Question

Calculate the volume of hydrogen at STP obtained by passing a current of 0.4 ampere through acidified water for 30 minutes

Answer 1

Answer : The volume of hydrogen gas obtained at STP is 0.0836 L or 83.6 mL

Explanation :

When a current is passed through acidified water, it causes decomposition of water into H2 and O2.

The decomposition equation is given below.

Reaction at Cathode : $2H2O (l) + 2e^{-}\rightarrow H_{2}(g)+ 2OH^{-}(aq)$

Reaction at Anode :$2H2O (l) +\rightarrow O_{2}(g)+ 4H^{+}(aq)+ 4e^{-}$

Overall reaction : $2H2O (l)\rightarrow 2H_{2} (g) + O_{2}(g)$

Step 1 : Find the amount of charge passed through the solution.

The number of coulombs can be calculated using following equation.

$Q = Ampere \times Seconds$

$Q = 0.4 A \times 30 min \times \frac{60 seconds}{1 min}$

$Q= 720 Coulombs$

Step 2 : Find moles of electrons transferred using the coulomb value

According to Faraday's law, 1 mole of electrons carry a charge of 96485 coulombs.

Let us use this to find the moles of electrons carrying a charge of 720 coulombs.

$720 coulombs \times \frac{1 mol}{96485 coulombs} = 0.00746mol$

Moles of electrons transferred is 0.00746

Step 3 : Use the mole ratio of electrons and H2 gas to find the number of moles  of the gas released

The mole ratio of H2 and electrons is 1 : 2 according to the reduction reaction that occurs at the cathode

$0.00746mol(e-) \times \frac{1mol(H_{2})}{2mol(e-)} = 0.00373mol H_{2}$

Step 4 : Use Ideal gas law and STP conditions to find the volume of the gas.

At STP, 1 mole of any gas occupies 22.4 L of volume.

We have 0.00373 mol.

$0.00373 mol H_{2} \times \frac{22.4L}{1 mol} = 0.0836 L$

The volume of hydrogen gas obtained at STP is 0.0836 L or 83.6 mL