If a water electrolysis cell operates at a current of 7.8 A, how long will it take to generate 25.0 L of hydrogen gas at a pressure of 25.0 atm and a temperature of 25 °C?

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Convert the volume of hydrogen gas from liters to moles using the ideal gas law: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin.

Calculate the moles of electrons required to produce the moles of hydrogen gas. Since the electrolysis of water produces hydrogen gas \( H_2 \), and each molecule of \( H_2 \) requires 2 electrons, multiply the moles of \( H_2 \) by 2.

Use Faraday's law of electrolysis to relate the charge to the moles of electrons: \( Q = nF \), where \( Q \) is the total charge in coulombs, \( n \) is the moles of electrons, and \( F \) is Faraday's constant (approximately 96485 C/mol).

Determine the time required to pass the calculated charge using the current: \( t = \frac{Q}{I} \), where \( t \) is time in seconds, \( Q \) is the charge in coulombs, and \( I \) is the current in amperes.

Convert the time from seconds to a more convenient unit if necessary, such as minutes or hours, for easier interpretation.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis state that the amount of substance produced at an electrode during electrolysis is directly proportional to the electric charge passed through the cell. This relationship allows us to calculate the moles of hydrogen gas generated based on the current and time, using the equation Q = I × t, where Q is the total charge, I is the current, and t is the time.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. In this context, it can be used to determine the number of moles of hydrogen gas produced under specific conditions of pressure and temperature, which is essential for calculating how much charge is needed for electrolysis.

Stoichiometry of Water Electrolysis

The stoichiometry of water electrolysis involves the balanced chemical reaction: 2H₂O(l) → 2H₂(g) + O₂(g). This indicates that for every 2 moles of water, 2 moles of hydrogen gas are produced. Understanding this ratio is crucial for converting the moles of hydrogen gas generated into the corresponding charge required for electrolysis.

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Textbook Question

A rechargeable battery is constructed based on a concentration cell constructed of two Ag/Ag⁺ half-cells. The volume of each half-cell is 2.0 L, and the concentrations of Ag⁺ in the half-cells are 1.25 M and 1.0×10^–3 M. a. How long can this battery deliver 2.5 Aof current before it goes dead?

Textbook Question

A rechargeable battery is constructed based on a concentration cell constructed of two Ag/Ag⁺ half-cells. The volume of each half-cell is 2.0 L, and the concentrations of Ag⁺ in the half-cells are 1.25 M and 1.0 × 10^–3 M. b. What mass of silver is plated onto the cathode by running at 3.5 A for 5.5 h?

Textbook Question

A rechargeable battery is constructed based on a concentration cell constructed of two Ag/Ag⁺ half-cells. The volume of each half-cell is 2.0 L, and the concentrations of Ag⁺ in the half-cells are 1.25 M and 1.0 × 10^–3 M. c. Upon recharging, how long would it take to redissolve 1.00 × 10² g of silver at a charging current of 10.0 amps?

Textbook Question

Calculate ∆G°_rxn and K for each reaction.

a. The disproportionation of Mn²⁺(aq) to Mn(s) and MnO₂(s) in acid solution at 25 °C.

b. The disproportionation of MnO₂(s) to Mn²⁺(aq) and MnO₄^–(aq) in acid solution at 25 °C.