Import Question JSON

Current Question (ID: 21486)

Question:

$\text{For a first-order reaction}$ $t_{67\%} = \left( \frac{x}{10} \right) t_{50\%} \ \&\ k = 3.84 \times 10^9 \ \text{sec}^{-1}, \ \text{the value of } x \ \text{will}$ $\text{(based on information given):}$ $\text{(Report your answer to the nearest integer)}$

Options:

1. $14$
2. $16$
3. $18$
4. $20$

Solution:

$\text{Hint: } t = \frac{2.303}{k} \log \left( \frac{a}{a-x} \right)$ $t_{67\%} = \frac{1}{k} \ln \left( \frac{100}{33} \right)$ $t_{50\%} = \frac{1}{k} \ln(2)$ $\frac{t_{67\%}}{t_{50\%}} = \frac{\ln \left( \frac{100}{33} \right)}{\ln 2}$ $\Rightarrow \frac{t_{67\%}}{t_{50\%}} = \frac{\log \left( \frac{100}{33} \right)}{\log 2}$ $\Rightarrow \frac{\log 3}{\log 2} = \frac{0.4771}{0.3} = 1.585$ $\text{So } x = 15.85$

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
}