Gases Kinetic Theory of Ideal Gas, Gas Laws & Equation Combined Gas Laws, Numerical value of R

The Unique Gas Phase Pressure Physical properties of a gas are nearly independent of its chemical identity! Gas behavior is markedly different than solid or liquid behavior and have lower densities than the liquid and solids. They assume the volume and shape of their containers. They are the most compressible state of matters Gases will mix evenly and completely when confined to the same container. Pressure Pressure is simply a force exerted over a surface area.

10 miles 0.2 atm 4 miles 0.5 atm Sea level 1 atm

Atmospheric Pressure Patm is simply the weight of the earth’s atmosphere pulled down by gravity. Barometers are used to monitor daily changes in Patm.

In the lab, we use manometers to measure pressures of gas samples.

Units of Pressure we have units such as torr and mm Hg. The derived SI unit for pressure is N/m2, known as the pascal (Pa). Standard conditions for gases (STP) occurs at 1 atm and 0 °C. Under these conditions, 1 mole of gas occupies 22.4 L. Note that 1 atm = 760 mm Hg = 760 torr = 101.325kPa =101,325Pa and 1000Pa= 1KPa

Kinetic-Molecular Theory postulates Gas consists of large number of particles (e.g atoms, molecules ) (that are hard spheres) separated by large distances compared to their diameters (the particles are negligibly small in size). The volume of each particle is so small that we assume they have mass but but have negligible volume. ) Gas molecules exert neither attractive nor repulsive forces on one another. (i.e No forces between particles except when they collide). Gas particles are in constant, rapid, straight-line motion in random directions. Gas particles colliding with each other and with containers wall in a perfectly elastic (i.e K.E is transferred without loss from one particle to the other. total K.E is constant) manner and particles continue in straight lines after collisions but changing direction.

Kinetic-Molecular Theory postulates 5) The average kinetic energy (a measure of particles speed) of a particle is proportional to the kelvin temperature of the gas. i.e Any two gases at the same temperature will have the same average kinetic energy

Imagining a Sample of Gas We imagine a sample of gas – chaos, molecules bumping into each other constantly. After a collision, 2 molecules may stop completely until another collision makes them move again. Some molecules moving really fast, others really slow. But, there is an average speed.

Gas Molecular Speeds As temp increases, avg. speed increases. i.e. avg. KE is related to temp!! Any 2 gases at same temp will have same avg. KE!

Why Do Gas Laws Work So Well? Recall that the gas laws apply to any gas – the chemical identity is not important. Gas particles only interact when they collide. Since this interaction is so short, chemical properties don’t have time to take effect!!

Volume and Pressure – Boyle’s Law The volume of a gas is inversely related to pressure, i.e. if P increases, V decreases. P P a 1/V P x V = constant P1 x V1 = P2 x V2

VI. Explaining Boyle’s Law

Volume and Temperature – Charles’s Law The volume of a gas is directly related to its temperature, i.e. if T is increased, V will increase. V a T V = constant x T V1/T1 = V2/T2

VI. Explaining Charles’s Law

As T increases V increases

V1/T1 = V2/T2 V1 = 3.20 L V2 = 1.54 L T1 = 398.15 K T2 = ? V2 x T1 V1 A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V1/T1 = V2/T2 V1 = 3.20 L V2 = 1.54 L T1 = 398.15 K T2 = ? V2 x T1 V1 1.54 L x 398.15 K 3.20 L = T2 = = 192 K charles law demonstration - Google Videos Giant Koosh Ball in Liquid Nitrogen! - YouTube

Volume and Moles – Avogadro’s Law The pressure of a gas is directly related to the number of moles of gas, i.e. if n increases, V will increase. V a number of moles (n) V = constant x n V1/n1 = V2/n2

4NH3 + 5O2 4NO + 6H2O 1 mole NH3 1 mole NO At constant T and P Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure? 4NH3 + 5O2 4NO + 6H2O 1 mole NH3 1 mole NO At constant T and P 1 volume NH3 1 volume NO

Explaining Avogadro’s Law

Mixtures of Gases Dalton's law of partial pressure states: the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

The Combined Gas Law Boyle’s and Charles’s Laws can be combined into a convenient form.

The Ideal Gas Law The ideal gas law is a combination of the combined gas law and Avogadro’s Law. R = 0.082058 L atm/K mole

Ideal Gas Law 1 Boyle’s law: V a (at constant n and T) P Charles’ law: V a T (at constant n and P) Avogadro’s law: V a n (at constant P and T) V a nT P V = constant x = R nT P R is the gas constant PV = nRT

Numerical value of R PV = nRT PV (1 atm)(22.414L) R = = nT The conditions 0 0C and 1 atm are called standard temperature and pressure (STP). Numerical value of R Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L. PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)(273.15 K) R = 0.082057 L • atm / (mol • K)

Gas Law Problems There are many variations on gas law problems. A few things to keep in mind: Temperature must be in Kelvin (0C +273) Pressure=force/surface area Volume(available)=V(container)- V(particles)1L=1000cm3=10-3m3 If problem involves a set of initial and final conditions, use combined gas law. If problem only gives information for one set of conditions, use ideal gas law.

Density (d) Calculations m is the mass of the gas in g m V = PM RT d = M is the molar mass of the gas Molar Mass (M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L

What is the volume (in liters) occupied by 49.8 g of HCl at STP? T = 0 0C = 273.15 K P = 1 atm PV = nRT n = 49.8 g x 1 mol HCl 36.45 g HCl = 1.37 mol V = nRT P V = 1 atm 1.37 mol x 0.0821 x 273.15 K L•atm mol•K V = 30.6 L

PV = nRT n, V and R are constant nR V = P T = constant P1 T1 P2 T2 = Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)? PV = nRT n, V and R are constant nR V = P T = constant P1 = 1.20 atm T1 = 291 K P2 = ? T2 = 358 K P1 T1 P2 T2 = P2 = P1 x T2 T1 = 1.20 atm x 358 K 291 K = 1.48 atm

I. Sample Problem What’s the final pressure of a sample of N2 with a volume of 952 m3 at 745 torr and 25 °C if it’s heated to 62 °C with a final volume of 1150 m3?

II Sample Problem What volume, in mL, does a 0.245 g sample of N2 occupy at 21 °C and 750 torr?

III. Sample Problem A sample of N2 has a volume of 880 mL and a pressure of 740 torr. What pressure will change the volume to 870 mL at the same temperature?

Other Uses of Ideal Gas Law The ideal gas law can be used to find other physical values of a gas that are not as obvious. gas density, d = mass/volume gas molar mass, MW = mass/mole stoichiometry, via moles and a balanced equation

VI. Sample Problem Find the density of CO2(g) at 0 °C and 380 torr.

V. Sample Problem An unknown noble gas was allowed to flow into a 300.0 mL glass bulb until the P = 685 torr. Initially, the glass bulb weighed 32.50 g, but now it weighs 33.94 g. If the temperature is 27.0 °C, what’s the identity of the gas?