Respuesta :
Answer : The number of molecules of nitrogen, oxygen, carbon dioxide and argon is, [tex]1.88\times 10^{23}[/tex], [tex]5.03\times 10^{23}[/tex], [tex]1.19\times 10^{20}[/tex] and [tex]2.23\times 10^{21}[/tex] respectively.
Explanation :
First we have to calculate the total moles of mixture of gas by using ideal gas equation.
[tex]PV=nRT[/tex]
where,
P = Pressure of mixture of gas = 1.59 atm
V = Volume of mixture of gas = 6.51 L
n = number of moles mixture of gas = ?
R = Gas constant = [tex]0.0821L.atm/mol.K[/tex]
T = Temperature of mixture of gas = [tex]43^oC=273+43=316K[/tex]
Putting values in above equation, we get:
[tex]1.59atm\times 6.51L=n\times (0.0821L.atm/mol.K)\times 316K[/tex]
[tex]n=0.399mol[/tex]
Now we have to calculate the moles of nitrogen, oxygen, carbon dioxide and argon.
Moles of nitrogen = [tex]78.08\% \times 0.399=\frac{78.08}{100}\times 0.399=0.312mol[/tex]
Moles of oxygen = [tex]20.94\% \times 0.399=\frac{20.94}{100}\times 0.399=0.0836mol[/tex]
Moles of carbon dioxide = [tex]0.0500\% \times 0.399=\frac{0.0500}{100}\times 0.399=0.000199mol[/tex]
Moles of argon = [tex]0.930\% \times 0.399=\frac{0.930}{100}\times 0.399=0.00371mol[/tex]
Now we have to calculate the number of molecules of nitrogen, oxygen, carbon dioxide and argon.
As, 1 mole of nitrogen contains [tex]6.022\times 10^{23}[/tex] number of molecules of nitrogen.
So, 0.312 mole of nitrogen contains [tex]0.312\times 6.022\times 10^{23}=1.88\times 10^{23}[/tex] number of molecules of nitrogen.
and,
As, 1 mole of oxygen contains [tex]6.022\times 10^{23}[/tex] number of molecules of oxygen.
So, 0.0836 mole of oxygen contains [tex]0.0836\times 6.022\times 10^{23}=5.03\times 10^{23}[/tex] number of molecules of oxygen.
and,
As, 1 mole of carbon dioxide contains [tex]6.022\times 10^{23}[/tex] number of molecules of carbon dioxide.
So, 0.000199 mole of carbon dioxide contains [tex]0.000199\times 6.022\times 10^{23}=1.19\times 10^{20}[/tex] number of molecules of carbon dioxide.
and,
As, 1 mole of argon contains [tex]6.022\times 10^{23}[/tex] number of molecules of argon.
So, 0.00371 mole of argon contains [tex]0.00371\times 6.022\times 10^{23}=2.23\times 10^{21}[/tex] number of molecules of argon.
Therefore, the number of molecules of nitrogen, oxygen, carbon dioxide and argon is, [tex]1.88\times 10^{23}[/tex], [tex]5.03\times 10^{23}[/tex], [tex]1.19\times 10^{20}[/tex] and [tex]2.23\times 10^{21}[/tex] respectively.
