SCH3U7 Quantitative Chemistry So far, we have looked at solids and liquids (solutions) Today we will look at gases and the laws that govern their behaviour in chemical reactions
4 Factors Affecting Gases Temperature (in K) Amount (in moles) Volume (in dm 3 ) Pressure (in a delightful variety of units)
Pressure Pressure is the force exerted on an object per unit of surface area. Standard:101.325 kpa = 1 atm = 760 mmhg = 760 torr
STP & SATP Standard pressure = 101.325 kpa = 1 atm = 760 mm Hg = 760 torr STP (standard temperature and pressure) = 0 0 C and 101.325 kpa SATP (standard ambient temperature and pressure) = 25 o C and 100 kpa
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Working with Gases The problem with gases is that they have no fixed volume. You must know the conditions (pressure and temperature) in which the gas is in to determine the volume. There are 3 laws which show us the relationship between Pressure, volume and temperature: Boyle s law Charles law Avogadro s law
Boyle s Law The pressure exerted by a given mass of gas at constant temperature is inversely proportional to the volume occupied by the gas Graphically: When pressure goes up, volume goes down PV = constant P1V1 = P2V2
What happens to marshmallows during a pressure change?
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Try it! 1. A balloon with a volume of 5.0 L is filled with air at 101.325 kpa pressure. The balloon is taken to Banff, where the atmospheric pressure is only 91 kpa (1386 m above sea level). If the temperature is the same in both places, what will be the new volume of the balloon? 5.6 dm 3 2. If a sample of gas has a volume of 100 ml when the pressure is 150 kpa, what is its volume when the pressure is increased to 200 kpa? (Temperature & mass are constant.) 75 cm 3 3. A balloon contains 5.0 L of air at a pressure of 149 kpa. If the temperature remains constant, what will be the pressure in the balloon if its volume is decreased to 4.0 L? 186 kpa
Charles Law At constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature Graphically: V/T = constant V1/T1 = V2/T2 Where T is in Kelvin
Charles Law
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Try it! 1. A balloon is filled with Helium gas to a volume of 1.2 L at a pressure of 105 kpa and a temperature of 15 degrees Celsius. If the pressure remains constant and the temperature rises to 30 degrees Celsius, calculate the new volume. 1.3 dm 3 2. If a sample of gas occupies 100 L at 200 K, what volume would it occupy at a temperature of 150 K? 75 dm 3 3. A balloon contains 5.0 L of air at 25 degrees Celsius. At what temperature would the balloon shrink to half the volume? Assume the pressure is held constant. 149 K
Gay-Lussac s Law The relationship between the pressure and temperature at constant volume Gas pressure is directly proportional to temperature if the volume and number of particles is constant.
Example About 10.0 L of H 2(g) is found to exert 97.0 kpa at 25.0 C. What would be the required temperature ( C) to change the pressure to standard pressure? V1 = 10.0 L T1 = 25.0 C P1 = 97.0 kpa T2 =? C P2 = 101.325 kpa P1 / T1 = P2 / T2 T2 = P2 T1 / P1 = (101.325)(298)/97.0 = 311 K
Try it! The pressure of oxygen gas inside a canister with a fixed volume is 5.00 atm at 298 K. What is the pressure of the oxygen gas inside the canister if the temperature changes to 263 K? 4.41 atm
Gay-Lussac s Law Pop Can Demo!
Avogadro s Law Yes, that same Avogadro! Avogadro s law states that gases with the same volume (at the same temperature and pressure) should have the same number of particles
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Avogadro s Law & Reactions We can use this law (and balanced equations) to predict amounts of gas needed or produced in a reaction CH4 + 2 O2 CO2 + 2 H2O This reaction is at constant T, P How much oxygen is needed to react with 10 dm 3 of CH4? 20 dm 3
Try it! What volume of CO2 is produced from complete combustion of 1000 dm 3 of C2H5OH (ethanol)? C2H5OH + 3 O2 2 CO2 + 3 H2O 2000 dm 3
The Ideal Gas Law So far, we have looked at 3 equations: If we combine them together: Tossing in a constant, R, we get: PV = nrt
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Simplify! If we are dealing with a fixed amount of gases (that is, moles aren t changing) then we can simplify the equation to:
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Molar Volume & Standard Conditions What is the volume of 1.0 mol of an ideal gas at 0 C at 101.325 kpa? 22.4 dm 3 is called MOLAR VOLUME, Vm This means that 1 mol of any gas should have a volume of 22.4 dm 3 at STP (0 C and 101.3 kpa)
Try it! Find moles of Cl2 using molar volume: 1 mol = 22.4 dm3 x 0.355 x=0.01585 Use the mole ratio to find moles of PCl 3. 6 moles Cl 2 = 4 moles PCl3 0.01585 x x = 0.010 mol of PCl3 Convert back to mass: m = nm = 0.010 x 137.32 = 1.45 g
Try it! Find moles of Mg using n = m/m n = 0.590 g/24.31 g/mol Find moles of O2 using equation: n = 0.02427 mol 0.01214 mol of O2 Convert moles of O2 into volume V = nrt/p = 0.283 dm 3
Summary