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Current Question (ID: 7420)

Question:

$\text{If 500 mL of a 5 M solution is diluted to 1500 mL, the molarity of the resultant solution is:}$

Options:

1. $1.5 \text{ M}$
2. $1.66 \text{ M}$
3. $0.017 \text{ M}$
4. $1.59 \text{ M}$

Solution:

$\text{Hint: Dilution equation} = \text{M}_1\text{V}_1 \text{ dilution)} = \text{M}_2\text{V}_2 \text{ dilution)}$ $\text{Step 1:}$ $\text{Given values are as follows:}$ $\text{M}_1 = 5 \text{ M}$ $\text{V}_1 = 500 \text{ mL}$ $\text{V}_2 = 1500 \text{ mL}$ $\text{M}_2 = \text{M}$ $\text{Step 2:}$ $\text{For dilution, a general formula is as follows:}$ $\text{M}_1\text{V}_1 \text{ dilution)} = \text{M}_2\text{V}_2 \text{ dilution)}$ $500 \times 5 \text{ M} = 1500 \times \text{M}$ $\text{M} = \frac{5}{3} = 1.66 \text{ M}$

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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
}