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Current Question (ID: 11112)

Question:

$\text{The equation of state for } 5\text{g of oxygen at a pressure } \text{P} \text{ and temperature } \text{T}, \text{ when occupying a volume } \text{V}, \text{ will be: (where } \text{R} \text{ is the gas constant)}$

Options:

1. $\text{PV} = 5\text{RT}$
2. $\text{PV} = \frac{5}{2}\text{RT}$
3. $\text{PV} = \frac{5}{16}\text{RT}$
4. $\text{PV} = \frac{5}{32}\text{RT}$ (Correct)

Solution:

$\text{The ideal gas equation of state is given by: } \text{PV} = \mu \text{RT}, \text{ where } \mu \text{ is the number of moles.}$ \\ $\text{To find the number of moles } (\mu) \text{ of } 5\text{g of oxygen, we use the formula:}$ \\ $\mu = \frac{\text{mass}}{\text{molar mass}}$ \\ $\text{Given mass of oxygen } (\text{O}_2) \text{ is } 5\text{g.}$ \\ $\text{The molar mass of oxygen } (\text{O}_2) \text{ is:}$ \\ $\text{Molar mass} = 2 \times \text{Molar mass of oxygen atom (O)}$ \\ $\text{Molar mass} = 2 \times 16 \text{ g/mol} = 32 \text{ g/mol}$ \\ $\text{Now, substitute the values into the formula for moles:}$ \\ $\mu = \frac{5\text{g}}{32\text{g/mol}} = \frac{5}{32}\text{ moles}$ \\ $\text{Substitute this value of } \mu \text{ back into the ideal gas equation:}$ \\ $\text{PV} = \frac{5}{32}\text{RT}$ \\ $\text{This corresponds to option (4).}$

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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
}