The gaseous state

Chapter 5The gaseous state 1

Learning objectives 2To define pressure and its units

To use Boyles law, Charles law, combined gas law, Avogadro Law & ideal gas law

To solve stoichiometry problems involving gas volumes

To calculate the partial pressure & mole fractions of a gas in a mixture

To point out the kinetic theory of an ideal gas

To explain how & why a real gas is different from an ideal gas

Learning outcomes 3students will be able to

Solve quantitative problems related to define Boyles law, Charles law, combined gas law, Avogadro Law, ideal gas law, calculate the partial pressure & mole fractions of a gas in a mixture, solve stoichiometry problems involving gas volumes

Solve the qualitative problems related to define pressure, kinetic theory of an ideal gas, why a real gas is different from an ideal gas

5.1 Gas pressure and its measurement

Pressure : The force exerted per unit area.

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The SI unit for pressure is the pascal, Pa.

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Gas pressure -exercise

Gas pressure -exercise6[1]The pressure of a gas in a flask is measured to be 797.7 mmHg. What is this pressure in pascals and atmospheres?

[2] The barometric pressure measured outside an airplane at9 km was 259 mmHg. Calculate the pressure in kPa.

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A barometer is a device for measuring the pressure of the atmosphere.

A manometer is a device for measuring the pressure of a gas or liquid in a vessel.

5.2 Empirical Gas Laws Boyles LawThe volume of a sample of gas at constant temperature varies inversely with the applied pressure.

The mathematical relationship: In equation form:

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Boyles Law -Exercise 9[1] A volume of oxygen gas occupies 38.7 mL at 751 mmHg and 21C. What is the volume if the pressure changes to 359 mmHg while the temperature remains constant?

[2] You have a cylinder of argon gas at 19.8 atm pressure at 19C. The volume of argon in the cylinder is 50 L. What would be the volume of this gas if you allowed it to expand to the pressure of the surrounding air (0.974 atm)? Assume the temperature remains constant.

10[3] You fill a balloon with helium gas to a volume of 2.68 L at 23C and 789 mmHg. Now you release the balloon. What would be the volume of helium if its pressure changed to 632 mmHg but the temperature were unchanged?

11Charless Law

The volume of a sample of gas at constant pressure is directly proportional to the absolute temperature (K).

The mathematical relationship:In equation form:

Charless Law -Exercise 12[1]You prepared carbon dioxide by adding HCl(aq) to CaCO3. According to your calculations, you should obtain 79.4 mL of CO2 at 0C and 760 mmHg. How many milliliters of gas would you obtain at 27C?

[2] A mole of gas at 0C and 760 mmHg occupies 22.41 L. What is the volume at 20C and 760 mmHg?

13[3] Helium gas at 22C and 1 atm occupied a vessel whose volume was 2.54 L. At a pressure of 1atm, What volume would this gas occupy if it were cooled to liquid-nitrogen temperature (-197C)?

14Combined Gas Law

The volume of a sample of gas at constant pressure is inversely proportional to the pressure and directly proportional to the absolute temperature.

The mathematical relationship:In equation form:

Combined Gas Law -Exercise 15

16Avogadros Law

Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.

Standard Temperature and Pressure (STP)

The reference condition for gases, chosen by convention to be exactly 0C and 1 atm pressure.

The molar volume, Vm, of a gas at STP is 22.4 L/mol.

5.3 The ideal gas law 17Ideal Gas LawThe ideal gas law is given by the equationPV=nRT

The molar gas constant, R, is the constant of proportionality that relates the molar volume of a gas to T/P

The ideal gas law -Exercise18[1] A 50L cylinder of nitrogen has a pressure of 17.1 atm at 23C. What is the mass of nitrogen in the cylinder?

[2] According to your calculations, a reaction should yield 5.67 g of oxygen. What do you expect the volume to be at 23C and 0.985 atm?

19[3] An experiment calls for 3.5 mol of chlorine. Whatvolume will this be if the gas volume is measured at 34C and 4 atm?

[4] In an experiment, you fill a heavy-walled 5L flask with methane gas. If the flask contains 7.13 g of methane at 19C, what is the gas pressure?

20Gas Density and Molar MassUsing the ideal gas law, it is possible to calculate the moles in 1 L at a given temperature and pressure. The number of moles can then be converted to grams (per liter).

To find molar mass, find the moles of gas, and then find the ratio of mass to moles.

In equation form:

Gas Density -Exercise 21

5.4 Stoichiometry Problems Involving Gas volumes 22Use the ideal gas law to find moles from a given volume, pressure, and temperature, and vice versa.

Exercise [1] When a 2L bottle of concentrated HCl was spilled, 1.2 kg of CaCO3 was required to neutralize the spill. What volume of CO2 was released by the neutralization at 735 mmHg and 20C?

23[2] CaC2(s) + 2H2O(l ) Ca(OH)2(aq) + C2H2(g)Calculate the volume (in liters) of acetylene produced at 26C and 684 mmHg from 0.05 mol CaC2 and excess H2O.

[3] Mg(s) + 2HCl(aq) MgCl2(aq) + H2(g)Calculate the volume (in liters) of hydrogen produced at 33Cand 665 mmHg from 0.084 mol Mg and excess HCl.

5.5 Gas mixtures: Law of Partial Pressures 24Originally (left), flask A contains He at 152 mmHg and flask B contains H2 at 608 mmHg. Flask A is then filled with oil forcing the He into flask B (right). The new pressure in flask B is 760 mmHg.

25Partial PressureThe pressure exerted (used) by a particular gas in a mixture.

He at 152 mmHgH2 at 608 mmHg

Daltons Law of Partial PressuresThe sum of the partial pressures of all the different gases in a mixture is equal to the total pressure of the mixture:

P = PA + PB + PC + . . .

Total pressure=760 mmHg

Law of Partial Pressures -Exercise 26[1] A 100mL sample of air exhaled from the lungs is analyzed and found to contain 0.083g N2, 0.0194 g O2, 0.0064 g CO2, and 0.00441 g water vapor at 35C. What is the partial pressure of each component and the total pressure of the sample?

27[2] Calculate the total pressure (in atm) of a mixture of 0.0300 mol of helium and 0.02 mol of oxygen in a 4L flask at 20C. Assume ideal gas behavior.

[3] Calculate the total pressure (in atm) of a mixture of 0.02 mol of helium and 0.01 mol of hydrogen in a 2.5L flask at 10C. Assume ideal gas behavior.

5.6 Kinetic theory of an ideal gas 28Gases are composed of molecules whose sizes are negligible.

Molecules move randomly in straight lines in all directions and at various speeds.

The forces of attraction or repulsion between two molecules in a gas are very weak or negligible, except when the molecules collide.

When molecules collide with each other, the collisions are elastic.

5.The average kinetic energy of a molecule is proportional to the absolute temperature.

5.7 Molecular speeds; diffusion and effusion 29Diffusion: a gas spreads out through another gas to occupy the space uniformly.

30Effusion: The process by which a gas flows through a small hole in a container.

5.8 Real gases31At high pressure the relationship between pressure and volume does not follow Boyles law.

The volume of a sample of gas at constant temperature varies inversely with the applied pressure

32At high pressure, some of the assumptions of the kinetic theory no longer hold true:

At high pressure, the volume of the gas molecule (Postulate 1) is not negligible.

2.At high pressure, the intermolecular forces (Postulate 3) are not negligible.

Low pressure: the volume of molecules is small fraction of the total volume & can be ignored Intermolecular forces are weak

High pressure:The volume of molecules is a significant fractions of the total volume & cannot be ignored. The ideal gas law is no longer a good approximation

Checking outcomes 33To define pressure and its units

To use Boyles law, Charles law, combined gas law, Avogadro Law & ideal gas law

To solve stoichiometry problems involving gas volumes

To calculate the partial pressure & mole fractions of a gas in a mixture

To point out the kinetic theory of an ideal gas

To explain how & why a real gas is different from an ideal gas

Thank you