A certain electricity deposited 0.54 g Ag from AgNO3 solution. What volume of hydrogen will the same quantity of electricity liberate at STP?

Question

Answer

Calculation of Volume of Hydrogen Liberated

To calculate the volume of hydrogen liberated at STP, we need to follow the steps given below:

Step 1: Calculate the Charge

We know that 1 Faraday of electricity deposits 1 equivalent of any substance. The equivalent weight of silver (Ag) is 108 g/mol. Therefore, to deposit 0.54 g of Ag, the charge required can be calculated as:

Charge = (0.54 g / 108 g/mol) x 1 F = 5 x 10^-3 F

Step 2: Calculate the Number of Moles of Hydrogen

According to Faraday's law of electrolysis, the amount of a substance liberated at an electrode is directly proportional to the number of coulombs of electricity passed through the electrolyte. One mole of electrons carries a charge of 96,500 C (coulombs). Therefore, the number of moles of electrons passed during electrolysis can be calculated as:

Moles of electrons = Charge / Faraday's constant = 5 x 10^-3 F / 96,500 C/mol = 5.18 x 10^-8 mol

Since the electrolysis of water produces two moles of hydrogen ions for every mole of electrons passed, the number of moles of hydrogen that will be liberated can be calculated as:

Moles of hydrogen = 2 x Moles of electrons = 2 x 5.18 x 10^-8 mol = 1.04 x 10^-7 mol

Step 3: Calculate the Volume of Hydrogen

At STP (standard temperature and pressure), one mole of any gas occupies 22.4 L of volume. Therefore, the volume of hydrogen liberated can be calculated as:

Volume of hydrogen = Moles of hydrogen x Molar volume at STP = 1.04 x 10^-7 mol x 22.4 L/mol = 2.33 x 10^-6 L or 2.33 µL

Explanation

The given problem deals with the calculation of the volume of hydrogen liberated during the electrolysis of water using the same quantity of electricity used to deposit 0.54 g of silver from AgNO3 solution. The process involves the conversion of electrical energy into chemical energy, which leads to the liberation of hydrogen gas at one electrode and oxygen gas at the other electrode. The chemical reaction can be represented as:

2H2O(l) → 2H2(g) + O2(g)

The amount of hydrogen liberated during the electrolysis of water depends on the quantity of electricity passed through the solution. The quantity of electricity can be calculated in terms of Faraday's constant, which relates the charge to the number of moles of electrons passed during electrolysis. The number of moles of hydrogen liberated can be calculated using the stoichiometry of the reaction, which shows that two moles of hydrogen are produced for every mole of electrons passed. Finally, the volume of hydrogen liberated can be calculated using the molar volume of gases at STP.

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