Gas Laws (1.4.4 – 1.4.8 )

Gas Laws

Gas Laws (1.4.4 1.4.8)Year 11 DP ChemistryRob SliderUnitsVolume (V)

SI unit: m3

1m3 = 1000 dm3 = 1000L

1dm3 = 1000cm3 = 1000mL

Pressure (P)

SI unit: Pa (pascal)

atm (atmosphere) the pressure acting on an object on Earth (standard pressure)

1atm = 1.013 x 105 Pa

1kPa = 103 Pa

1atm = 101.3 kPa

Temperature (T)

SI unit: K (Kelvin)

K = 0C + 273

0C = K - 273

Absolute zero = 0K or -2730C

F.P. (water) = 273K or 00C

Avogadros HypothesisLaw of Combining Gas VolumesThe volume of gases taking part in a chemical reaction show simple whole number ratios to one another when those volumes are measured at the same temperature (T) and pressure (P) Avogadros LawWhen gases are at the same T & P, the same volume of any gas has the same amount of particles (moles)Practice ProblemThe molar and volume ratios of the following reaction are 2:1:2 since the reactants and products are gases.

2H2(g) + O2(g) -----> 2H2O(g)

So, if there is 50mL of hydrogen gas, what are the volumes of oxygen gas and water vapour?50mL of hydrogen gas would react with 50 x = 25mL oxygen gas to produce 50mL of water vapourExampleThe molar ratio of the following reaction to produce ammonia gas is 1:3:2.

N2(g) + 3H2(g) -----> 2NH3(g)

Since all the reactants and products are gases, the mole ratio is the same as the ratio of the volumes of gases.So,10mL of nitrogen gas reacts with10 x 3 = 30mL of hydrogen gas to produce 10 x 2 = 20mL ammonia gas Note all of the reactants/products are gasesMolar Volume of a Gas:At stp, 1 mole of any gas occupies 22.4dm3

(stp is 273K and 101.3kPa)When liquid water undergoes electrolysis to produce hydrogen gas and oxygen gas, the volumes of hydrogen gas and oxygen gas are produced in the ratio of 2:1 but the volume of liquid water required does not follow this relationship since the liquid water is not a gas 2H2O(l) ----> 2H2(g) + O2(g)Under Standard Laboratory Conditions (S.L.C.) of 25oC (298K) and 101.3kPa (1 atm), 1 mole of liquid water has a volume of 18mL and will undergo electrolysis to produce 2 moles of hydrogen gas with a volume of 48.94L and 1 mole of oxygen gas with a volume of 24.47L. Source: http://www.ausetute.com.au/boylelaw.html

Exercises 1Find the volume occupied by 8g of oxygen gas at STP.

How many cm3 are there, at STP, in 1.72 g of phosphorous pentoxide (P2O5)?

What is the mass of 3.2 dm3 of nitrogen gas measured at STP?

Find the mass of 275 cm3 of phosphorous trichloride gas measured at STP.5.6 dm3

271 cm3

4.0 g

1.69 gBoyles Law (P vs V)At constant temperature:Volume of a given quantity of gas is inversely proportional to pressure: V= 1/P(E.g. if the volume of a gas is doubled, its pressure is halved.)ORThe product of a gass volume and its pressure is a constant : PV = constant, PV = k

So, at constant temperature for a given quantity of gas : PiVi = PfVfwhere,Pi and Vi are the initial pressure and volume, Pf and Vf are the final pressure and volume.

Note: pressures and volumes must be in the same units of measurement on each side.

Ideal vs. Real gasesAll gases approximate Boyle's Law at high temperatures and low pressures. Ideal Gas - a hypothetical gas which obeys Boyle's Law at all temperatures and pressures Real Gas - approaches Boyle's Law behaviour as the temperature is raised or the pressure lowered.

The following site has a calculator showing the relationship between pressure and volumehttp://www.ausetute.com.au/boylelaw.html

Boyles Law inversely proportional

Note how the volume changes in relation to the pressure exerted on a gas.

At a given temperature, this relationship is predictable for an ideal gas. Twice the pressure (P2) = half the volume (V2)Boyles Law - Graph

P vs V gives a parabolic shape

V vs 1/P gives a linear shapeExercises 2A sample of 200 cm3 of a gas has a pressure of 1.00 atm. The pressure is increased to 1.10 atm at a constant temperature. Find the new volume of the gas.

180 mL of a gas is compressed to 135 mL with no change in temperature. If the original pressure was 1.05 x 105 Pa, what is the new pressure?

2.70 dm3 of gas was originally at a pressure of 1.20 atm. Under constant temperature conditions, what pressure in kPa would be needed to change the volume to 2.50 dm3?182 cm3

1.40 x 105 Pa

131 kPa8Charles Law (T vs V)At constant pressure,Volume of a given quantity of gas is directly proportional to the absolute temperature : V T (in Kelvin)(E.g. if the temperature (K) is doubled, the volume of gas is also doubled.)ORThe ratio of its volume and the absolute temperature is a constant : V/T = constant, V/T = k So, at constant pressure: Vi/Ti = Vf/Tfwhere, Ti and Vi are the initial temperature and volume, Tf and Vf are the final temperature and volume. Note: Ti and Tf must be in Kelvin NOT Celsius. (temperature in Kelvin = temperature in Celsius + 273) (approximately) Ideal vs. Real gasesAll gases approximate Charles' Law at high temperatures and low pressures. Well above its condensation point, the volume of a real gas decreases linearly as it is cooled at constant pressure. However, as the gas approaches the condensation point, the decrease in volume slows down. At condensation, the gas turns to a liquid and, therefore, does not obey Charles LawAbsolute zero (OK) is the temperature where the volume of a gas would theoretically be zero if it did not condense.As a Real Gas is cooled at constant pressure from a point well above its condensation point, its volume begins to increase linearly. As the temperature approaches the gases condensation point, the line begins to curve (usually downward) so there is a marked deviation from Ideal Gas behaviour close to the condensation point. Once the gas condenses to a liquid it is no longer a gas and so does not obey Charles' Law at all.Absolute zero (0K, -273oC approximately) is the temperature at which the volume of a gas would become zero if it did not condense and if it behaved ideally down to that temperature.

Note how the volume changes in relation to temperature with constant pressure applied

At a given pressure, the pressure is directly proportional to the volume. (As temperature goes up, so does the pressure)Try this: fill a balloon with air, then put it in the freezer. What happened? How does this demonstrate Charles Law? Increase the temperature and the volume goes upSame pressureCharles Law - Graph

Volume is directly proportional to absolute temperature (linear)

Extrapolate this relationship back to absolute zero where the volume of a gas is theoretically zero and all molecular motion stops. Is this possible?Exercises 3A given sample of gas has a volume of 5.0 m3 at a temperature of -230C. What volume would it occupy at 300 K assuming the pressure remains constant?

360 cm3 of a gas is heated from 00C to 910C. Assuming no pressure change, find the new volume.

When heated under constant pressure, the volume of a gas increased from 2.42 dm3 to 2.67 dm3. If the initial temperature was 190C, find the final temperature in 0C.

6.0 m3

480 cm3

490CGay-Lussacs Law (P vs T)At constant volume,Pressure of a given quantity of gas is directly proportional to its temperatureORthe ratio of pressure and temperature is equal to a constant p/T = k (a constant)So, at constant volume: pi/Ti = pf/Tfwhere, pi and Ti are the initial pressure and temperature, pf and Tf are the final pressure and temperature. Note: pressures and temperature (Kelvin) must be in the same units of measurement on each side. Gay-Lussacs Law

Note the effect that increased temperature has on the pressure of the container which is at constant volume.An increase in temperature leads to increased pressureGay-Lussac - Graph

Note how pressure increases as the temperature increases as the average kinetic energy of the particles exerts more force on a container of constant volumeHow does this photo relate to Gay-Lussacs Law??

Exercises 4At a given temperature of 70C, a sample of gas has a pressure of 1.40 atm. If it is heated to 320 K, while the volume stays constant, what would the new pressure be?

The pressure of a gas is reduced from 102.5 kPa to 97.5 kPa. If the volume does not change, calculate the final temperature in Celsius if the initial temperature was 150C.

A sample of gas has an initial temperature of 100C. If the pressure is doubled, find the resulting temperature in Celsius assuming constant volume.1.60 atm

10C

2930CCombined Gas LawIf we combine all three individual gas laws into one, we can show how pressure, temperature and volume are related in one equation.pi Vi =pf Vf Ti TfThis equation can be used if there is more than one variable changing at once.Temperature must be in Kelvin. Pressure and volume can be in any unit as long as they are the same on both sides of the equation.Exercises 5A gas sample of 32.0 cm3 has a pressure of 1.05 atm and a temperature of 27.00C. What would be the volume of the gas at a pressure of 1.12 atm and a temperature of 7.00C?

At 0.75 atm and -230C a gas has a volume of 100 cm3. Find the volume at STP.

A sample of gas occupies 0.654 m3 at 1.14 atm and 90C. Calculate the volume at STP.

When measured at 103.5 kPa and 22.00C, some gas has a volume of 232 mL. What would be the volume in litres at STP?28 cm3

82 cm3

0.722 m3

0.219 LIdeal Gas LawAn Ideal Gas (perfect gas) is one which obeys Boyle's Law, Charles' Law and G-Ls Law exactly.

An Ideal Gas obeys the Ideal Gas Law (General gas equation):

PV = nRT

where, P=pressure, V=volume, n=moles of gas, T=temperature, R=the gas constant (dependent on the units of pressure, temperature and volume)

R = 8.314 J K-1 mol-1 P is in (Pa), V is in (m3), T is in (K) (note: J = m3Pa)R = 0.0821 L atm K-1 mol-1 P (atm), V (L), T (K)

Presumptions Is any gas ideal?Presumptions of an Ideal Gas according to Kinetic Theory of Gases: Gases consist of molecules which are in continuous random motion The volume of the molecules present is negligible relative to the total volume occupied by the gas Intermolecular forces are negligible Pressure is due to the gas molecules colliding with the walls of the container

Real Gases deviate from Ideal Gas Behaviour because at low temperatures the gas molecules have less kinetic energy (move around less) so they do attract each other at high pressures the gas molecules are forced closer together so that the volume of the gas molecules becomes significant compared to the volume the gas occupies

The Overall PresumptionUnder ordinary conditions, deviations from Ideal Gas behaviour are so slight that they can be neglected. A gas which deviates from Ideal Gas behaviour is called a non-ideal gas.

Gas Law SummaryCharles LawVi/Ti = Vf/TfBoyles LawPiVi = PfVfGay-Lussacs Lawpi/Ti = pf/TfIdeal Gas LawpV = nRTExercises 6 5 moles of a gas at 250C and 1.15 atm occupies what volume?

Magnesium reacts with hydrochloric acid to produce hydrogen gas and magnesium chlorideWhat volume of gas is evolved at 273 K and 1 atm pressure when 0.623 g of Mg reacts with 27.3 cm3 of 1.25 mol dm-3 hydrochloric acid.Calculate the volume occupied by the hydrogen gas evolved if it is collected at 220C and 1.12 atm pressure.If the actual volume of hydrogen collected was 342 cm3, what is the percentage yield?