GASES Chapter 10

Example: Air 78% nitrogen 21% oxygen Molecules only take up about 0.1% of total volume (the rest is empty space)  extremely low density Gases:  easily compressible fluid  no fixed volume or shape  always form homogeneous mixtures with other gases

PRESSURE Pressure is the force that acts on a given area. Units: SI unit – Pascal = Pa (N.m -2 ) Other units: 1 atm = 760 torr = 760 mm Hg = kPa 1 bar = 100 kPa

Atmospheric pressure Due to gravity the atmosphere exerts a downward force and hence a pressure on the earth’s surface.

Mercury Barometer Atmospheric pressure can be measured using a barometer.

If P gas < P atm : P gas + P h2 = P atm If P gas > P atm : P gas = P atm + P h2 Manometer Measures the pressure of gases not open to the atmosphere.

THE IDEAL GAS LAWS Charle’s Law (T-V Relationship) Boyle’s Law (P-V Relationship) Avogadro’s Law (n-V Relationship)

BOYLE’S LAW (P-V RELATIONSHIP) (T and n constant) The volume of a fixed amount of gas maintained at constant temperature is inversely proportional to pressure.

Demonstration of Boyle’s Law:

The volume of a fixed amount of gas maintained at constant pressure is directly proportional to it absolute temperature. CHARLE’S LAW (T-V RELATIONSHIP) (P and n constant)

The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of gas. AVOGADRO’S LAW (n-V RELATIONSHIP) (T and P constant)

IDEAL GAS EQUATION (T and n constant) (P and n constant) Thusor

R is the gas constant. R = L.atm.mol -1.K -1 R = m 3.Pa.mol -1.K -1 R = J.mol -1.K -1 If we have a gas under two sets of conditions, then See examples in textbook constant

If 1 mole of ideal gas at 1 atm and 0 o C ( K), then: V = L STP for gases: 1 atm and 0 o C ( K) V = (1 mol)( L.atm.mol -1.K -1 )( K) (1 atm)

Comparison of an ideal gas to some real gases at STP

Rearrange: DENSITY OF GASES PV = nRT E.g.:  (CO 2 ) >  (O 2 )  used in fire extinguishers

Gas Mixtures and Partial Pressures DALTON’S LAW OF PARTIAL PRESSURES DALTON’S LAW OF PARTIAL PRESSURES: In a gas mixture the total pressure is given by the sum of partial pressures of each component. Since gas molecules are so far apart, we can assume they behave independently. Each gas in the mixture obeys the ideal gas equation:

Consider one gas in a mixture of gases: P 1 = n 1 RT/V P t = n t RT/V mole fraction   

Example A miniature volcano can be made in the lab with ammonium dichromate. When ignited it decomposes in a fiery display. (NH 4 ) 2 Cr 2 O 7 (s)  N 2 (g) + 4H 2 O(g) + Cr 2 O 3 (s) If 5.0 g of ammonium dichromate is used, and if the gases from this reaction are trapped in a 3.0 L flask at 23 o C, what is the total pressure (in atm) of the gas in the flask? (Ignore the air in the flask) Challenge: Do not ignore the air in the flask.

To find the amount of gas produced by a reaction  collect gas by displacing a volume of water. Note: there is water vapour mixed in with the gas. To calculate the amount of gas produced, we need to correct for the partial pressure of the water vapour: E.g. 2KClO 3 (s)  2KCl(s) + 3O 2 (g) Raise or lower container until the water levels inside and outside are the same. P water = 0.031atm at 25 o C

Kinetic Molecular Theory Why do gases behave as they do? Look at molecular level. Assumptions: Gases consist of a large number of molecules in constant random motion. Volume of individual molecules negligible compared to volume of container. Intermolecular forces (forces between gas molecules) negligible. Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. Average kinetic energy of molecules is proportional to temperature.

Magnitude of pressure given by how often and how hard the molecules strike the container. Absolute temperature is a measure of the average kinetic energy of its molecules. Molecules also collide with each other and can transfer energy between each other. E k = 1 / 2 mu 2 u = root mean square speed u  average speed

EXERCISE Using Kinetic Molecular Theory explain what happens when: 1) the volume of a gas increase at constant temperature? 2) the temperature of a gas increase at constant volume?

Different types of gas molecules of that have the same kinetic energy do not necessarily move at the same speed. Why?

Effusion The escape of gas molecules through a tiny hole into an evacuated space When will a gas molecule move through the hole? The faster molecules move, the greater the probability that they will effuse.

Graham’s Law of Effusion: Consider two gases under identical PV-conditions with effusion rates r 1 and r 2, then: i.e. rate of effusion is inversely proportional to the square root of its molar mass.

Two balloons are filled to the same volume. After 48 hours Explain!

Diffusion The spread of a substance throughout a space or throughout a second substance. A gas molecule will move in a straight line till it collides with the walls of the container or with other gas molecules  results is a fairly random path. Mean free path The lower the mass of a molecule, the faster it can move and the faster it can diffuse

Real Gases Real gases do not behave ideally under high pressure Consider 1 mol of gas and low temperatures. T ~ 300 K N2N2

Why do we see these deviations? Ideal gas molecules are assumed to occupy no space and have no intermolecular forces between them. Real molecules do occupy space – the higher the pressure the more critical this becomes. Intermolecular forces play a bigger role when molecules are closer together. Pressure appears lower. Also at lower temperature, less kinetic energy to overcome these attractive forces.

Corrections for Non-ideal Behaviour Van der Waals equation for real gases: Ideal gas equation: Correction for volume of molecules b Van der Waals constant b is a measure of the volume occupied by a mole of gas molecules. b Unit for b: L/mol

Correction for molecular attraction n 2 a/V 2 The pressure is reduced by the factor n 2 a/V 2 (n/V) 2 Attractive forces between pairs of molecules increases as the square of the number of molecules per unit volume i.e. (n/V) 2 a Van der Waals constant a reflects how strongly gas molecules attract each other. a Unit for a: L 2 atm/mol 2

a and b generally increase with an increase in molecular mass

Example Consider 1.00 mol of CO 2 (g) stored in a 3.00 L container at 0.0 o C. What will the pressure predicted by the ideal gas equation be? And the van der Waals equation? Explain.