Liquefied natural gas (LNG) is mainly methane. A tank is constructed to store LNG at –164°C and 1atm — States of Matter and Gaseous State Chemistry Question
Question
Liquefied natural gas (LNG) is mainly methane. A $10.0 \text{ m}^3$ tank is constructed to store LNG at –164°C and 1atm pressure, under which conditions its density is $416 \text{ kg/m}^3$. The volume (in $\text{m}^3$) of a storage tank capable of holding the same mass of LNG as a gas, at 27°C and 1.642 atm pressure, is
💡 Solution & Explanation
Mass of LNG $= 10.0 \text{ m}^3 \times 416 \text{ kg/m}^3 = 4160 \text{ kg} = 4.16 \times 10^6 \text{ g}$. Moles of methane ($CH_4$, $M=16$) $= 4.16 \times 10^6 / 16 = 260000 \text{ mol}$. Volume of gas $V = \frac{nRT}{P} = \frac{260000 \times 0.0821 \times 300}{1.642} = \frac{260000 \times 24.63}{1.642} = 260000 \times 15 = 3900000 \text{ L}$. Converting to cubic meters ($1 \text{ m}^3 = 1000 \text{ L}$), $V = 3900 \text{ m}^3$. Therefore, correct answer is 3900.