charge\:transferred} = \mathrm{Electrons\:transferred} \cdot 96485\ \mathrm{C/mol}\]
06

Calculate the average current

Finally, we can find the average current by dividing the total charge transferred by the time duration in seconds: \[\mathrm{Average\:current} = \frac{\mathrm{Total\:charge\:transferred}}{\mathrm{Time\:duration}}\] The time duration given is \(90\ \mathrm{min} = 5400\ \mathrm{s}\). Now we can calculate the average current and express it in amperes, where 1 A = 1 C/s.

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Most popular questions from this chapter

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?

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