Answer to Question #93992 in Molecular Physics | Thermodynamics for Hannah Chevis

Question

A 25.0L tank contains 2.0 kg of neon gas with a pressure fo 98.0 atm at 250 degrees celsius. How any kilograms of O2 can fill the tank under the same pressure and temperature?

Answer 1

Solution. We use the equation

$$PV=\frac {m} {M} RT$$

where P=98atm=9.93*10^5Pa is pressure; V=25*10^(-3) m^3 is volume; m=2kg is mass of neon gas; M=20.2*10^(-3) kg/mol is molar mass of neon gas; R=8.31 J/(mol*K) is constant; T=250 C=523K is temperature. From equation get

$$m=\frac {PVM} {RT}$$

Similarly for oxygen we get the equation

$$m_1=\frac {PVM_1} {RT}$$

where M1=32*10^(-3) kg/mol is molar mass of oxygen; m1 is mass of oxygen. Dividing the first equation by the second equation we get

$$\frac {m} {m_1} = \frac {M} {M_1}.$$

Hence

$$m_1=\frac {mM_1} {M}=\frac {2 \times 32\times 10^{-3}} {20.2 \times 10^{-3}}=3.17kg$$

Answer. 3.17kg.