What will be the pressure exerted by a mixture of 3.2 g of methane and 4.4 g of carbon dioxide contained in a `9 dm^(3)` flask at `27^(@)C` ?

Explanation

Calculation of Partial Pressure :
Methane `(CH_(4))=3.2` gm
Molecular mass of methane = 16 g `mol^(-1)`
Mole of `CH_(4)=(3.2)/(16)=0.2 = n`
`V=9 dm^(3)=9xx10^(-3)m^(-3)`
`T=(27+273)=300K`
`R=8.314 p_(a)m^(3)K^(-1)mol^(-1)`
If partial pressure of methane is `p_(SH_(4))` then,
`p_(CH_(4))=(n)/(V)RT`
`= ((3.2 mol)(8.314 p_(a)m^(3)K^(-1)mol^(-1))(300 K))/(16xx9xx10^(-3)m^(3))`
`= 55.43xx10^(3)p_(a)=5.543xx10^(4)p_(a)`
Calculation of Partial Pressure of `CO_(2)` :
Weight of `CO_(2)(m)=4.4 g`
Molecular mass of `CO_(2)=12+2(16)=44g mol^(-1)`
Mole of `CO_(2)(n)=(4.4g)/(44 g mol^(-1))=0.1` mol
If Partial Pressure of `CO_(2)` is `p_(CO_(2))` then,
`p_(CO_(2))=(n)/(V)RT`
`= ((0.1 mol)(8.314 p_(a)m^(3)K^(-1)mol^(-1))(300 K))/(9xx10^(-3)m^(3))`
`= 27.713xx10^(3)p_(a)=2.7713xx10^(4)p_(a)`
`p_("total")=(p_(CO_(2))+p_(CH_(4)))`
`= (2.7713xx10^(4)+5.543xx10^(4))p_(a)`
`= 8.314xx10^(4)p_(a)`
OR
`p_("total")=(p_(CH_(4))+p_(CO_(2)))`
`= ((0.2+0.1)(8.314 p_(a)m^(3)K^(-1)mol^(-1))(300K))/(9xx10^(-3)m^(3))`
`= 8.314xx10^(4)p_(a)`