Question

A 25.0L tank contains 2.0kg of neon gas with a pressure of 98.0 atm at 28 degrees celcius. How many kilograms of oxygen can fill the tank under the same pressure and temperature?

Answer 1

Let us write the classical ideal gas law for neon and oxygen respectively: $p_1 V_1 = \frac{m_1}{M_1} R T_1$, $p_2 V_2 = \frac{m_2}{M_2} R T_2$. Dividing two equations of state, obtain: $\frac{p_1 V_1}{p_2 V_2} = \frac{m_1}{m_2}\frac{M_2}{M_1}\frac{T_1}{T_2}$. According to the given conditions, the tank has a fixed volume, hence $V_1 = V_2$, and the pressure and temperature is the same, hence $p_1 = p_2$, $T_1 = T_2$. Hence, two equations of state simplify to $1 = \frac{m_1}{m_2}\frac{M_1}{M_2}$ , from where $m_2 = m_1 \frac{M_2}{M_1}$ . The molar masses of neon and oxygen are $M_1 = 10 \frac{g}{mol}$ and $M_2 = 16 \frac{g}{mol}$ respectively, hence the mass of the oxygen is $m_2 = 2 kg \cdot \frac{16 \frac{g}{mol}}{10 \frac{g}{mol}} = 3.2 kg$.