Import Question JSON

Current Question (ID: 8480)

Question:

$\text{How much water should be added to 400 mL of HCl solution in order to raise the pH by one unit?}$

Options:

1. $360 \text{ mL}$
2. $1000 \text{ mL}$
3. $600 \text{ mL}$
4. $3600 \text{ mL}$

Solution:

$\text{Hint: } M_1V_1 = M_2V_2$ $\text{Step 1:}$ $\text{Let the initial concentration of H}^+ \text{ ion is } 10^{-2} \text{ and initial volume is 400 mL. As the pH of the solution is increased by one unit, hence the new concentration of H}^+ \text{ ion is } 10^{-3}\text{. Calculate the final volume of solution as follows:}$ $M_1V_1 = M_2V_2$ $10^{-2} \times 400 = 10^{-3} \times V_2$ $V_2 = \frac{10^{-2} \times 400}{10^{-3}}$ $V_2 = 4000 \text{ mL}$ $\text{Step 2:}$ $\text{The final volume of the solution is 4000 mL. The initial volume of the solution is 400 mL. Thus, the volume of water added to 400 mL of HCl solution is:}$ $= 4000 - 400$ $= 3600 \text{ mL}$ $\text{Hence, option fourth is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}