Answer:
a) [tex]P_{CO_2} =0.188 torr[/tex]
b) [tex]6.71\times 10^{21} \frac{molecules}{m^3}[/tex]
c) [tex]6.71 \times 10^{15} \frac{molecules}{cm^3}[/tex]
Explanation:
a) The partial pressure of CO₂ is given by:
[tex]P_{CO_2} = x_{CO_2} \times P_{T}[/tex]
Since the molar fraction of the gas is directly proportional to the volume of the gas, the molar fraction is given by:
[tex]x_{CO_2} = \frac{moles \ CO_2}{total \ moles} =\frac{volume\ of\ CO_2}{total\ volume}[/tex]
[tex]x_{CO_2}=\frac{3.0\times 10^2 ppmv}{10^6} =3.0\times 10^{-4}[/tex]
Hence,
[tex]P_{CO_2} =3.0\times 10^{-4} \times 628 torr=0.188 torr[/tex]
b) Using the Ideal Gas Law, we can find the number of moles of CO₂:
[tex]P_{CO_2}V=n_{CO_2}RT[/tex]
where:
[tex]P_{CO_2}=0.19torr\frac{1 atm}{760torr} =2.5\times10^{-4} atm[/tex]
[tex]T=0 + 273K=273K[/tex]
[tex]R=0.0822\frac{l.atm}{mol.K}[/tex]
The concentration of CO in molecules per cubic meter is:
[tex]\frac{n_{CO_2}}{V} = \frac{ P_{CO_2}}{RT}[/tex]
[tex]\frac{n_{CO_2}}{V} = \frac{ 2.5\times10^{-4} atm}{0.0822\frac{l.atm}{mol.K}\times 273K}\times \frac{1000l}{1m^3} \times \frac{6.022\times 10^{23} molecules}{1 mole}=6.71\times 10^{21} \frac{molecules}{m^3}[/tex]
c) The concentration of CO in molecules per cubic centimeter is:
[tex]6.71\times 10^{21} \frac{molecules}{m^3}\times\frac{1 m^3}{(100cm)^3}= 6.71 \times 10^{15} \frac{molecules}{cm^3}[/tex]
