Gases
We are all familiar with the gaseous state – air.
Air represents a mixture of different gases. ● Mostly Nitrogen (78%), Oxygen (21%)
● Other elements/compounds gases at room temperature ● Hydrogen, Flourine, Chlorine, Noble gases (monatomic)
● Example compounds that are gases: Carbon Dioxide, hydrogen cyanide, carbon monoxide, carbon dioxide, methane, C2H4 (Ethylene), C3H8 (propane), nitrous oxide (N2O), sulfur dioxide, ammonia…
Note: 1) the compounds that are gases are composed entirely of non-metals; and 2) have simple molecular formulas – thus low molecular mass.
Gas molecules are relatively far apart, this results in several properties that differ from those of liquids and solids
● Gas expands to fill its container ● Gases are highly compressible
● Gases form homogenous mixtures regardless of relative properties of individual gases.
Properties of gases that can be measured are Pressure, temperature and volume
Pressure= force/area
● result of gravitational attraction:
● note that because individual molecules have such a tiny mass, the thermal energies of motion offset the gravitational attraction such that a thin layer of gas does not build up on the surface.
● However, gravity keep the gas (most, hydrogen and helium escape) around the Earth. ● Gas about the Earth decreases in density as altitude is gained.
● Mass of air above presses down – creating a pressure.
The concept of air pressure was confirmed by Torricellis – who devised a simple experiment with an inverted tube of mercury in a dish…taken to different altitudes. The mercury would rise or fall in the tube according to altitude.
760 mm of mercury would remain in the tube at sea level. 1 mm Hg = 1 Torr, the first unit of pressure.
Column of air about 1 m^2 in cross section extending through the atmosphere has a mass of about 10,000 kg. So, F = 9.8 * 10,0000 = 1 X 10^5 N. Divided by the area, the pressure is thus 1 X 10^5 N/m^2 = 1 X 10^5 Pa = 1 X 10^2 KPa
The Pascal is the SI unit of pressure. Other units of pressure:
and altitude)]; Torr = 1 mm Hg {Atmospheres (atm): defined as the pressure sufficient to support a column of mercury 760 mm in height. (US unit)}; PSI or Pounds per square inch (US unit)
1 atm = 760 mm Hg = 760 Torr = 1.01325 X 10^5 Pa = 101.325 KPa = 14.69 psi
Converting between units…a big part since we continue to use non-standard units.
Gas Laws – equations expressing relationships among four variables needed to define the physical condition (state) of a gas.
Temperature (T), Pressure (P), Volume (V) and the amount of gas (n) in moles.
Boyles Law: Pressure and Volume
● Boyle (1627-1691) investigated pressure of a gas and its volume
● First scientist to carry out experiments in which one variable was held constant while another was systematically changed.
● He used J- shaped tube and mercury (draw picture) to investigate air pressure. o see data on page 378….
o Graph – curve…large pressure and small volume to small pressure and large volume (put on board).
● Boyles Law: the volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure.
▪ V = constant X 1/P or PV = constant.
This relationship can be used to predict what happens to one variable if one of the original conditions is altered.
P1V1 = constant = P2V2
The product of pressure and volume of a contained gas at constant temperature and mole quantity is constant.
Consider a compressor on a refrigerator containing the old gas Freon: Initial conditions
P1 = 60 Torr, V1 = 1.5 L; If the final pressure is 180 Torr, what is the final Volume? Determine the final pressure above in atm, kPa and psi.
A fixed quantity of gas at 23 C exhibits a pressure of 748 torr and occupies a volume of 10.3 L. calculate the V of gas at 23 C if pressure is 1.88 atm.
A sample of gas with volume 1248 ft^3 at 0.988 atm and 28 C, calculate the pressure of the gas if its volume is decreased to 978 ft^3 while temp is held constant.
Charles Law: temperature-Volume
Hot air balloons…rise, because as air is heated, the greater thermal energy of the molecules makes them move farther apart. As temperature decreases, molecules are not as far apart – at some point, they are close enough so that the molecules interact in a manner that places them in the liquid or solid state.
The relationship between T and V was discovered by J. Charles (1746-1823). – he found that the volume of a fixed quantity of a gas at constant pressure increases linearly with T.
A plot of volume vs. T yields a straight line. Whereas the lines for individual gases are not the same, all lines, if extrapolated, run through the same point. This point was proposed by Lord Kelvin in 1848 as Absolute Zero – the point at which no further
compression could occur as a negative volume would then result. (Note: the Kelvin scale of temp…absolute zero = -273.15 C)
Note, however, that in reality, gases become liquids or solids at extremely low temp!
Charles Law in terms of the Kelvin Scale: The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature.
V = constant X T; or V/T = constant So, V1/T1 = V2/T2
Example: Problem example: Page 409, number 32. V = 25.0 L at 0 C, V = 50.0 L at ? C
V = 247 ml at 25 C, V = 255 ml at ? C V = 1.00 ml at -272 C, V = ? at 25 C
Intro Text Questions Page 408-409, 25-37 odd
Volume and Moles: Avogadro’s Law and the Ideal Gas Law ● Quantity-Volume relationship: Avagadro’s Law
● Louis Gay-Lussac observed (and stated) the law of combining volumes: at a given pressure and temperature, the volumes of gases that react with one another are in the ratios of small whole numbers. Example: two volumes of hydrogen and one volume of water = 2 volumes of water vapor.
● Avagadro proposed a hypothesis to explain this: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
● Avagadro’s Law – the volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas.
V = constant X n So, V/n = constant; thus, V1/n1 = V2/n2
the ratio of volume to moles at a given pressure and temperature is constant so volume 1 divided by mole quantity 1 equals volume 2 divided by mole quantity 2
Review of previous content:
Thus far, three laws that describe behavior of gases with 4 variables: ● P in Pascals; V in liters, T in Kelvin, n in moles
● Note that all variables not in the equation are being held constant.
Boyle’s Lax: PV = constant Charles’s Law: V/T = constant Avagadro’s Law: V/n = constant
These laws can all be combined into the Ideal Gas equation Solve for volume for each yields:
V = (1/P)(constant) V = (T)(constant) V =(n)(constant)
V = (Tn/P)(constant), or as it is commonly written, PV = nRT where R is the constant. Temperature must always be in K, units for P and V can vary but each gives a different R. List on the board; circle the one with atm, L, and K.
R = 0.08206 L-atm/K-mol R = 62.36 L-torr/K-mol R = 8.314 L-Pa/K-mol
Suppose we have 1.000 mol of an ideal gas at 1.000 atm and 0.00 C (273.15 K): V = nRT/P = (1.000 mol)(0.08206 L-atm/K-mol)/(1.000 atm) = 22.41 L
Combined Gas Law
The ideal gas law can be represented by Constant = PV/nT For a given mole quantity, P1V1/T1 = P2V2/T2
Intro P 408-9, 45-49
Key Concepts
● If you can rememebr PV = nRT then you can solve for any relationship that would be constant given a description of what is/isn’t changing.
Conditions of 0 C and 1 atm are called Standard Temperature and Pressure (STP). The volume occupied by 1 mol at STP is called the Molar Volume
The volume occupied by
any
(real) gas at STP is 22.4 L.
Specific stoichimetric relationships and the Molar Volume
● For reactions involving gases, the mole ratio is also the volume ratio. ● At STP, the volume of the gas is the coefficient X 22.4 L.
○ thus, if you have L of a gas at STP you can divide to get moles!
● By Le Chatlier’s Principle, if you increase the Pressure of a reaction, the reaction will proceed in the direction that reduces the MOLES (or liters) of gas.
See strategies on page 393 Brown and the sample exercises.
Note: The actual behavior of gases differs slightly from that predicted by the Ideal Gas Law because real gases have finite volume and molecules do interact. The Law deviates from actual behavior more as the pressure increases, temperature decreases.
● As pressure increases, the free space in which the molecules can move becomes a smaller fraction of the container volume, thus, volume tends to be slightly greater than predicted. ● As temperature decreases, molecules are deprived the kinetic energy necessary to avoid each
other! Thus, attractive forces between them become increasingly important.
● Equations have been developed to deal with deviations…but, we will not worry about them!
Dalton’s law of partial pressures
Dalton’s Law: For a mixture of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present.
The partial pressure is the pressure that gas would exert alone in the container. P = P1 + P2 + P3
Rearrange PV = nRT; P = nRT/V
Assuming each gas behaves ideally, the partial pressures can be represented as: Ptotal = n1RT/V + n2RT/V…etc. = ntotal(RT/V)
The volume of the individual gases particles and the forces among the particles is not important. What is important is the number of particles, not the identity.
Kinetic Molecular Theory of Gases – model to explain the behavior of an ideal gas ● Gases consist of tiny particles
● The size of particles is so small compared to the distance between them that the volume can be assumed to be zero for each particle.
● The particles are in constant random motion – colliding with the containing walls, causing pressure.
● Particles do not attract or repel each other.