Question

At \(T\) K, \(100\,\text{g}\) of \(98%\) \(H_2SO_4\) (w/w) aqueous solution is mixed with \(100\,\text{g}\) of \(49%\) \(H_2SO_4\) (w/w) aqueous solution. What is the mole fraction of \(H_2SO_4\) in the resultant solution? (Given: Atomic mass \(H = 1\,u,\; S = 32\,u,\; O = 16\,u\). Assume that temperature after mixing remains constant.)

• A. \(0.337\)
• B. \(0.1\)
• C. \(0.9\)
• D. \(0.663\)

Hint:

For w/w solutions, always convert percentage into actual mass first before calculating mole fraction.

Answer 1

The Correct Option is A

To find the mole fraction of \( H_2SO_4 \) in the resultant solution, we follow these steps: 

1. First, calculate the moles of \( H_2SO_4 \) and water in each solution separately.
2. Determine the amount of \( H_2SO_4 \) in the first solution:
   • Weight of \( H_2SO_4 \) = \( 98\% \) of \( 100\,\text{g} = 98\,\text{g} \)
   • Molecular weight of \( H_2SO_4 = (2 \times 1) + 32 + (4 \times 16) = 98 \, \text{u} \)
   • Moles of \( H_2SO_4 = \dfrac{98\,\text{g}}{98\,\text{g/mol}} = 1 \, \text{mol} \)
   • Moles of water in the first solution = \(\dfrac{2\,\text{g}}{18\,\text{g/mol}} \approx 0.111 \, \text{mol} \)
3. Determine the amount of \( H_2SO_4 \) in the second solution:
   • Weight of \( H_2SO_4 = 49\% \) of \( 100\,\text{g} = 49\,\text{g} \)
   • Moles of \( H_2SO_4 = \dfrac{49\,\text{g}}{98\,\text{g/mol}} = 0.5 \, \text{mol} \)
   • Moles of water = \(\dfrac{51\,\text{g}}{18\,\text{g/mol}} \approx 2.833 \, \text{mol} \)
4. Add the moles of \( H_2SO_4 \) from both solutions:
   • Total moles of \( H_2SO_4 = 1 + 0.5 = 1.5 \, \text{mol} \)
5. Add the moles of water from both solutions:
   • Total moles of water = \( 0.111 + 2.833 = 2.944 \, \text{mol} \)
6. Calculate the total moles in the resultant solution:
   • Total moles = \( 1.5 + 2.944 = 4.444 \, \text{mol} \)
7. Calculate the mole fraction of \( H_2SO_4 \):
   • Mole fraction of \( H_2SO_4 = \dfrac{\text{moles of } H_2SO_4}{\text{total moles}} = \dfrac{1.5}{4.444} \approx 0.337 \)

Thus, the mole fraction of \( H_2SO_4 \) in the resultant solution is \(0.337\), which matches the correct answer option provided.