Answer:
[tex]\boxed{\text{0.780 atm}}[/tex]
Explanation:
Hermione is pretty smart. She realizes that, according to Dalton's Law of Partial Pressures, each gas exerts its pressure independently of the others, as if the others weren't even there.
She shows Ron how to use the Ideal Gas Law to solve the problem.
pV = nRT
She collects the data:
V = 1.00 L; n = 0.0319 mol; T = 25.0 °C
She reminds him to convert the temperature to kelvins
T = (25.0 +273.15) K = 298.15 K
Then she shows him how to do the calculation.
[tex]p \times \text{1.00 L} = \text{0.0319 mol} \times \text{L}\cdot\text{atm}\cdot\text{0.082 06 K}^{-1}\text{mol}^{-1} \times \text{298.15 K}\\\\1.00p = \text{0.7805 atm}\\\\p = \textbf{0.780 atm}\\\\\text{The partial pressure of the nitrogen is } \boxed{\textbf{0.780 atm}}[/tex]
Isn't she smart?
The partial pressure of N2 is 0.78 atm.
The following are information contained in the question;
Volume (V) = 1.00 L
Total number of moles of the gases(n) = Number of moles of N2 + Number of moles of O2 + Nuber of moles of Ar = 0.0319 mol + 0.00856 mol + 0.000381 mol = 0.041 moles
Temperature(T) = 25.0◦C + 273 = 298 K
Using PV = nRT
Where;
P = pressure of the gas (the unknown)
V = volume of the sample = 1.00 L
T = absolute temperature = 298K
R = molar gas constant = 0.082 atmLK-1Mol-1
n = total number of moles present = 0.041 moles
Making P the subject of the formula and substituting values;
P = nRT/V
P = 0.041 moles × 0.082 atmLK-1Mol-1 × 298 K/1.00 L
P = 1 atm
Recall that partial pressure = mole fraction × total pressure
Mole fraction of N2 = 0.00856 mol /0.00856 mol + 0.0319 mol + 0.000381 mol =
Partial pressure of N2 =0.0319 mol /0.041 moles × 1 atm
Partial pressure of N2 = 0.78 atm
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