# Gas leaks from a container

## Homework Statement

Into a 56[liter] container oxigen is filled in with manometric pressure of 4[atm] and temp' 470C. what is the mass.
Then a leak happens and the pressure drops to 3.5[atm] and temp' 270C.
How much oxigen escaped.

## Homework Equations

$$PV=nRT$$
$$R\left[\frac{liter\cdot atm'}{mole\cdot ^0K}\right]=0.08208$$
Atomic number O2=16

## The Attempt at a Solution

The initial conditions: ##3[atm]\cdot 56[liter]=n\cdot 0.08208\cdot 320^0K\rightarrow n=6.4[mole]##
$$m=6.4\cdot 16=102.3[gr]$$
Second stage:
$$\frac{P_1V_1}{n_1T_1}=\frac{P_2V_2}{n_2T_2}\rightarrow\frac{P_1V_1}{m_1T_1}=\frac{P_2V_2}{m_2T_2}$$
Our volume is fixed, so: ##\frac{3}{102.3\cdot 320}=\frac{2.5}{m_2\cdot 300}\rightarrow m_2=90.97[gr]##
Is it correct?

ehild
Homework Helper

## Homework Statement

Into a 56[liter] container oxigen is filled in with manometric pressure of 4[atm] and temp' 470C. what is the mass.
Then a leak happens and the pressure drops to 3.5[atm] and temp' 270C.
How much oxigen escaped.

## Homework Equations

$$PV=nRT$$
$$R\left[\frac{liter\cdot atm'}{mole\cdot ^0K}\right]=0.08208$$
Atomic number O2=16

## The Attempt at a Solution

The initial conditions: ##3[atm]\cdot 56[liter]=n\cdot 0.08208\cdot 320^0K\rightarrow n=6.4[mole]##
$$m=6.4\cdot 16=102.3[gr]$$

Why did you calculate with 3 atm?
And the oxygen gas consists of O2 molecules. The atomic mass of oxygen is 16 g, but you have to work with the molar mass.

manometric pressure is the pressure above atmospheric, right? so i have to take absolute pressures, it's then 5 atm.
And the molar mass is 32[gr]
$$5[atm]\cdot 56[liter]=n\cdot 0.08208\cdot 320^0K\rightarrow n=10.7[mole]$$
$$m=10.7\cdot 32=341.1[gr]$$

ehild
Homework Helper
manometric pressure is the pressure above atmospheric, right? so i have to take absolute pressures, it's then 5 atm.
And the molar mass is 32[gr]
$$5[atm]\cdot 56[liter]=n\cdot 0.08208\cdot 320^0K\rightarrow n=10.7[mole]$$
$$m=10.7\cdot 32=341.1[gr]$$

I know pressure above atmospheric as "gauge pressure". You have to know what manometric pressure is. I never heard that.

Yes, it's gauge pressure