Chapter 6. The Gas Phase

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Chapter 6. The Gas Phase. Gas Pressure. P = pressure (Pa = kg m -1 s -2 ) F = force (N = kg m s -2 ) A = area (m 2 ). Let’s calculate the pressure exerted by my feet on the ground. My mass is 85 kg and we will assume that my feet have an area of 0.0600 m 2. m = mass (kg)

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Chapter 6. The Gas Phase

Gas Pressure

P = pressure (Pa = kg m-1 s-2)

F = force (N = kg m s-2)

A = area (m2)

Let’s calculate the pressure exerted by my feet on the ground. My mass is 85 kg and we will assume that my feet have an area of 0.0600 m2.

m = mass (kg)

g = acceleration due to gravity

= 9.8 m s-2

And if I was wearing high heals, standing on the heal, ~2 cm2, the pressure would be…

A penny, having a mass of 2.5 g and radius of 9.3 mm exerts a pressure of ~100 Pa, and atmospheric pressure is 101 325 Pa. The Pa is a very small unit.

Because of this chemists have conventionally used other units of Pressure as well.

1 atmosphere (atm) = 101 325 Pa

760 mmHg = 1 atm

760 torr = 1 atm

1 bar = 105 Pa

Measuring Pressure: The Mercury Barometer

A barometer is a tube ~1m long, closed at one end, filled with mercury and inverted into a dish containing more mercury.

When the tube is inverted some of the mercury flows out forming a vacuum above the mercury in the tube.

At sea level and under normal atmospheric conditions the mercury stops flowing out when the level of mercury in the tube and above the pool of mercury is 760 mm.

Why not use water?

The ratio of heights (h) of liquid columns is inversely related to the ratio of densities (d) of the liquids.

a bit more convenient to use Hg.

From

Boyle Works, The Works of Robert Boyle, Hunter, M., and Davis, E. B. (eds.), 14 vols., London: Pickering and Chatto, 1999-2000

The Gas Laws

Boyle’s Law

“till further trial hath more clearly informed me, I shall not venture to determine, whether or no the intimated theory will hold universally and precisely, either in condensation of air, or rarefaction: all that I shall now urge being, that…the trial already made sufficiently proves the main thing, for which I here allege it;

since by it, it is evident, that as common air, when reduced to half its wonted extent, obtained near about twice as forcible a spring as it had before, so this thus comprest air being further thrust into half this narrow room, obtained thereby a spring about as strong again as that it last had, and consequently four times as strong as that of the common air”

Robert Boyle (1627 – 1691)

Boyle’s Law: at constant temperature the volume occupied by a fixed amount of gas is inversely proportional to the applied pressure.

Charles’ Law (also known as Gay-Lussac’s law)

It was curious that Boyle’s Law was true only at constant temperature. The relationship between temperature and volume was investigated independently in the 1800’s by French scientists, Charles and Gay-Lussac.

Jacques Alexandre César Charles (1746-1823)

Joseph Louis Gay-Lussac (1778–1850)

“equal volumes of all gases expand equally with the same increase temperature”

Charles’ Law: at constant Pressure, the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature.

William Thompson (Lord Kelvin) found that if you extend or extrapolate any V vs T plot back to 0 L they all intersect at -273.15 oC. Based on this observation it led Lord Kelvin to devise the absolute temperature scale.

T = t + 273.15

where T is the absolute temperature and

t is the temperature in oC.

Other Relationships from Charles’ and Boyle’s Laws

Pressure-temperature relationship: at constant volume the pressure exerted by a fixed amount of gas is directly proportional to the absolute temperature.

The combined gas law: A simple combination of Charles’ and Boyle’s laws yields the combined gas law.

If you have a set of initial conditions (P, V, and T) and you change two of the conditions, you can find the third by using the combined gas law,

eg. A 1 L steel tank is filled with a safety valve that opens if the internal pressure exceeds 1.00 x 103 torr. It is filled with helium at 23 oC and 0.991 atm and placed in boiling water at exactly 100 oC. Will the safety valve open?

Solution.

eg. Divers working from a North Sea drilling platform experience pressures of 50.0 atm at a depth of 5.0x102 m. If a balloon is inflated to a volume of 5.0 L (roughly the same volume as a lung) at that depth of water and at 4 oC, what would the volume of the balloon be on the surface at a pressure of 1.00 atm at 25 oC.

• ~1800 two English chemists, Nicholson and Carlise showed that water could be decomposed by an electric current into two volumes of Hydrogen gas and one volume of Oxygen a simple whole number ratio of 2:1
• Gay-Lussac’s “Law of Combining Volumes,” water was H2O!
• Dalton insisted that water was composed of one atom of oxygen and one of hydrogen, the formula being HO! He believed that elements were atoms and they combined 1:1 to form compounds…
• The law of conservation of mass and the law of combining volumes could not both be correct if water was HO and oxygen and hydrogen existed as O and H, as Dalton insisted.

“equal volumes of all gases at the same temperature and pressure contain the same number of molecules”

• both laws are obeyed, only Dalton’s deeply seeded beliefs were at odds
• still wasn’t accepted for half a century due to the belief that similar elements could not combine to form molecules due to a lack of “electrostatic attraction”

-relates the volume and the amount of substance

- at a fixed temperature and pressure, the volume of gas is directly proportional to the amount (moles) of gas…any gas,

Gas Behaviour at Standard Conditions

standard temperature

and pressure

The Ideal Gas Law

• Boyle’s Law
• Charles’ Law

what is “c”

we give the constant the symbol R and it is called the universal gas constant.

• show that both Pa m3 K-1 mol-1 and kPa L K-1 mol-1 are equivalent to J K-1 mol-1

- the ideal gas law (equation)

Applying the gas laws:

eg. A steel tank has a volume of 438 L and is filled with 0.885 kg of O2. Calculate the pressure of O2 at 21 oC.

eg. The maximum safe pressure that a certain 4.00 L vessel can hold is 3.50 atm. If the vessel contains 0.410 mol of gas, what is the maximum temperature (in degrees Celsius) to which this vessel can be subjected?

eg. 2.0 L of argon gas at STP is heated to 500 K under constant pressure. What volume does the gas occupy after heating?

Gas Density

eg. a) Calculate the density (in g L-1) of carbon dioxide and SF6 at standard temperature and pressure (STP).

b) Also calculate the number of molecules per cm3 at STP.

Solution.

eg. A chemist vaporized a liquid compound and determined its density to be 1.585 g/L at 90oC and 753 mm Hg. What is the molecular weight of the compound?

many gases more dense than air have been involved in disasters both intentional and accidental

• dense gases in smog blanket urban centres like LA and Toronto contributing to respiratory illness
• in WWI phosgene (OCCl2) was used against ground troops as they lay in trenches
• in 1984 methyl isocyanate was unintentionally released from Union Carbide India Ltd. killing thousands of people as vapors spread into the city from the plant in the outskirts (http://www.bhopal.com/)
• in 1986 in Cameroon, CO2 was released from Lake Nyos and suffocated thousands of villagers and livestock as it flowed down the valleys into the villages.
• (http://www.globalchange.umich.edu/globalchange1/current/lectures/kling/killer_lakes/
• killer_lakes.html)

Determining Molar Mass of a Volatile Liquid

• Dumas (1800 – 1884)
• mass spectrometry works also!

eg. An organic chemist isolates a colorless liquid with the properties of cyclohexane (C6H12) from a petroleum sample. She uses the Dumas method and obtained the following data.

Volume of flask = 213 mL T = 100.0 oC

mass of flask and gas = 78.416 g mass of flask = 77.834 g

atmospheric pressure = 754 mm Hg

Determine the molar mass of the isolate.

Partial Pressure

In experiments with humidity Dalton discovered that when water vapor is added to dry air, the total pressure rises by an increment equal to the pressure of the water vapor,

Each gas exerts a partial pressure which is a portion of the total pressure. The pressure exerted by each component in the mixture is the same as the pressure it would exert by itself.

Dalton’s law of partial pressures: in a mixture of unreactive gases, the total pressure is the sum of the partial pressures of individual gases,

• gases mix homogenously to form a solution in any proportion
• as long as there is no chemical reaction, each gas behaves as if it were the only gas present

eg. In a study of O2 uptake by muscle at high altitude, a physiologist prepares an atmosphere consisiting of 79.0 % N2, 17.0 % 16O2, and 4.0 % 18O2 by volume. The pressure of the mixture is 0.75 atm to simulate high altitude. Calculate the mole fraction and partial pressure of 18O2 in the mixture.

Solution. Do we need to calculate the moles of each component?

eg. The gas from a certain volcano had the following composition in mole fraction: 65.0% CO2, 25.0 % H2, 5.4 % HCl, 2.8 % HF, 1.7 % SO2, and 0.1 % H2S. What would be the partial pressure of each of these gases if the total pressure of volcanic gas were 760 mm Hg?