The density of a gas (in g/litre) depends on pressure (in atm) at 300 K as: The molar mass of gas (i — States of Matter and Gaseous State Chemistry Question
Question
The density of a gas (in g/litre) depends on pressure (in atm) at 300 K as: $d = 4P + 0.02P^2 + 0.001P^3 + \dots$ The molar mass of gas (in g/mol) is ($R = 0.08 \text{ l-atm/K-mol}$)
💡 Solution & Explanation
For an ideal gas at low pressure (where higher order terms vanish), the density is given by $d = \frac{PM}{RT}$. The coefficient of the linear term in the density power series with respect to pressure represents this ideal behavior at the limit $P \rightarrow 0$. From the given equation, $\frac{d}{P}$ as $P \rightarrow 0$ is 4. Thus, $\frac{M}{RT} = 4 \implies M = 4RT$. Given $R = 0.08\text{ L-atm/K-mol}$ and $T = 300\text{ K}$, $M = 4 \times 0.08 \times 300 = 4 \times 24 = 96\text{ g/mol}$. Formatted as a four-digit integer, it is 0096. Therefore, correct answer is 0096.