Monday February 6, 2012

1. MondayFebruary 6, 2012 (The Ideal Gas Law)

2. Bell RingerMonday, 2-6-12 A chemist has two identical 5.00 liter containers. Into one of these he puts hydrogen gas and into the other he puts nitrogen gas. He brings both containers to 40oC and establishes pressures of 2.00 atm in each. If the chemist put 6.00 moles of hydrogen gas into one of the containers, how much nitrogen gas did he put into the other container? … by what law? 6.00 moles Avogadro’s Law

4. Announcements • I will be available this afternoon after school until 4:45.

5. The Ideal Gas Law • Remember, there are three quantities that are needed to describe a gas sample: • Pressure • Volume • Temperature • A gas sample can be further characterized using a fourth quantity: • the number of moles of the gas.

6. The Ideal Gas Law • The number of molecules or moles present will always affect at least one of the other three quantities. • Ex) If the number of molecules is increased for a sample at constant volume and temperature, the collision rate increases, therefore, the pressure increases. • Ex) If the pressure and temperature were kept constant while the number of molecules increased, the volume would increase. • Gas pressure, volume, temperature, and the number of moles are all interrelated.

7. The Ideal Gas Law • There is a mathematical relationship that describes the behavior of a gas sample for any combination of these conditions: • The ideal gas law is the mathematical relationship among pressure, volume, temperature and the number of moles of a gas.

8. The Ideal Gas Law V = nRT/P or PV = nRT V = volume N = moles T = temperature P = pressure R = the ideal gas constant

9. 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. • The volume of one mole of an ideal gas at STP (1 atm and 273.15 K) is 22.414 10 L. - use this value in ideal gas law calculations when the volume is in liters, the pressure is in atmospheres, and the temperature is in kelvins. • See Table 11-1 (next slide) for the value of R when other units for n,P,V, and T are used:

10. The Ideal Gas Constant

11. The Ideal Gas Constant • The ideal gas law can be applied to determine the existing conditions of a gas sample when three of the four variables, P,V,T, and n, are known. • It can also be used to calculate the molar mass or density of a gas sample. • Be sure to match the units of the known quantities and the units of R. • You will be using R = 0.0821 L•atm/(mol•K).

12. The Ideal Gas Constant • Your first step in solving any ideal gas law problem should be to check the known values to be sure you are working with the correct units. • If necessary, you must convert volumes to liters, pressures to atmospheres, temperatures to kelvins, and masses to numbers of moles before using the ideal gas law.

13. The Ideal Gas Constant Sample Problem • What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K? Given: V of N2 = 10.0 L n of N2 = 0.500 mol T of N2 = 298 K Unknown: P of N2 in atm PV = nRT P = nRT/V P = (0.500 mol)(0.0821 Latm/molK)(298 K)/10.0 L P = 1.22 atm

14. The Ideal Gas Constant Sample Problem • What is the volume, in liters, of 0.250 mol of oxygen gas at 20.0°C and 0.974 atm pressure? Given: P of O2 = 0.974 atm n of O2 = 0.250 mol T of O2 = 20.0°C+ 273.2 = 293.2 K Unknown: V of O2 in L V = nRT/P V = (0.250 mol O2)(0.0821 Latm/molK)(293.2K)/0.974 atm V = 6.17 L O2

15. The Ideal Gas Constant Sample Problem • What mass of chlorine gas, Cl2, in grams, is contained in a 10.0 L tank at 27°C and 3.50 atm of pressure? Given: P of Cl2 = 3.50 atm V of Cl2 = 10.0 L T of Cl2 = 27°C+ 273.2 = 300 K Unknown: mass of Cl2 in grams PV = nRT n = PV/RT n = (3.50 atm)(10.0 L Cl2)/(0.0821 Latm/molK)(300 K) n = 1.42 mol Cl2 Mass of Cl2 = 1.42 mol x 70.90 g/mol = 101 g Cl2

16. Worksheet The Ideal Gas Law