Import Question JSON

Current Question (ID: 21109)

Question:

$\text{The amount of water in litres that must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2, is:}$

Options:

1. $2.0 \ \text{L}$
2. $9.0 \ \text{L}$
3. $0.1 \ \text{L}$
4. $0.9 \ \text{L}$

Solution:

$\text{Hint: Use the formula of dilution that is, } M_1 \times V_1 = M_2 \times V_2$ $\text{Step 1:}$ $\text{Calculate the concentration of } \text{H}^+ \text{ ion when pH is 1 and pH is two respectively.}$ $\text{pH} = -\log[\text{H}^+]$ $1 = -\log[\text{H}^+]$ $[\text{H}^+] = 10^{-1}$ $\text{Same ar pH 2, } [\text{H}^+] = 10^{-2} . \text{H}^+ \text{ ion concentration tell about the concentration of acid.}$ $\text{Step 2:}$ $\text{Calculate the amount of water in litres must be added to 1 litre of an aqueous solution of HCl as follows:}$ $M_1 \times V_1 = M_2 \times V_2$ $10^{-1} \times (1 \text{L}) = 10^{-2} \times V_2$ $V_2 = 10 \ \text{L}.$ $V_{\text{water}} = V_2 - V_1 = 9 \ \text{L}$ $\text{Hence, option second is the correct answer.}$

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
}