Problem:
A certain amount of electricity deposited 0.54g of Ag from an AgNO3 solution. What volume of hydrogen will the same quantity of electricity liberate at 27 degrees Celsius and 728mmHg pressure?

Solution:

Step 1: Calculate the number of moles of silver deposited.
To determine the number of moles of silver deposited, we need to use the molar mass of silver (Ag). The molar mass of Ag is 107.87 g/mol.

Number of moles of Ag = Mass of Ag / Molar mass of Ag
Number of moles of Ag = 0.54g / 107.87 g/mol
Number of moles of Ag = 0.005 mol

Step 2: Determine the number of moles of hydrogen gas produced.
According to Faraday's law of electrolysis, the amount of a substance produced or consumed during electrolysis is proportional to the number of moles of electrons transferred. The balanced equation for the electrolysis of water is:

2H2O(l) -> 2H2(g) + O2(g)

From the equation, we can see that 2 moles of electrons are required to produce 1 mole of hydrogen gas. Therefore, the number of moles of hydrogen gas produced is equal to half the number of moles of electrons.

Number of moles of H2 = 0.005 mol / 2
Number of moles of H2 = 0.0025 mol

Step 3: Apply the ideal gas law to determine the volume of hydrogen gas.
The ideal gas law relates the number of moles of a gas to its volume, temperature, and pressure. The equation is:

PV = nRT

Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)

We need to convert the given temperature from degrees Celsius to Kelvin.

T(K) = T(°C) + 273.15
T(K) = 27°C + 273.15
T(K) = 300.15 K

Now, we can rearrange the ideal gas law equation to solve for the volume of hydrogen gas.

V = (nRT) / P
V = (0.0025 mol * 0.0821 L·atm/mol·K * 300.15 K) / (728 mmHg * 1 atm/760 mmHg)
V ≈ 0.00796 L
V ≈ 7.96 mL

Therefore, the volume of hydrogen gas liberated is approximately 7.96 mL at 27 degrees Celsius and 728 mmHg pressure.