Gas leaks from a container

  • Thread starter Karol
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  • #1
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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?
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,909

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.
 
  • #3
1,380
22
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]
$$5[atm]\cdot 56[liter]=n\cdot 0.08208\cdot 320^0K\rightarrow n=10.7[mole]$$
$$m=10.7\cdot 32=341.1[gr]$$
 
  • #4
ehild
Homework Helper
15,543
1,909
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.
 
  • #5
1,380
22
Yes, it's gauge pressure
 

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