Respuesta :
Answer : The mass of nitrogen dissolved is, 79.4 grams
Explanation :
The Raoult's law for liquid phase is:
[tex]p_{N_2}=x_{N_2}\times p_T[/tex]
where,
[tex]p_{N_2}[/tex] = partial vapor pressure of nitrogen = ?
[tex]p_T[/tex] = total pressure = 1.0 atm
[tex]x_{N_2}[/tex] = mole fraction of nitrogen = 0.78
Now put all the given values in the above formula, we get:
[tex]p_{N_2}=0.78\times 1.0atm[/tex]
[tex]p_{N_2}=0.78atm[/tex]
Now we have to calculate the mass of nitrogen.
Using ideal gas equation:
[tex]PV=nRT\\\\PV=\frac{w}{M}RT[/tex]
where,
P = pressure of gas = 0.78 atm
V = volume of gas = 89.0 L
T = temperature of gas = [tex]25^oC=273+25=298K[/tex]
R = gas constant = 0.0821 L.atm/mole.K
w = mass of gas = ?
M = molar mass of nitrogen gas = 28 g/mole
Now put all the given values in the ideal gas equation, we get:
[tex](0.78atm)\times (89.0L)=\frac{w}{28g/mole}\times (0.0821L.atm/mole.K)\times (298K)[/tex]
[tex]w=79.4g[/tex]
Therefore, the mass of nitrogen dissolved is, 79.4 grams
