© All Rights reserved @ LearnWithDash
Step-by-Step Solution
Step 1: State the Relevant Concept
We use Faraday's laws of electrolysis to relate the mass of substance deposited (or liberated) to the quantity of electric charge passed and their equivalent masses.
Step 2: Identify the Known Data
1. Mass of aluminium deposited: 4.5 g
2. Atomic mass of aluminium: 27 amu
3. Aluminium is in the form of Al3+ ions (thus for every 1 mol of Al deposited, 3 Faradays of charge are required).
4. We wish to find the volume of hydrogen liberated at STP by this same quantity of charge.
Step 3: Relate Masses using Faraday’s Law
From Faraday’s second law of electrolysis, the mass of substances deposited or liberated is proportional to their equivalent masses. We can write:
$ \frac{m_{Al}}{m_H} = \frac{E_{Al}}{E_H} $
where $m_{Al}$ is the mass of aluminium deposited, $m_H$ is the mass of hydrogen liberated, $E_{Al}$ is the equivalent mass of aluminium, and $E_H$ is the equivalent mass of hydrogen.
Step 4: Calculate the Equivalent Masses
The equivalent mass of aluminium, when it is in the +3 oxidation state, is given by:
$ E_{Al} = \frac{\text{Atomic mass of Al}}{\text{valency of Al}} = \frac{27}{3} = 9 $
For hydrogen, in electrolysis context (H+ forming H2), the equivalent mass $ E_H $ is typically 1 g (since 1 mol of H atoms has a mass of 1 g; 2 H atoms form 1 molecule of H2 but each H+ is counted separately in electrolysis).
Hence our formula becomes:
$ \frac{4.5}{m_H} = \frac{9}{1} $
Step 5: Solve for the Mass of Hydrogen Liberated
$ \frac{4.5}{m_H} = 9 \\
m_H = \frac{4.5}{9} = 0.5 \text{ g}
$
Step 6: Convert Hydrogen Mass to Volume at STP
The molar mass of hydrogen gas (H2) is 2 g/mol, and 1 mole of any gas at STP occupies 22.4 L.
Given that 2 g of H2 occupies 22.4 L, 0.5 g of H2 will occupy:
$ \text{Volume at STP} = \frac{22.4 \times 0.5}{2} = 5.6 \text{ L}
$
Step 7: Conclude the Answer
Therefore, the volume of hydrogen produced at STP by the same quantity of electric charge that deposits 4.5 g of Al is 5.6 L.
