Question

An ideal gas mixture consists of 80% N$_2$ and 20% O$_2$ on mass basis. If the total pressure is 300 kPa, then the partial pressure of N$_2$ (in kPa) is
(Molecular weights of N$_2$ = 28 kg/kmol and O$_2$ = 32 kg/kmol)

• A. 246.15
• B. 230.34
• C. 254.78
• D. 213.54

Hint:

Mass fractions must be converted into mole fractions before applying Dalton’s law of partial pressures.

Answer 1

The Correct Option is A

Mass fractions are: $w_{N_2} = 0.8$ and $w_{O_2} = 0.2$. Convert to mole fractions:
\[ n_{N_2} = \frac{0.8}{28}, \qquad n_{O_2} = \frac{0.2}{32}. \] Total moles:
\[ n = \frac{0.8}{28} + \frac{0.2}{32}. \] Mole fraction of N$_2$:
\[ x_{N_2} = \frac{\frac{0.8}{28}}{\frac{0.8}{28} + \frac{0.2}{32}} \approx 0.8205. \] Thus, partial pressure:
\[ p_{N_2} = x_{N_2} \times 300 = 0.8205 \times 300 \approx 246.15\text{ kPa}. \]