Calculating the Pressure for Oxygen Gas Density
1. Given Data:
- Density of oxygen at 25°C = 1.458 mg/litre
- Desired density = 2 * 1.458 mg/litre = 2.916 mg/litre
2. Using Ideal Gas Law:
- The ideal gas law equation is given by PV = nRT, where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the temperature in Kelvin
3. Converting Density to Molar Mass:
- The molar mass of oxygen (O2) is 32 g/mol.
- Convert the given density of oxygen gas to molar concentration:
- 1.458 mg/litre = 1.458 x 10^-3 g/litre
- Using molar mass, the molar concentration is 1.458 x 10^-3 g/litre / 32 g/mol = 4.556 x 10^-5 mol/litre
4. Calculating the Number of Moles:
- At the desired density, the number of moles = 2.916 x 10^-3 g/litre / 32 g/mol = 9.1125 x 10^-5 mol/litre
5. Substitute Values into Ideal Gas Law:
- (P * V) / (n * R) = T
- Since the volume and temperature remain constant, the equation simplifies to P1 / n1 = P2 / n2
- Substitute the initial and final values to find the pressure at the desired density.
6. Calculating the Final Pressure:
- P1 = 1 atm
- n1 = 4.556 x 10^-5 mol/litre
- n2 = 9.1125 x 10^-5 mol/litre
- P2 = (P1 * n2) / n1 = (1 atm * 9.1125 x 10^-5 mol/litre) / 4.556 x 10^-5 mol/litre = 2 atm
Therefore, oxygen gas will have a density twice the initial value at a pressure of 2 atmospheres.

2atm