Respuesta :
Answer : The mass of helium present in the gas mixture are, 1.216 grams.
Solution : Given,
Moles of [tex]N_2[/tex] = 0.25 mole
Moles of [tex]O_2[/tex] = 0.25 mole
Total volume of gas mixture = 18 L
Total pressure of gas mixture = 1 atm
Total temperature of gas mixture = [tex]0^oC=0+273=273K[/tex]
Molar mass of helium = 4 g/mole
First we have to calculate the total moles of mixture of gas.
using ideal gas equation,
[tex]PV=nRT\\\\n=\frac{PV}{RT}[/tex]
where,
P = total pressure of gas mixture
T = total temperature of gas mixture
n = total mole of gas mixture
V = total volume of gas mixture
R = gas constant = 0.0821 Latm/moleK
Now put all the given values in the above formula, we get the total moles of mixture of gas.
[tex]n=\frac{1atm\times 18L}{0.0821Latm/moleK\times 273K}=0.804mole[/tex]
Now we have to calculate the moles of helium gas.
[tex]\text{Total moles of gas mixture}=\text{Moles of }N_2+\text{Moles of }O_2+\text{Moles of }He[/tex]
[tex]0.804=0.25+0.25+\text{Moles of }He[/tex]
[tex]\text{Moles of }He=0.304mole[/tex]
Now we have to calculate the mass of helium.
[tex]\text{Mass of }He=\text{Moles of }He\times \text{Molar mass of }He[/tex]
[tex]\text{Mass of }He=0.304mole\times 4g/mole=1.216g[/tex]
Therefore, the mass of helium present in the gas mixture are, 1.216 grams.
The mass of helium gas that present in the gas mixture is 1.216 grams.
The ideal gas equation
[tex]\bold {pV =n RT}[/tex]
where,
P = total pressure of gas mixture
T = total temperature of gas mixture
n = total mole of gas mixture
V = total volume of gas mixture
R = gas constant = 0.0821 Latm/moleK
Put the values, and solve it for n,
[tex]\bold {n = \dfrac {1\times 18}{0.0831\times 273}}[/tex]
[tex]\bold {n = 0.804 mol}[/tex]
The number of moles of the helium gas
[tex]\bold {0.804 = 0.25 +0.25 + moles\ of \ helium}\\\\\bold {moles\ of \ helium = 0.304 mol}[/tex]
The mass of the helium gas
[tex]\bold {mHe = 0.304 \times 4}\\\\\bold {mHe = 1.216}[/tex]
Therefore, the mass of helium gas that present in the gas mixture is 1.216 grams.
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