Answer: The partial pressure of carbon dioxide is 476.
Explanation:
We are given:
Moles of oxygen gas = 3.63 moles
Moles of nitrogen gas = 1.49 moles
Moles of carbon dioxide gas = 6.16 moles
Total number of moles = [3.63 + 1.49 + 6.16] = 11.28 moles
Mole fraction of a substance is given by:
[tex]\chi_A=\frac{n_A}{n_A+n_B}[/tex]
Mole fraction of carbon dioxide, [tex]\chi_{CO_2}=\frac{n_{CO_2}}{n_T}[/tex]
So, [tex]\chi_{CO_2}=\frac{6.16}{11.28}=0.546[/tex]
To calculate the partial pressure of carbon dioxide, we use the equation given by Raoult's law, which is:
[tex]p_{CO_2}=p_T\times \chi_{CO_2}[/tex]
where,
[tex]p_A[/tex] = partial pressure of carbon dioxide = ?
[tex]p_T[/tex] = total pressure = 871 mmHg
[tex]\chi_{CO_2}[/tex] = mole fraction of carbon dioxide = 0.546
Putting values in above equation, we get:
[tex]p_{CO_2}=871mmHg\times 0.546\\\\\chi_{CO_2}=475.6mmHg=476.mmHg[/tex]
Hence, the partial pressure of carbon dioxide is 476.
