Respuesta :
Answer: The partial pressure of nitrogen gas is 405.76 mmHg and that of hydrogen gas is 257.24 mmHg
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
- For nitrogen gas:
Given mass of nitrogen gas = 3.46 g
Molar mass of nitrogen gas = 28 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of nitrogen gas}=\frac{3.46g}{28g/mol}=0.123mol[/tex]
- For hydrogen gas:
Given mass of hydrogen gas = 0.156 g
Molar mass of hydrogen gas = 2 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of hydrogen gas}=\frac{0.156g}{2g/mol}=0.078mol[/tex]
Mole fraction of a gas is calculated by using the formula:
[tex]\chi_{A}=\frac{n_{A}}{n_{A}+n_{B}}[/tex] ......(1)
- For nitrogen gas:
Putting values in equation 1, we get:
[tex]\chi_{\text{nitrogen gas}}=\frac{0.123}{0.123+0.078}=0.612[/tex]
- For hydrogen gas:
Putting values in equation 1, we get:
[tex]\chi_{\text{hydrogen gas}}=\frac{0.078}{0.123+0.078}=0.388[/tex]
The partial pressure of a gas is given by Raoult's law, which is:
[tex]p_A=p_T\times \chi_A[/tex] ......(2)
where,
[tex]p_A[/tex] = partial pressure of substance A
[tex]p_T[/tex] = total pressure = 663 mmHg
[tex]\chi_A[/tex] = mole fraction of substance A
- For nitrogen gas:
[tex]p_{\text{Nitrogen gas}}=663mmHg\times 0.612\\\\p_{\text{Nitrogen gas}}=405.76mmHg[/tex]
- For hydrogen gas:
[tex]p_{\text{Hydrogen gas}}=663mmHg\times 0.388\\\\p_{\text{Hydrogen gas}}=257.24mmHg[/tex]
Hence, the partial pressure of nitrogen gas is 405.76 mmHg and that of hydrogen gas is 257.24 mmHg
