Question

A sample of a smokestack emission was collected into a 1.25-l tank at 752 mm hg and analyzed. the analysis showed 92% co2, 3.6% no, 1.2% so2, and 4.1% h2o by mass. what is the partial pressure exerted by each gas?

Answer 1

Partial pressure of
`P_{CO_(2)}` = 639.952 mmHg

Partial pressure of
`P_(NO)` = 36.757 mmHg

Partial pressure of
`P_{SO_(2)}` = 5.757 mmHg

Partial pressure of
`P_{H_(2)O}` = 69.533 mmHg

Solution : Given,

Total pressure,
`P_(T)` = 752 mmHg

From the periodic table, the molar masses of
`CO_(2)`, NO,
`SO_(2)` and
`H_(2)O` are 44, 30, 64, 18 respectively.

92%
`CO_(2)` by mass means 92g
`CO_(2)` is present in 100g of smoke.

3.6% NO by mass means 3.6g NO is present in 100g of smoke.

1.2%
`SO_(2)` by mass means 1.2g
`SO_(2)` is present in 100g of smoke.

4.1%
`H_(2)O` by mass means 4.1g
`H_(2)O` is present in 100g of smoke.

step 1 : First calculate the number of moles of each gas.

Formula used :

Number of moles =
`\frac{\text{ Given mass}}{\text{ Molar mass}}` ........(1)

Moles of
`CO_(2)`,
`n_{CO_(2)}` =
`(92g)/(44g/mole)` = 2.09 moles

Moles of NO,
`n_(NO)` =
`(3.6g)/(30g/mole)` = 0.12 moles

Moles of
`SO_(2)`,
`n_{SO_(2) }` =
`(1.2g)/(64g/mole)` = 0.018 moles

Moles of
`H_(2)O`,
`n_{H_(2)O}` =
`(4.1g)/(18g/mole)` = 0.227 moles

Total number of moles,
`n_(T)` is calculated as

`n_(T)` =
`n_{CO_(2)}` +
`n_(NO)` +
`n_{SO_(2) }` +
`n_{H_(2)O}` = 2.09 + 0.12 + 0.018 + 0.227 = 2.455 moles

step 2 : Now calculate the partial pressure of each gas.

Formula used :

`P_(x)=(n_(x) )/(n_(T))* P_(T)` .........(2)

where,

`P_(x)` = partial pressure of x

`n_(x)` = moles of x

`n_(T)` = total moles

`P_(T)` = total pressure

Now put all the values in above formula (2), we get

`P_{CO_(2)}=\frac{n_{CO_(2)} }{n_(T)}* P_(T)` =
`(2.05)/(2.455)* 752mmHg` = 639.952 mmHg

`P_(NO)=(n_(NO) )/(n_(T))* P_(T)` =
`(0.12)/(2.455)* 752mmHg` = 36.757 mmHg

`P_{SO_(2)}=\frac{n_{SO_(2)} }{n_(T)}* P_(T)` =
`(0.018)/(2.455)* 752mmHg` = 5.5136 mmHg

`P_{H_(2)O}=\frac{n_{H_(2)O} }{n_(T)}* P_(T)` =
`(0.227)/(2.455)* 752mmHg` = 69.533 mmHg