Videos 1. Crash course Partial pressures: YuWy6fYEaX9mQQ8oGr 2. Crash couse Effusion/Diffusion:

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1 Videos 1. Crash course Partial pressures: YuWy6fYEaX9mQQ8oGr 2. Crash couse Effusion/Diffusion: zzyuwy6fyeax9mqq8ogr 3. Crash course Ideal gas law: zyuwy6fyeax9mqq8ogr

2 Chapter 3 Section 3 Counting Atoms Relating Mass to Numbers of Atoms The Mole The mole is the SI unit for amount of substance. A mole (abbreviated mol) is the amount of a substance that contains as many particles as there are atoms in exactly 12 g of carbon-12. Avogadro s Number Avogadro s number is the number of particles in exactly one mole of a pure substance.

3 Chapter 3 Section 3 Counting Atoms Relating Mass to Numbers of Atoms, continued Molar Mass The mass of one mole of a pure substance is called the molar mass of that substance. Molar mass is usually written in units of g/mol. The molar mass of an element is numerically equal to the atomic mass of the element in atomic mass units.

4 Chapter 3 Section 3 Counting Atoms Relating Mass to Numbers of Atoms, continued Gram/Mole Conversions Chemists use molar mass as a conversion factor in chemical calculations. For example, the molar mass of helium is 4.00 g He/mol He. To find how many grams of helium there are in two moles of helium, multiply by the molar mass g He 2.00 mol He = 8.00 g He 1 mol He

5 Chapter 3 Section 3 Counting Atoms Relating Mass to Numbers of Atoms, continued Conversions with Avogadro s Number Avogadro s number can be used to find the number of atoms of an element from the amount in moles or to find the amount of an element in moles from the number of atoms. In these calculations, Avogadro s number is expressed in units of atoms per mole.

6 Avogradro s Number How many particles of He are in 2 moles of He?

7 Section 3 Gas Volumes and the Ideal Gas Law Molar Volume of a Gas Recall that one mole of a substance contains a number of particles equal to Avogadro s constant ( ). example: one mole of oxygen, O 2, contains diatomic molecules. According to Avogadro s law, one mole of any gas will occupy the same volume as one mole of any other gas at the same conditions, despite mass differences. The volume occupied by one mole of gas at STP is known as the standard molar volume of a gas, which is L (rounded to 22.4 L).

8 Section 3 Gas Volumes and the Ideal Gas Law Molar Volume of a Gas, continued Knowing the volume of a gas, you can use the conversion factor 1 mol/22.4 L to find the moles (and therefore also mass) of a given volume of gas at STP. example: at STP, 1 mol 5.00 L of gas mol of gas 22.4 L You can also use the molar volume of a gas to find the volume, at STP, of a known number of moles or a known mass of gas. example: at STP, 22.4 L mol of gas 17.2 L of gas 1 mol

9 Section 3 Gas Volumes and the Ideal Gas Law Molar Volume of a Gas, continued Sample Problem G a. What volume does mol of gas occupy at STP? b. What quantity of gas, in moles, is contained in 2.21 L at STP?

10 Section 3 Gas Volumes and the Ideal Gas Law Molar Volume of a Gas, continued Sample Problem G Solution a. Given: mol of gas at STP Unknown: volume of gas Solution: Multiply the amount in moles by the conversion factor, 22.4 L. 1 mol 22.4 L mol of gas 1.53 L of gas 1 mol

11 Section 3 Gas Volumes and the Ideal Gas Law Molar Volume of a Gas, continued Sample Problem G Solution, continued b. Given: 2.21 L of gas at STP Unknown: moles of gas Solution: Multiply the volume in liters by the conversion factor, 1 mol L 1 mol 2.21 L of gas mol of gas L

12 Section 3 Gas Volumes and the Ideal Gas Law The Ideal Gas Law All of the gas laws you have learned thus far can be combined into a single equation, the ideal gas law: the mathematical relationship among pressure, volume, temperature, and number of moles of a gas. It is stated as shown below, where R is a constant: PV = nrt

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14 Section 3 Gas Volumes and the Ideal Gas Law The Ideal Gas Law, continued The Ideal Gas Constant In the equation representing the ideal gas law, the constant R is known as the ideal gas constant. Its value depends on the units chosen for pressure, volume, and temperature in the rest of the equation. PV (1 atm)( L) L atm R nt (1 mol)( K) mol K

15 Remember Standard Temperature and Pressure

16 Section 3 Gas Volumes and the Ideal Gas Law Numerical Values of the Gas Constant

17 Section 3 Gas Volumes and the Ideal Gas Law The Ideal Gas Law, continued Sample Problem I What is the pressure in atmospheres exerted by a mol sample of nitrogen gas in a 10.0 L container at 298 K?

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19 Section 3 Gas Volumes and the Ideal Gas Law The Ideal Gas Law, continued Sample Problem I Solution Given: V of N 2 = 10.0 L n of N 2 = mol T of N 2 = 298 K Unknown: P of N 2 in atm Solution: Use the ideal gas law, which can be rearranged to find the pressure, as follows. PV nrt P nrt V

20 Section 3 Gas Volumes and the Ideal Gas Law The Ideal Gas Law, continued Sample Problem I Solution, continued Substitute the given values into the equation: P nrt V P (0.500 mol)( L atm)(298 K) 10.0 L 1.22 atm

21 Versions of ideal gas law

22 Section 4 Diffusion and Effusion Diffusion and Effusion The constant motion of gas molecules causes them to spread out to fill any container they are in. The gradual mixing of two or more gases due to their spontaneous, random motion is known as diffusion. Effusion is the process whereby the molecules of a gas confined in a container randomly pass through a tiny opening in the container.

23 Section 4 Diffusion and Effusion Graham s Law of Effusion From the equation relating the kinetic energy of two different gases at the same conditions, one can derive an equation relating the rates of effuses of two gases with their molecular mass: rate of effusion of rate of effusion of A B M M B A This equation is known as Graham s law of effusion, which states that the rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

24 Section 4 Diffusion and Effusion Graham s Law

25 Section 4 Diffusion and Effusion Graham s Law of Effusion, continued Sample Problem J Compare the rates of effusion of hydrogen and oxygen at the same temperature and pressure.

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27 Section 4 Diffusion and Effusion Graham s Law of Effusion, continued Sample Problem J Solution Given: identities of two gases, H 2 and O 2 Unknown: relative rates of effusion Solution: The ratio of the rates of effusion of two gases at the same temperature and pressure can be found from Graham s law. rate of effusion of rate of effusion of A B M M B A

28 Section 4 Diffusion and Effusion Graham s Law of Effusion, continued Sample Problem J Solution, continued Substitute the given values into the equation: rate of effusion of rate of effusion of A B MB g/mol g/mol 3.98 M 2.02 g/mol 2.02 g/mol A Hydrogen effuses 3.98 times faster than oxygen.

29 Effusion rate Calculate the ratio of diffusion rates for Carbon monoxide and carbon dioxide.

30 Effusion rate Calculate the ratio of diffusion rates for Carbon monoxide and carbon dioxide.

31 Practice Problems Calculate the number of moles of gas contained in a 3.0 L container at 3.00 x 10 2 K with a pressure of 1.50 atm.

32 Practice Problems What is the pressure in atmospheres by a mol sample of nitrogen gas in a 10.0 L container at 298 K?

33 Practice Problems What volume at STP will be occupied by mol of methane, CH 4?