Answer to Question #294880 in Molecular Physics | Thermodynamics for Xander

Question

A gas is filled with oxygen at a temperature of 2atm. If the temperature is increased to 50°c and the pressure is increased to 5atm,by what factor does the density of the oxygen increases by

Answer 1

The task contains several mistakes:

1) "A gas is filled with oxygen", which does not have any physical sense.

2) "at a temperature of 2atm" - atmosphere is the unit of pressure, not temperature.

To solve this problem, both initial and final temperature and pressure should be known. However, it still can be partly solved with given data. The formula for gas density is

$D=\frac{PM}{RT}$ , where P is the pressure, M is the molar mass (32.00 g/mol for oxygen), R is the gas constant ($0.08206\frac{L\cdot{atm}}{mol\cdot{K}}$ ), and T is the temperature in Kelvins (273 + 50 = 323 K in case of final temperature).

So the final density can be calculated:

$D_2=\frac{P_2M}{RT_2}=\frac{5\ atm\times32.00\ g/mol}{0.08206\frac{L\cdot{atm}}{mol\cdot{K}}\times323\ K}=6.04\frac{g}{L}$ (1)

The initial density could be calculated the same way if the temperature was known:

$D_1=\frac{P_1M}{RT_1}=\frac{2\ atm\times32.00\ g/mol}{0.08206\frac{L\cdot{atm}}{mol\cdot{K}}\times{T_1}}$ (2)

The remaining steps are:

1) Substitute the value of T₁ into the equation (2) to calculate D₁ ;

2) The ratio $\frac{D_2}{D_1}$ would be the final answer.