Respuesta :
Explanation:
Moles of helium gas = [tex]n_1=4.00 mol[/tex]
Moles of hydrogen gas = [tex]n_2=2.00 mol[/tex]
Moles of carbon dioxide gas = [tex]n_3=3.00 mol[/tex]
Moles of argon gas = [tex]n_4=5.00 mol[/tex]
Mole fraction of helium gas = [tex]\chi_1=\frac{n_1}{n_1+n_2+n_3+n_4}=\frac{4.00 mol}{14.00 mol}=0.2857[/tex]
Mole fraction of hydrogen gas = [tex]\chi_2=\frac{n_2}{n_1+n_2+n_3+n_4}=\frac{2.00 mol}{14.00 mol}=0.1428 [/tex]
Mole fraction of carbon dioxide gas = [tex]\chi_3=\frac{n_3}{n_1+n_2+n_3+n_4}=\frac{3.00 mol}{14.00 mol}=0.2143[/tex]
Mole fraction of argon gas = [tex]\chi_4=\frac{n_4}{n_1+n_2+n_3+n_4}=\frac{5.00 mol}{14.00 mol}=0.3571 [/tex]
Mole percent of helium = [tex]\chi_1\times 100=0.2857\times 100=28.57\%[/tex]
Mole percent of hydrogen= [tex]\chi_2\times 100=0.1428 \times 100=14.28\%[/tex]
Mole percent of helium = [tex]\chi_3\times 100=0.2143\times 100=21.43\%[/tex]
Mole percent of helium = [tex]\chi_4\times 100=0.3571 \times 100=35.71\%[/tex]
Total pressure of the mixture = P = 2900 mmHg
Partial pressure of helium gas = [tex]p_1[/tex]
Partial pressure of hydrogen gas = [tex]p_2[/tex]
Partial pressure of carbon dioxide gas = [tex]p_3[/tex]
Partial pressure of argon gas = [tex]p_4[/tex]
[tex]p_i=P\times \chi_i[/tex]
[tex]chi_i[/tex] = Mole fraction of ith component
[tex]p_1=P\times \chi_1=P\times \frac{n_1}{n_1+n_2+n_3+n_4}[/tex]
[tex]p_1=2900 mmHg\times \frac{4.00 mol}{4.00 mol+2.00 mol+3.00 mol+5.00 mol}=828.57 mmHg[/tex]
[tex]p_2=P\times \chi_2=P\times \frac{n_2}{n_1+n_2+n_3+n_4}[/tex]
[tex]p_2=2900 mmHg\times \frac{2.00 mol}{4.00 mol+2.00 mol+3.00 mol+5.00 mol}=828.57 mmHg[/tex]
[tex]p_3=P\times \chi_3=P\times \frac{n_3}{n_1+n_2+n_3+n_4}[/tex]
[tex]p_3=2900 mmHg\times \frac{3.00 mol}{4.00 mol+2.00 mol+3.00 mol+5.00 mol}=414.28 mmHg[/tex]
[tex]p_4=P\times \chi_4=P\times \frac{n_4}{n_1+n_2+n_3+n_4}[/tex]
[tex]p_4=2900 mmHg\times \frac{5.00mol}{4.00 mol+2.00 mol+3.00 mol+5.00 mol}=1,035.71 mmHg[/tex]
