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A binary mixture of oxygen and nitrogen with partial pressures in the ratio 0.21 and 0.79 is contained in a vessel at 300 K. If the total pressure of the mixture is 1 * 10 5 N/m2, find mass fraction of oxygen 
  • a)
    0.133
  • b)
    0.233
  • c)
    0.333
  • d)
    0.433
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A binary mixture of oxygen and nitrogen with partial pressures in the ...
Explanation: 0.269/1.156 = 0.233.
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Most Upvoted Answer
A binary mixture of oxygen and nitrogen with partial pressures in the ...
To find the mass fraction of oxygen in the binary mixture, we need to use the partial pressures of oxygen and nitrogen and the total pressure of the mixture.

Given:
Partial pressure of oxygen (PO2) = 0.21 * 1 * 10^5 N/m^2
Partial pressure of nitrogen (PN2) = 0.79 * 1 * 10^5 N/m^2
Total pressure of the mixture (Ptotal) = 1 * 10^5 N/m^2
Temperature (T) = 300 K

We can use Dalton's law of partial pressures to find the mole fraction of oxygen (XO2) in the mixture:

PO2 = XO2 * Ptotal
0.21 * 1 * 10^5 = XO2 * 1 * 10^5
XO2 = 0.21

Next, we can use the ideal gas law to relate the mole fraction of oxygen to the mass fraction of oxygen (WO2):

XO2 = (WO2 * MO2) / [(WO2 * MO2) + (WN2 * MN2)]

Where:
MO2 = molar mass of oxygen = 32 g/mol
MN2 = molar mass of nitrogen = 28 g/mol
WO2 = mass fraction of oxygen
WN2 = mass fraction of nitrogen

We can rearrange the equation to solve for WO2:

WO2 = (XO2 * [(WO2 * MO2) + (WN2 * MN2)]) / MO2

Substituting the given values:

WO2 = (0.21 * [(WO2 * 32) + ((1 - WO2) * 28)]) / 32

Simplifying the equation:

WO2 = 0.21 * (WO2 + 0.875 - 0.875WO2)
WO2 = 0.21 * (0.125WO2 + 0.875)
WO2 = 0.02625WO2 + 0.18375
0.97375WO2 = 0.18375
WO2 = 0.18375 / 0.97375
WO2 = 0.1886

Therefore, the mass fraction of oxygen in the binary mixture is approximately 0.1886, which is closest to option 'B' (0.233).
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A binary mixture of oxygen and nitrogen with partial pressures in the ratio 0.21 and 0.79 is contained in a vessel at 300 K. If the total pressure of the mixture is 1 * 105N/m2, find mass fraction of oxygena)0.133b)0.233c)0.333d)0.433Correct answer is option 'B'. Can you explain this answer?
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