Gases Chapter 14

Review from Chapter 13 Pressure Describing gases: To describe a gas fully, you need to state the 4 measurable quantities: 1. Volume 3. Temperature 2. # of molecules 4. Pressure Definition: The force per unit of area on a surface Equation:

Measuring Pressure A barometer is a device used to measure atmospheric pressure Introduced by Torricelli with experiments involving mercury (Hg) He determined the air (atmosphere) could support a column of Hg 760 mm high The height of the Hg depends on the air pressure What would happen to the height of the column in the mountains? What would happen to the height of the column 100ft under water?

Units of Pressure Pressure can be measured in many units Most common: mm of Hg 1 mm Hg = 1 torr (in honor of Torricelli) Atmospheric Pressure at sea level and 0oC is 760 mm Hg Other units of pressure include: Atmospheres (atm) and Pascal (Pa)

CONVERSIONS 760 mm Hg= = 760 torr = 1 atm = 29.92 in Hg = 14.7 psi = 101325 Pa = 101.325 kPa

Standard Temperature and Pressure (STP) To compare volume of gases, it is necessary to know the pressure at which the volume is measured For purpose of comparison, scientists have agreed on standard conditions STP= 1 atm pressure and 0oC

Review Calculation The atmospheric pressure in Denver is 0.830 atm. Express this in mmHg and kPa.

Boyle’s Law Robert Boyle studied the relationship between pressure and volume Boyle’s Law: States that the volume of a fixed mass of gas varies inversely with the pressure at constant temperature Can be written as: P1V1= P2V2

Practice Problem P1V1= P2V2 A sample of oxygen gas has a volume of 150. mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant? P1= V1= P2= V2=

Charles’s Law Jacques Charles studied the relationship between volume and temperature Charle’s Law: States that the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature. Can be written as:

Kelvin Temperature? The Kelvin scale is K= 273 + oC -273 oC is the lowest possible temperature to achieve (absolute zero) Absolute zero is given the value of zero on the Kelvin scale

Practice Problem A sample of neon gas occupies a volume of 752 mL at 25 oC. What will the volume of the gas occupy at 50oC if the pressure remains constant? V1= T1= V2= T2=

Gay-Lussac’s Law Gay-Lussac determined the relationship between temperature and pressure Gay-Lussac’s Law: The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature Can be written as: Pressure (atm)

Practice Problem The gas in an aerosol can is at a pressure of 3.00 atm at 25oC. Directions on the can warn the user not to keep in a place where the temperature exceeds 52oC. What would the pressure in the can be at the 52oC? P1= T1= P2= T2=

The Combined Gas Law A gas sample often undergoes changes in temperature, pressure and volume. Combining all three (Boyle’s, Charles’, and Gay-Lussac’s) will give us a valid equation Can be written as:

Practice Problem A helium filled balloon has a volume of 50.0 L at 25oC and 1.08 atm. What volume will it have at 0.855 atm and 10.oC? P1= T1= V1 = P2= T2= V2 =

Avogadro’s Principal Equal volumes of gases at the same temperature and pressure contain equal numbers of particles From Chapter 11: 1 mole= 6.02 x1023 particles Molar volume for a gas is the volume that one mole occupies at 0.00oC and 1.00 atm pressure. (STP conditions) Avogadro showed experimentally that one mole of any gas will occupy a volume of 22.4L at STP. Conversion Factor:

Practice Problem What volume will 0.416 g of krypton gas occupy at STP?

The Ideal Gas Law PV=nRT Describes the physical behavior of an ideal gas in terms of pressure, volume, temperature, and the number of moles of gas present PV=nRT R represents an experimentally determined constant that is referred to as the ideal gas constant (depends on the units used for pressure)

Numerical Values of the Gas Constant, R Units of R Numerical Value of R P V T n 0.0821 atm L K mol 8.314 kPa 62.4 mm Hg

Real vs. Ideal Gas An ideal gas is one whose particles take up no space and have no intermolecular attractive forces In the real world, no gas is truly ideal. Real gases deviate most from ideal gas behavior at extremely high pressures and low temperatures

Practice Problem What is the pressure in atm exerted by a 0.500 mol samples of nitrogen gas in a 10.0L container at 298K?

Applying the Ideal Gas Law Rearranging the PV=nRT equation allows you to also calculate the molar mass and density of a gas sample if the mass of the sample is known Recall from Chapter 12- n (moles) = m (mass)/ M (molar mass) D= Density (mass/volume)

Practice Problem Calculate the grams of N2 gas present in a 0.600 L sample kept at 1.00 atm pressure and a temperature of 22.0oC.

Gas Stoichiometry Gas volume A moles A moles B mass B Why are we using stoichiometry? Suppose we need to determine the volume of something other than our known (the given), we can apply stoichiometry to achieve the desired products/reactants “Plan of Attack” Start with a BALANCED equation. Use stoichiometry first to get into the desired substance Use the Ideal Gas Law (IGL) to convert into volume of that substance Gas volume A moles A moles B mass B Mass A moles A moles B gas volume B

Practice Problem What volume of chlorine gas at 38oC and 1.63 atm is needed to react completely with 10.4 g of sodium to form NaCl? (Cl2 + 2Na  2NaCl)