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Current Question (ID: 8505)

Question:

$\text{The concentration of }[\text{H}^+]\text{ ion in a solution containing 0.1 M HCN and 0.2 M NaCN will be:}$ $(K_a \text{ for HCN} = 6.2 \times 10^{-10})$

Options:

1. $3.1 \times 10^{10}$
2. $6.2 \times 10^{5}$
3. $6.2 \times 10^{-10}$
4. $3.1 \times 10^{-10}$

Solution:

$\text{Hint: Henderson-Hasselbalch equation}$ $\text{Step 1: Calculate }\text{pK}_a\text{ value as follows:}$ $[\text{H}^+] = \text{Buffer solution}$ $-\log K_a = \text{pK}_a$ $\text{pK}_a = -\log(6.2 \times 10^{-10}) = 9.2$ $\text{Step 2: Apply Henderson-Hasselbalch equation:}$ $\text{pH} = \text{pK}_a + \log \frac{[\text{NaCN}]}{[\text{HCN}]}$ $\text{pH} = 9.2 + \log\left(\frac{0.2}{0.1}\right) = 9.2 + \log(2) = 9.2 + 0.3 = 9.5$ $\text{Step 3: Calculate }[\text{H}^+]\text{ value:}$ $\text{pH} = -\log[\text{H}^+]$ $9.5 = -\log[\text{H}^+]$ $[\text{H}^+] = 10^{-9.5} = 3.1 \times 10^{-10}$

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
}