Gas leaks from a container

[Karol]

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 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.

 

[Karol]

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]

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.

 

[Karol]

Yes, it's gauge pressure