Respuesta :
Answer : The partial pressure of helium is, [tex]1.815\times 10^4KPa[/tex]
Solution : Given,
Molar mass of [tex]O_2[/tex] = 32 g/mole
Molar mass of helium = 4 g/mole
Molar mass of [tex]N_2[/tex] = 28 g/mole
Total pressure of gas = [tex]2.07\times 10^4KPa[/tex]
As we are given gases in percent, that means 10 g of oxygen gas, 50 g of helium gas and 40 g of nitrogen gas present in 100 g of mixture.
First we have to calculate the moles of oxygen, helium and nitrogen gas.
[tex]\text{Moles of }O_2=\frac{\text{Mass of }O_2}{\text{Molar mass of }O_2}=\frac{10g}{32g/mole}=0.3125moles[/tex]
[tex]\text{Moles of }He=\frac{\text{Mass of }He}{\text{Molar mass of }He}=\frac{50g}{4g/mole}=12.5moles[/tex]
[tex]\text{Moles of }N_2=\frac{\text{Mass of }N_2}{\text{Molar mass of }N_2}=\frac{40g}{28g/mole}=1.428moles[/tex]
Now we have to calculate the total number of moles of gas mixture.
[tex]\text{Total number of moles of gas}=\text{Moles of oxygen gas}+\text{Mole of helium gas}+\text{Moles of nitrogen gas}[/tex]
[tex]\text{Total number of moles of gas}=0.3125+12.5+1.428=14.24moles[/tex]
Now we have to calculate the moles fraction of helium gas.
[tex]\text{Mole fraction of He gas}=\frac{\text{Moles of He gas}}{\text{Total number of moles of gas}}=\frac{12.5}{14.25}=0.877[/tex]
Now we have to calculate the partial pressure of helium.
[tex]p_{He}=X_{He}\times P_T[/tex]
where,
[tex]p_{He}[/tex] = partial pressure of helium
[tex]P_T[/tex] = total pressure
[tex]X_{He}[/tex] = mole fraction of helium
Now put all the given values in this formula, we get
[tex]p_{He}=(0.877)\times (2.07\times 10^4KPa)=1.815\times 10^4KPa[/tex]
Therefore, the partial pressure of helium is, [tex]1.815\times 10^4KPa[/tex]
