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Current Question (ID: 8464)

Question:

$\text{The number of } \text{H}^+ \text{ ions present in } 1 \text{ mL of a solution whose pH} = 4, \text{ is given as:}$ $(N_A = \text{Avogadro's number})$

Options:

1. $10^{-7} N_A$
2. $10^{-8} N_A$
3. $10^{-16} N_A$
4. $10^{-14} N_A$

Solution:

$\textbf{Hint: } \text{pH} = -\log[\text{H}^+]$ $\textbf{Step 1:}$ $\text{Calculate } \text{H}^+ \text{ ion concentration at pH} = 4$ $\text{pH} = -\log[\text{H}^+]$ $4 = -\log[\text{H}^+]$ $[\text{H}^+] = 10^{-4} \text{ M}$ $\textbf{Step 2:}$ $\text{The concentration of } \text{H}^+ \text{ ion is } 10^{-4} \text{ M. It indicates that } 10^{-4} \text{ mol of } \text{H}^+ \text{ in } 1000 \text{ mL}$ $\text{Calculate in } 1 \text{ mL:}$ $1000 \text{ mL solution contain } 10^{-4} \text{ mol of } \text{H}^+ \text{ ion}$ $1 \text{ mL solution contain } \frac{10^{-4}}{1000} \text{ mol of } \text{H}^+ \text{ ion}$ $= 10^{-7} \text{ mol of } \text{H}^+ \text{ ion}$ $1 \text{ mol } \text{H}^+ \text{ ion contains } 6.022 \times 10^{23} \text{ or } N_A \text{ ions}$ $10^{-7} \text{ mol of } \text{H}^+ \text{ ion} = 10^{-7} N_A$ $\text{Hence, option 1 is correct}$

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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
}