The Gaseous State

The Gaseous State Notes

A gas is a community of molecules that completely fills any container and takes on the shape and volume of that container. The kinetic molecular theory can be used to explain the behavior of gases. The earth’s atmosphere is a gas which is not in a closed container. The attraction of the earth’s gravity keeps the molecules from escaping into outer space. The atmosphere pushes with a certain force against every unit of area of an object placed in it. This force per unit area is called atmospheric pressure. Atmospheric pressure is equal in every direction, but it becomes gradually less at higher elevations and reaches zero in the vacuum of outer space.

Measuring Gases We can measure four important properties of gas: 1. The mass of the gas. The mass will depend on the kind and number of gas molecules in the container. As long as no molecules are allowed to enter or leave, the mass will not change. Units of mass are usually grams. 2. The volume of the gas. We can change this by changing the volume of the container. Volume may be measured in units of milliliters (mL) or liters (L). 3. The temperature of the gas. This can be measured in degrees Celsius, using a thermometer, then converted to Kelvin (K=°C + 273 ) 4. The pressure of the gas. A gas pushes out with a force against the walls of the container. The force acting on a unit area of the wall is the pressure. Thus pressure = force/area. Pressure may be measured in kilopascals (kPa), cm Hg, mm Hg, or atmospheres (atm).

Development of the Gas Laws Boyle’s Law – for a given mass of gas at constant temperature, the volume of a gas varies inversely with pressure; pressure x volume = a constant (PV=k);

P1V1=P2V2

Example: A balloon is filled with 30.0 L of helium at 1atm. What is the volume when the balloon rises to an altitude where the pressure is 25.5 kPa?

Charles’ Law – the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure if kept constant; pressure /temperature = a constant (P/T=b);

P1 = P2 T1 T2

Example: A 1 L sample of gas is at a temperature of 300 K. When the temperature increases to 600 K the volume increases to? Gay-Lussac’s Law – the pressure of a gas is directly proportional to the Kelvin temperature if the volume is kept constant V1 = V2 T1 T2

Example: A gas inside a used aerosol can at 1 atm pressure and 27°C is heated to 927°C. What is the internal pressure?

Avogadro”s Law- equal volumes of different gases under the same conditions of temperature and pressure contain equal numbers of molecules (or moles); volume/ moles = a constant (V/n = a)

V1 = V2 n1 n2

Ideal Gas Law – the ideal gas equation includes all of the information contained in Boyle’s, Charles’, and Avogadro’s Laws. Starting with this equation, you can derive any of the other gas laws. P = pressure in kPa (101.3 kPa=1 atm=760 mm Hg or 76 cm Hg); V= volume in liters (L); n = number of moles; R = the ideal gas constant (8.31 L kPa/mol K); T = temperature in Kelvin

PV = nRT

How is the gas constant (R) calculated?

Example: A rigid steel cylinder with a volume of 20 L is filled with N2 gas to a final pressure of 255kPa at 27°C. How many moles of N2 gas does the cylinder contain?

Dalton’s Law of Partial Pressures – at constant volume and pressure, the sum of the partial pressures of all the different gases in a mixture is equal to the total pressure of the mixture.

Ptotal + P1 + P2 + P3

Partial pressure is the contribution of each gas to the total pressure of the gas; so the # of moles of each gas has its own partial P n1 = P1 nTOT PTOT