Import Question JSON

Current Question (ID: 21175)

Question:

$\text{For a weak acid } \text{HA} \text{ with a degree of dissociation } x, \text{ which of the following gives the correct expression for } (\text{pH} - \text{pK}_a)?$

Options:

1. $\log(1+2x)$
2. $\log\left(\frac{1-x}{x}\right)$
3. $0$
4. $\log\left(\frac{x}{1-x}\right)$

Solution:

$\text{Hint: } K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$ $\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$ $t=0 \quad a$ $t=t \quad a(1-x) \quad ax \quad ax$ $K_a = \frac{ax \left(\frac{x}{1-x}\right)}{a(1-x)}; \quad [\text{H}^+] = ax$ $-\log(K_a) = -\log(ax) - \log\left(\frac{x}{1-x}\right)$ $\text{pK}_a = \text{pH} - \log\left(\frac{x}{1-x}\right)$ $\text{pH} - \text{pK}_a = \log\left(\frac{x}{1-x}\right)$

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
}