Question

Correct expression for density of an ideal gas mixture of two gases 1 and 2, where $m_1$ and $m_2$ are masses and $n_1$ and $n_2$ are moles and $M_1$ and $M_2$ are molar masses.

• A. $d = \frac{(m_1 + m_2)}{(M_1 + M_2)}$
• B. $d = \frac{(m_1 + m_2)}{(n_1 + n_2)} \frac{P}{RT}$
• C. $d = \frac{(n_1 + n_2)}{(m_1 + m_2)} \times \frac{P}{RT}$
• D. None of these

Answer 1

Answer: (B)

$d = \frac{(m_1 + m_2)}{(n_1 + n_2)} \frac{P}{RT}$

Answer 2

Step 1: Recall that density $d = \frac{\text{total mass}}{\text{volume}}$.
Step 2: For an ideal gas mixture, $V = \frac{(n_1 + n_2)\,RT}{P}$.
Step 3: Total mass $= m_1 + m_2$.
Step 4: Substitute into $d = \frac{m_1 + m_2}{V}$:

$$d = \frac{m_1 + m_2}{\frac{(n_1 + n_2)\,RT}{P}} = \frac{m_1 + m_2}{n_1 + n_2}\,\frac{P}{RT}.$$

Hence, option (b) is correct.