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Current Question (ID: 21018)

Question:

$\text{For one mole of an ideal gas, which of these statements must be true?}$ $\text{(I) U and H each depend only on temperature.}$ $\text{(II) Compressibility factor z is not equal to 1.}$ $\text{(III) C}_{p,m} - C_{v,m} = R$ $\text{(IV) dU = C}_{v}\text{dT for any process.}$

Options:

1. $\text{(I), (III) and (IV)}$
2. $\text{(I), (II) and (IV)}$
3. $\text{(III) and (IV)}$
4. $\text{(I) and (III)}$

Solution:

$\text{Hint: For compressibility factor Z for an ideal gas is equal to 1}$ $\text{For ideal gas,}$ $\text{The internal energy and enthalpy of ideal gases depends only on temperature, not on volume or pressure.}$ $U = f(T), H = f(T)$ $\text{For compressibility factor Z for an ideal gas is equal to 1}$ $\text{For 1 mole of ideal gas, the relation between C}_p \text{ and C}_v \text{ is-}$ $C_p - C_v = R$ $\text{The formula of dU is as follows:}$ $\text{dU = C}_v\text{dT}$

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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
}