Respuesta :
Answer :
Partial pressure of [tex]P_{CO_{2}}[/tex] = 639.952 mmHg
Partial pressure of [tex]P_{NO}[/tex] = 36.757 mmHg
Partial pressure of [tex]P_{SO_{2}}[/tex] = 5.757 mmHg
Partial pressure of [tex]P_{H_{2}O}[/tex] = 69.533 mmHg
Solution : Given,
Total pressure, [tex]P_{T}[/tex] = 752 mmHg
From the periodic table, the molar masses of [tex]CO_{2}[/tex], NO, [tex]SO_{2}[/tex] and [tex]H_{2}O[/tex] are 44, 30, 64, 18 respectively.
92% [tex]CO_{2}[/tex] by mass means 92g [tex]CO_{2}[/tex] is present in 100g of smoke.
3.6% NO by mass means 3.6g NO is present in 100g of smoke.
1.2% [tex]SO_{2}[/tex] by mass means 1.2g [tex]SO_{2}[/tex] is present in 100g of smoke.
4.1% [tex]H_{2}O[/tex] by mass means 4.1g [tex]H_{2}O[/tex] is present in 100g of smoke.
step 1 : First calculate the number of moles of each gas.
Formula used :
Number of moles = [tex]\frac{\text{ Given mass}}{\text{ Molar mass}}[/tex] ........(1)
Moles of [tex]CO_{2}[/tex], [tex]n_{CO_{2}}[/tex] = [tex]\frac{92g}{44g/mole}[/tex] = 2.09 moles
Moles of NO, [tex]n_{NO}[/tex] = [tex]\frac{3.6g}{30g/mole}[/tex] = 0.12 moles
Moles of [tex]SO_{2}[/tex], [tex]n_{SO_{2} }[/tex] = [tex]\frac{1.2g}{64g/mole}[/tex] = 0.018 moles
Moles of [tex]H_{2}O[/tex], [tex]n_{H_{2}O}[/tex] = [tex]\frac{4.1g}{18g/mole}[/tex] = 0.227 moles
Total number of moles, [tex]n_{T}[/tex] is calculated as
[tex]n_{T}[/tex] = [tex]n_{CO_{2}}[/tex] + [tex]n_{NO}[/tex] + [tex]n_{SO_{2} }[/tex] + [tex]n_{H_{2}O}[/tex] = 2.09 + 0.12 + 0.018 + 0.227 = 2.455 moles
step 2 : Now calculate the partial pressure of each gas.
Formula used :
[tex]P_{x}=\frac{n_{x} }{n_{T}}\times P_{T}[/tex] .........(2)
where,
[tex]P_{x}[/tex] = partial pressure of x
[tex]n_{x}[/tex] = moles of x
[tex]n_{T}[/tex] = total moles
[tex]P_{T}[/tex] = total pressure
Now put all the values in above formula (2), we get
[tex]P_{CO_{2}}=\frac{n_{CO_{2}} }{n_{T}}\times P_{T}[/tex] = [tex]\frac{2.05}{2.455}\times 752mmHg[/tex] = 639.952 mmHg
[tex]P_{NO}=\frac{n_{NO} }{n_{T}}\times P_{T}[/tex] = [tex]\frac{0.12}{2.455}\times 752mmHg[/tex] = 36.757 mmHg
[tex]P_{SO_{2}}=\frac{n_{SO_{2}} }{n_{T}}\times P_{T}[/tex] = [tex]\frac{0.018}{2.455}\times 752mmHg[/tex] = 5.5136 mmHg
[tex]P_{H_{2}O}=\frac{n_{H_{2}O} }{n_{T}}\times P_{T}[/tex] = [tex]\frac{0.227}{2.455}\times 752mmHg[/tex] = 69.533 mmHg
