Unit IX: Gases Chapter 11… think we can cover gases in one day? Let’s find out, shall we…

Why Study Gases? First, some common elements and compounds exist in the gaseous state under normal conditions of pressure and temperature Second, our gaseous atmosphere provides one means of transferring energy and material throughout the globe Third, study of gases is compelling –Can be described qualitatively and quantitatively

Characteristics of Gases Unlike liquids and solids, gases –expand to fill their containers; –are highly compressible; –have extremely low densities

Gas Pressure Pressure is the amount of force applied to an area. Atmospheric pressure is the weight of air per unit of area. P = FAFA

Units of Pressure mm Hg or torr –These units are literally the difference in the heights measured in mm ( h ) of two connected columns of mercury. Atmosphere –1.00 atm = 760 torr

Units of Pressure Pascals –1 Pa = 1 N/m 2 Bar –1 bar = 10 5 Pa = 100 kPa

Standard Pressure Normal atmospheric pressure at sea level is referred to as standard pressure. It is equal to –1.00 atm –760 torr (760 mm Hg) – kPa

Manometer This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

Gas Laws: Boyle’s Law Robert Boyle(1627 – 1691) studied the compressibility of gases (ability to squeeze it into a smaller volume) The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

Gas Laws: Boyle’s Law A plot of V versus P results in a curve. Since V = k (1/P) This means a plot of V versus 1/P will be a straight line.

Gas Laws: Boyle’s Law PV = C B when n and T are constant –C B is the proportionality constant The product of the pressure and volume of a gas sample is a constant at a given temperature P 1 V 1 = P 2 V 2 at constant n and T

Gas Laws: Boyle’s Law Use Boyle’s Law to solve for the final pressure given these values: P 1 = 745 mm Hg V 1 = 65.0 L P 2 = ? V 2 = 25.0 L P 2 = 1940 mm Hg

Gas Laws: Charles’ Law In 1787 Jacques Charles discovered that the volume of a fixed quantity of gas at constant pressure decreases with decreasing temperature A plot of V versus T will be a straight line i.e., VTVT = k

Gas Laws: Charles’ Law V 1 /T 1 = V 2 /T 2 at constant n and P –T must always be expressed in kelvins!!!! Why? Solve for the missing value: V 1 = 25.0 mL T 1 = 20.0 °C V 2 = ? T 2 = 37.0 °C V 2 = 26.5 mL

Gas Laws: Combined Gas Laws What do you do when pressure and temperature change? –Pressure is inversely proportional to volume –Volume is directly proportional to temperature General Gas Law or Combined Gas Law: – P 1 V 1 / T 1 = P 2 V 2 / T 2 for a given amount, n –It is applied specifically to situations in which the amount of gas does not change

Gas Laws: Combined Gas Laws Helium-filled balloons are used to carry scientific instruments high into the atmosphere. Suppose a balloon is launched when the temperature is 22.5°C and the barometric pressure is 754 mm Hg. If the balloon’s volume is 4.19 x 10 3 L (and no helium escapes from the balloon), what will the volume be at a height of 20 miles, where the pressure is 76.0 mm Hg and the temperature is -33.0°C? 3.38 x 10 4 L

Avagadro’s Hypothesis 1811 Amedeo Avagadro and Joseph Gay- Lassac proposed that equal volumes of gases under the same conditions of temperature and pressure have equal numbers of particles (Avagadro’s Hypothesis) –Volume at a given temperature and pressure is directly proportional to the amount of gases in moles V ∝ n at constant T and P

Avagadro’s Hypothesis Nitrogen monoxide reacts with oxygen to give nitrogen dioxide. 2 NO (g) + O 2 (g)  2 NO 2 (g) –If you mix NO and O 2 in the correct stoichiometric ratio and NO has a volume of 150mL, what volume of O 2 is required (at the same pressure and temperature)? 75 mL of O 2

Ideal Gas Law So far we’ve seen that V  1/P (Boyle’s law) V  T (Charles’s law) V  n (Avagadro’s law) Combining these, we get V V  nT P

Ideal Gas Law Introducing a proportionality constant (now called R, universal gas constant) gives this equation: or nT P V = R PV = nRT

Ideal Gas Law Universal Gas Constant (R) –using standard temperature and pressure ( K and 1 atm), and the standard molar volume (which says that 1 mol of gas occupies L) we can calculate the value of R PV nT R = (1.0000atm)(22.414L) ( mol)(273.15K) R =

Ideal Gas Law The constant of proportionality is known as R, the gas constant.

Ideal Gas Laws The nitrogen gas in an automobile air bag, with a volume of 65 L, exerts a pressure of 829 mm Hg at 25°C. What amount of N 2 gas (in moles) is in the air bag? 2.9 moles

Density of Gases n = mass / molar mass = m / M Substitute this into the equation:PV = nRT and we get: PV = m / M RT PVM = mRT PM = m / V RT PM = dRT d = PM / RT

Density of Gases Calculate the density of CO 2 at STP. Is CO 2 more or less dense than air? –The density of dry air at STP is 1.2 g/L –Density of CO 2 = 1.96 g/L

Density of Gases You are trying to determine, by experiment, the formula of a gaseous compound to replace chlorofluorocarbons in air conditioners. You have determined the empirical formula is CHF 2, but now you want to know the molecular formula. To do this, you need the molar mass of the compound. You therefore do another experiment and find that a 0.100g sample exerts a pressure of 70.5 mm Hg in a 256mL container at 22.3°C. What is the molar mass of the compound? What is its molecular formula?

Density of Gases d = 0.100g / 0.256L = g/mL M = dRT / P M = (0.391)( )(295.5) / (0.0928) Molar mass = 102 g/mol Formula of the compound = C 2 H 2 F 4