Regents Chemistry



Honors Chemistry –Kinetic Molecular Theory and Gas Laws

Pressure and Temperature

You will define pressure in terms of the molecular theory.

• You will define and explain the significance of STP.

• You will define and measure temperature.

• You will convert between degrees Celsius and Kelvin

A. Pressure:

Gas Pressure – The force resulting from the collisions of billions of gas particles on an object

Atmospheric pressure – the force resulting from the collisions of air molecules with objects

Units: (atmospheric pressure at sea level)

1 atm = 760 torr = 760 mmHg = 101.3 kPa (Please note, you will only use KPa in Physics)

B. Temperature:

A measure of the average kinetic energy of the particles in the substance (do not use the term speed)

1. Celsius Scale:

i. 0°C is the ice-water (solid-liquid) equilibrium temperature at exactly 1 atmosphere pressure. (Freezing point)

ii. 100°C is the water-steam (liquid-gas) equilibrium temperature at exactly 1 atmosphere pressure. (Boiling point)

2. Kelvin or Absolute Scale:

i. 0 K = absolute zero

(Theoretical point where all motion stops)

ii. Conversions from Celsius to Kelvin:

K = °C + 273

0°C = 273K

100°C = 373K

Special note: Temperature is how average Kinetic Energy is measured. We only use the term speed when we compare different particles with identical kinetic energies. You will use the following equation in physics where kinetic energy depends upon the mass and velocity of body. 

KE = ½ mv2

Smaller particle will move faster

C. Standard Temperature and Pressure (STP):

Because it is difficult to weigh quantities of a gas, the quantity of a gas is usually expressed in units of volume rather than weight (or mass). However, since the volume of a gas varies considerably with its temperature and pressure, the quantity cannot be specified by volume alone. The temperature and pressure must also be known. In order to avoid the inconvenience of stating temperature and pressure every time a gas volume is given, certain standard conditions of temperature and pressure (STP) have been adopted.

Standard conditions of pressure (STP):

Temperature = 0°C = 273K

Pressure = 760 torr = 760 mm Hg = 1 atm = 101.3 kPa (Please note, you will only use KPa in Physics)

II: Kinetic Theory and The Nature of Gases

• You will describe the kinetic theory of gases and compare the behavior of an “ideal” gas to a “real” gas.

• You will be able to describe the effects of various factors on pressure, volume and temperature.

A. Kinetic Theory of Gases:

A study of behavior of gases has led to a model called the kinetic theory of gases.

Assumptions of the kinetic theory of gases:

1. All gases are composed of individual particles (atoms or molecules)

2. The particles are “small spheres” with negligible (virtually no) volume. Between the particles is empty space.

3. The particles are in continuous random motion. They move in a straight-line path until they are deflected by some force. They collide with the walls of a container. The collisions with the walls cause the pressure exerted by the gas.

4. No forces of attraction or repulsion are considered to exist between the particles.

5. Collisions of gas particles may transfer energy from one particle to another, but the total kinetic energy remains the same. The average Kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas.

Remember, the kinetic theory of gases is theoretical and describes the “ideal” behavior of a gas. No “real” gas behaves exactly like this theoretical model. In real gases, the following factors contribute to the deviations from the ideal model:

1. Real gases have a small but significant volume.

2. Gas particles do exert some attractive force on each other.

BIG IDEA: These factors become quite significant in gases at low temperature, when they have relatively low kinetic energy, or under high pressures, when the particles are relatively close together.

Real Gases that are the closest to ideal behavior due to small volume and weak IMF:

1. Hydrogen (H)

2. Helium (He)

B. General Observations of P, V, T and Gases:

1. Adding or Removing Gas:

At a constant temperature, the pressure in the container is directly proportional to the number of particles in the container. Students have trouble identifying indirect and direct relationships. When using PV=nRT. Remember variables on the same side of an equation have indirect relationships, whereas, variables on different sides of the equal sign have direct relationships.

2. Changing the Size of the Container:

At a constant temperature, the pressure in a container is inversely proportional to the size of the container.

3. Changing the Temperature:

• At a constant volume, the pressure in a container is directly proportional to the temperature.

• T results in a P

• T is typically the independent variable

• Note T and P are inversely proportional

• Students often say if T decreases P decreases - this is wrong. If T decreases, P will increase and vice versa. They are indirectly related.

III: The Gas Laws

You will describe and apply Dalton’s law, Avogadro’s law, Boyle’s law, Charles’ law, Gay-Lussac’s law, the combined gas law and the ideal gas law.

You will solve for various temperatures, volumes, pressures, and numbers of moles of a gas under given conditions using the gas laws.

A. Dalton’s Law of Partial Pressures:

Many gases exist as mixtures, such as air. It is a mixture of O2, N2, CO2, plus trace amounts of other gases. The particles in a gas at the same temperature have the same average kinetic energy. Gas pressure depends only on the number of gas particles in a given volume and their average kinetic energy. The kind of particle is unimportant. If we know the pressure exerted by each gas in a mixture, we can add the individual pressures and get the total gas pressure.

Partial Pressure: The pressure exerted by each individual gas is a gaseous mixture. Each gas acts as if it is the only gas present.

Dalton’s Law of Partial Pressures:

At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures.

Ptotal = P1 + P2 + P3 +.....

Sample Problems:

1. What is the total pressure of a gas mixture that contains the following gases with the following pressures?

PO2 = 150 mmHg

PN2 = 350 mmHg

PHe = 200 mmHg

Total: 700 mmHg

2. Assuming that air is 25.00% oxygen and 75.00% nitrogen, if the pressure of the air in the room is 750.0 mmHg, what is the partial pressure of the oxygen gas in the room?

P O2 = (750.0 mmHg)(.2500) = 187.5 mmHg

P N2 = (750.0 mmHg)(.7500) = 562.5 mmHg

B. Moles and Molar Volume: A mole is a unit used to compare quantities of different substances.

a. 1 mole = 6.02 x 1023 particles This is also called Avogadro’s number.

b. molar volume: Since the mole contains a fixed number of particles, by Avogadro’s Hypothesis, 1 mole of any gas will occupy the same volume at a given temperature and pressure. At STP molar volume = 22.4 liters/1 mol

Calculations and Practice Problems

1. What volume of oxygen gas at STP contains 1.35 moles?

Solution: 1.35moles x 22.4L/mole = 30.24L

Sig. Figs. = 30.2L

2. What is the volume of 4.15 x 1022 molecules of a gas at STP?

Solution:

4.15E22molecules x 1mol/6.02E23 molecules x 22.4L/mol= 1.54L

3. What is the number of moles in 175 ml of a gas (at STP)?

Solution:

0.175L x 1mol/22.4L = 7.81 x 10–3 moles

Ideal Gas Law:

Describes the relationship among the four variables P, V, T and n, where n indicates the number of moles.

PV = nRT

Since rarely does the number of moles of gas change when altering P, V or T this breaks down to the combined gas law in most instances.

What is R? It is the ideal gas constant.

P = Pressure in atm

V = Volume in L

n = Number of moles

T = Temperature in K

R = 0.0821 atm*L/mol*K

Where did that come from?

R = PV/ nT

At STP R = (1.00atm)(22.4L)/(1.00mol)(273K)

Combined Gas Law: (This is just one rearrangement of PV=nRT)

When either pressure or temperature varies, the other factor almost always changes also. To deal with problems in which pressure and temperature change simultaneously, the equations of Boyle’s and Charles’ Laws are combined into a “Combined Gas Law” equation.

Equation:

P1 = initial pressure P2 = final pressure

V1 = initial volume V2 = final volume

T1 = initial temp. (K) T2 = final temp. (K)

P1V1 = P2V2

T1 T2

Remember to convert to K and check that all the pressure values are in the same unit!!!

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