Question

What volume of gaseous NH₃ at 0°C and 1 atm will be required to be passed into 30 ml of N-H₂SO₄ solution to bring down the acid strength of this solution to 0.2 N?

• A. 537.6 ml
• B. 268.8 ml
• C. 1075.2 ml
• D. 371.3 ml

Answer 1

Answer: (A)

537.6 ml

Answer 2

1. Calculate initial and final equivalents of $H_2SO_4$:

   • Initial Normality ($N_1$) = 1 N
   • Volume ($V$) = 30 ml
   • Initial equivalents = $N_1 \times V = 1 \text{ N} \times 30 \text{ ml} = 30 \text{ meq}$.
   • Final Normality ($N_2$) = 0.2 N
   • Volume ($V$) = 30 ml
   • Final equivalents = $N_2 \times V = 0.2 \text{ N} \times 30 \text{ ml} = 6 \text{ meq}$.

2. Calculate equivalents of $H_2SO_4$ reacted:

   • Equivalents reacted = Initial equivalents - Final equivalents
   • Equivalents reacted = $30 \text{ meq} - 6 \text{ meq} = 24 \text{ meq}$.

3. Relate equivalents of $H_2SO_4$ to moles of $H_2SO_4$:

   • Sulfuric acid ($H_2SO_4$) is a diprotic acid, so its n-factor is 2.
   • Moles of $H_2SO_4$ reacted = Equivalents reacted / n-factor
   • Moles of $H_2SO_4$ reacted = $24 \text{ meq} / 1000 \text{ meq/mol} / 2 = 0.012$ moles.

4. Determine moles of $NH_3$ required using stoichiometry:

   • The reaction is: $2NH_3 + H_2SO_4 \rightarrow (NH_4)_2SO_4$.
   • From the balanced equation, 2 moles of $NH_3$ react with 1 mole of $H_2SO_4$.
   • Moles of $NH_3$ required = $2 \times$ Moles of $H_2SO_4$ reacted
   • Moles of $NH_3$ required = $2 \times 0.012 \text{ moles} = 0.024$ moles.

5. Calculate the volume of $NH_3$ gas at STP:

   • The conditions given are 0°C and 1 atm, which is considered Standard Temperature and Pressure (STP).
   • At STP, the molar volume of any gas is 22.4 L/mol.
   • Volume of $NH_3$ = Moles of $NH_3 \times$ Molar volume at STP
   • Volume of $NH_3$ = $0.024 \text{ mol} \times 22.4 \text{ L/mol} = 0.5376$ L.

6. Convert volume to milliliters:

   • Volume of $NH_3$ = $0.5376 \text{ L} \times 1000 \text{ ml/L} = 537.6$ ml.