Chapter 10Gases and their properties

2-1213, 14, 21, 2327-3031-33, 35, 37, 39, 41, 4349, 51, 53, 57, 59, 6163-65, 67, 69, 71, 7577, 81, 83, 85, 87, 9193, 95, 96, 97104, 108, 110, 115, 116, 117, 121, 123, 129

Recommended problems – Ch 10

Gases Assume shape and volume of container Highly compressible Easily diffuse/mix

Liquids Assume shape of container Not very compressible Easily mix

Solids Keep shape Incompressible Diffusion (if any) occurs very slowly

The nature of matter

States of Matter

The fundamental difference between states of matter is the distance between particles. Because in the solid and liquid states particles are closer together, we refer to them as condensed phases.

The States of Matter

The state of a substance at a particular temperature and pressure depends on two antagonistic entities:

--- kinetic energy of the particles (proportional to the temperature of the system)--- potential energy between particles (IM attractions/repulsions)

Pressure – a defining characteristic of a gas

Pressure is the amount of force applied to an area.

Atmospheric pressure is the weight of air per unit area.

P =FA

Pascals◦ 1 Pa = 1 N/m2

Atmospheres◦ 1 atm = 14.7 lb/in2 (psi) = 101325 Pa

Torr (or mm Hg)◦ 760 torr = 760 mm Hg = 1 atm

Units of Pressure

Normal atmospheric pressure at sea level.

Standard Pressure

• It is equal to1.00 atm760 torr (760 mm Hg)101.325 kPa

Kinetic-Molecular Theory

A model that aids in our understanding of what happens to gas particles as environmental conditions change.

1. Gases consist of large numbers of molecules that are in continuous, random motion.

2. The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

3. Attractive and repulsive forces between gas molecules are negligible.

Tenets of Kinetic-Molecular Theory

Tenets of Kinetic-Molecular Theory

4. Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

Tenets of Kinetic-Molecular Theory

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

What happens to pressure when volume decreases?

What happens when volume increases?

How does KMT explain gas behavior?

What happens to volume when temperature increases?

What happens when temperature decreases?

How does KMT explain gas behavior?

What happens to volume when amount of gas (moles) increases?

What happens when amount of gas decreases?

How does KMT explain gas behavior?

Boyle Charles Avogadro

Review of General Gas Laws

Boyle’s Law

The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

PV = constant [when temperature and amount of gas (moles) stays the same]

As volume decreases, the pressure increases (such that product = constant)

P1V1 = P2V2

Boyle’s Law

P and V areinversely proportional

A plot of V versus P results in a curve.Since

V = k (1/P)

This means a plot of V versus 1/P will be a straight line.

PV = k

Charles’s Law

The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

A plot of V versus T will be a straight line.

VT

= k

V/T = constant (or V = kT)

As temperature increases, volume increases.

V1/T1 = V2/T2

Charles’s Law

Avogadro’s Law

The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.

Mathematically, this means V = kn

So far we’ve seen that:V 1/P (Boyle)V T (Charles)V n (Avogadro)

We can combine these to get:

V

Ideal Gas Equation

nTP

The relationship

Ideal Gas Equation

then becomes

which has the more familiar form: PV = nRT

nTP

V

nTP

V = R

Ideal Gas Equation

… where the constant of proportionality is known as R, the gas constant.

k (Boltzmann constant) = 1.381 x 10-23 J/K

Note units!

From the ideal gas law, PV=nRT, remember that

So you can use this general equation in many instances…

Using the general gas law

nTPV

R

22

22

11

11

TnVP

TnVP

The long cylinder of a bicycle pump has a volume of 1131 cm3. The outlet valve is sealed shut and the pump handle is pushed down until the volume of the air is 517 cm3. What is the resulting pressure inside the pump?

A scientist studying the properties of hydrogen at low temperatures takes a volume of 2.50 L hydrogen at atmospheric pressure and a temperature of 25.00oC and cools the gas at constant pressure to -200.00oC. What is the resulting volume of the gas?

A 5.00 L sample of Argon gas is known to contain 0.965 mol. If the amount of gas is increased by the addition of 0.835 moles, what will the new volume be (at an unchanged temperature and pressure)?

Using the general gas law

Nitric acid acts on solid copper to give NO2 and dissolved copper ions according to the equation:

Cu(s) + 4H+(aq) + 2NO3-(aq) 2NO2(g) + Cu2+(aq) + 2 H2O(l)

Suppose that 6.80 g Cu is consumed in excess acid and that the NO2 is collected at a pressure of 0.970 atm and a temperature of 45 oC. What volume of NO2 is produced?

answer 5.76L

Stoichiometry using the Ideal Gas Equation

We can derive the density of a gas, if we divide both sides of the ideal-gas equation by V and by RT.

We know thatmoles molecular mass (M) = mass

n x M = m

Density of a Gas

nV

PRT

=

Density of a GasMultiplying both sides by the molecular mass ( ) gives

And since D = m/V (=g/L) D = PM/RT

Therefore, we can know the density of a gas if we measure its pressure and temperature.

PRT

mV

=

We can manipulate the density equation to enable us to find the molar mass of an known gas:

Molar Mass

becomes

PRT

d =

dRTP =

The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.

In other words Ptotal = P1 + P2 + P3 + …

Dalton’s Law of Partial Pressures

For a mixture of gases, we sometimes use a quantity called the mole fraction, Χ:

Xi = ni/ntotal

The relationship between partial pressure, pi, and Xi is:

pi = Xi Ptotal

Mole fractions

Partial Pressures

When one collects a gas over water, there is water vapor mixed in with the gas.To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

From Kinetic-Molecular Theory, all molecules have the same average kinetic energy at the same temperature (regardless of their mass).

The KE of a molecule is given by ½ mv2

The avg KE depends upon T(Kelvin)

The avg KE of all molecules in a gas is related to urms

Molecular speed

The relationship between mass, urms, and T is:urms =

where

Note: urms has a slightly different value from the average speed

Root-mean-square speed

Boltzmann Distributions

Diffusion

The spread of one substance throughout a space or throughout a second substance.

Effusion

The escape of gas molecules through a tiny hole into an evacuated space.

Graham’s law of effusion

Real Gases

In the real world, the behavior of gases conforms to the ideal-gas equation only at certain conditions, such as relatively high temperature and low pressure.

Deviations from Ideal Behavior

The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature.

Deviations from Ideal Behavior

The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.

Corrections for Nonideal Behavior

The corrected ideal-gas equation is known as the van der Waals equation.

Whereas ideal gas equation posits

van der Waals accounts for attraction btw molecules AND finite volume of molecules by

van der Waals Equation

The van der Waals Equation

) (V − nb) = nRTn2aV2(P +