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Chapter 18: Problem 96

What volumes of \(\mathrm{H}_{2}(g)\) and \(\mathrm{O}_{2}(g)\) at STP are produced from the electrolysis of water by a current of \(2.50 \mathrm{~A}\) in \(15.0 \mathrm{~min} ?\)

Short Answer

Expert verified
The volumes of H鈧�(g) and O鈧�(g) produced at STP from the electrolysis of water by a current of 2.50 A in 15.0 minutes are approximately 0.261 L and 0.1305 L, respectively.

Step by step solution

01

Calculate the electric charge passed

Electric charge, Q, is calculated using the formula: Q = I 脳 t, where Q is the electric charge, I is the current (in Amperes, A), and t is the time in seconds (s). We are given: Current, I = 2.50 A Time, t = 15.0 minutes = 15.0 脳 60 seconds = 900 s Now let's calculate the charge passed: Q = I 脳 t Q = 2.50 A 脳 900 s Q = 2250 Coulombs (C)
02

Calculate moles of electrons transferred

Using Faraday's Law, we can calculate the moles of electrons transferred: \(n_e = \frac{Q}{F_e}\), where \(n_e\) is the moles of electrons, Q is the electric charge, and \(F_e\) is the Faraday constant (96485 C/mol). \(n_e = \frac{2250 C}{96485 C/mol}\) \(n_e = 0.0233 \, mol\)
03

Calculate moles of H鈧� and O鈧� produced

For the electrolysis of water, the balanced chemical equation is: 2H鈧侽 (l) 鈫� 2H鈧� (g) + O鈧� (g) For every 4 moles of electrons, 2 moles of H鈧� and 1 mole of O鈧� are produced. Moles of H鈧� produced: \(n_{H_2} = \frac{1}{2} n_e\) Moles of O鈧� produced: \(n_{O_2} = \frac{1}{4} n_e\) \(n_{H_2}=\frac{1}{2} \times 0.0233\, mol = 0.01165 \, mol \) \(n_{O_2}=\frac{1}{4} \times 0.0233\, mol = 0.005825 \, mol \)
04

Convert moles to volume at STP

The molar volume of any gas at Standard Temperature and Pressure (STP) is 22.4 L/mol. To find the volumes of H鈧� and O鈧� produced, we can use the formula: Volume = Moles 脳 Molar Volume Volume of H鈧� produced: \(V_{H_2} = n_{H_2} \times 22.4 \, L/mol\) Volume of O鈧� produced: \(V_{O_2} = n_{O_2} \times 22.4 \, L/mol\) \(V_{H_2} = 0.01165 \, mol \times 22.4 \, L/mol = 0.261 \, L\) \(V_{O_2} = 0.005825 \, mol \times 22.4 \, L/mol = 0.1305 \, L\) The volumes of H鈧�(g) and O鈧�(g) produced at STP from the electrolysis of water by a current of 2.50 A in 15.0 minutes are approximately 0.261 L and 0.1305 L, respectively.

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