Atomic Mass and Atomic Mass Number · 2019-08-25 · the gas temperature is 27ºC. You double the...

© 2017 Pearson Education, Inc. Slide 18-1

Atomic Mass and Atomic Mass Number

The mass of an atom is determined primarily by its most

massive constituents: protons and neutrons in its nucleus.

The sum of the number of protons and neutrons is called

the atomic mass number:

A = number of protons + number of neutrons

1 u = 1.66 ×10–27 kg

The atomic mass, in u,

is close, but not exactly,

equal, to the atomic

mass number.

u is the atomic mass unit:


Moles and Molar Mass

By definition, one mole of

matter, be it solid, liquid, or gas,

is the amount of substance

containing Avogadro’s number

NA of particles.

NA = 6.02 ×1023 mol–1

The number of moles in a

substance containing N basic

particles is

One mole of helium, sulfur,

copper, and mercury.


Moles and Molar Mass

The molar mass of a substance is the mass of 1 mol

of substance.

The molar mass, which we’ll designate M, has units g/mol. kg/mol should be used in SI calculations.

The number of moles in a system of mass m consisting of atoms or molecules with molar mass M is

𝑛 =𝑚

𝑀

For example, water has a molar mass

of 18 g/mol. Therefore, 63 grams of

water would contain 3.5 moles of

water or 2.1 x 1024 molecules of

water.


Which contains more molecules, a mole of

hydrogen gas (H2) or a mole of oxygen gas (O2)?

A. The hydrogen

B. The oxygen

C. They each contain the same number of

molecules.

D. Can’t tell without knowing their temperatures.

QuickCheck


Example 1

How many moles of oxygen is in 100 g of oxygen gas?

Also, how many molecules are there in 100 g of oxygen

gas?


Ideal Gases

The ideal-gas model is one in which we model atoms

in a gas as being hard spheres.

Such hard spheres fly through space and occasionally

interact by bouncing off each other in perfectly elastic

collisions.

Experiments show that the ideal-gas model is quite

good for gases if two conditions are met:

1.The density is low (i.e., the atoms occupy a volume

much smaller than that of the container), and

2.The temperature is well above the condensation

point.


The Ideal-Gas Law

The pressure p, the volume V,

the number of moles n and the

temperature T of an ideal gas

are related by the ideal-gas

law as follows:

where R is the universal gas constant: R = 8.31 J/mol K

Or:

where N is the number of molecules and kB is

Boltzman’s constant: kB = 1.38×10–23 J/K


If the volume of a sealed container of gas is

decreased, the gas temperature

A. Increases.

B. Stays the same.

C. Decreases.

D. Not enough information

to tell.

QuickCheck


Two identical cylinders, A and B, contain the same type

of gas at the same pressure. Cylinder A has twice as

much gas as cylinder B. Which is true?

A. TA < TB

B. TA = TB

C. TA > TB

D. Not enough information

to make a comparison.

QuickCheck


Two cylinders, A and B, contain the same type of gas at the

same temperature. Cylinder A has twice the volume as

cylinder B and contains half as many molecules as cylinder

B. Which is true?

A. pA = 4pB

B. pA = 2pB

C. pA = pB

D. pA = pB

QuickCheck

14

12


Example 2

100 g of oxygen gas is distilled into an evacuated 600 cm3

container. What is the gas pressure at a temperature of

150ºC?


Example 3

An “empty” aluminum scuba tank contains 11.0 L of air at

21ºC and 1 atm. When the tank is filled rapidly from a

compressor, the air temperature is 42ºC and the gauge

pressure is 2.10 x 107 Pa. What mass of air was added?


Ideal Gases

All ideal-gas problems involve a gas in a sealed container.

The number of moles (and number of molecules) will not change during a problem.

In that case,

If the gas is initially in state i, characterized by the state variables pi, Vi, and Ti, and at some later time in a final state f, the state variables for these two states are related by


The temperature of a rigid (i.e., constant-volume),

sealed container of gas increases from 100ºC to

200ºC. The gas pressure increases by a factor of

A. 2

B. 1.3

C. 0.8

D. 0.5

QuickCheck


A quantity of an ideal gas is contained in a balloon. Initially

the gas temperature is 27ºC. You double the pressure on the

balloon and change the temperature so that the balloon

shrinks to one-quarter of its original volume. What is the new

temperature of the gas?

A. 54ºC

B. 27ºC

C. 13.5ºC

D. –123ºC

QuickCheck


Example 4

In an automobile engine, a mixture of air and vaporized gasoline is

compressed in the cylinders before being ignited. A typical engine has

a compression ratio of 9.00 to 1. If the quantity of gas is constant, what

is the final temperature of the compressed gas if its initial temperature

is 27ºC and the initial and final pressures are 1.00 atm and 21.7 atm,

respectively?


In-class Activity #1

What is the volume of a container that holds exactly 1 mole

of an ideal gas at STP (standard temperature and

pressure, defined to be 0ºC and 1 atm)?

The van der Waals equation

• The model used for the ideal-gas equation ignores the

volumes of molecules and the attractive forces between them.

• The van der Waals equation is a more realistic model:

© 2016 Pearson Education Inc.

pV-diagrams

• These show isotherms, or constant-temperature curves, for a

constant amount of an ideal gas.


© 2016 Pearson Education, Inc.

This p-V diagram shows three

possible states of a certain amount

of an ideal gas. Which state is at

the highest temperature?

A. state #1

B. state #2

C. state #3

D. Two of these are tied for highest temperature.

E. All three of these are at the same temperature.

QuickCheckp

V

1

2

3

O

pV-diagrams

• A pV-diagram for a nonideal gas shows isotherms for

temperatures above and below the critical temperature Tc.

• At still lower temperatures

the material might undergo

phase transitions from

liquid to solid or from gas

to solid.



Why does a gas have pressure?

The pressure in a gas is due to collisions of the molecules with the

walls of its container.

The steady rain of a vast number of molecules striking a wall each

second exerts a measurable macroscopic force.

The gas pressure is the force per unit area (p = F/A) resulting from

these molecular collisions.

Pressure in a Gas

The figure shows a molecule that

collides with a wall, exerting an

impulse on it.The average force on

the wall is


The pressure is the average force on the walls of the

container per unit area:

(N/V ) is the number density of the gas in m−3.

Note that the average velocity of many molecules

traveling in random directions is zero.

vrms is the root-mean-square speed of the molecules,

which is the square root of the average value of the

squares of the speeds of the molecules:

Pressure in a Gas

Molecular speeds and kinetic energies

The root-mean-square speed of the molecules in a gas is:

Thus the average kinetic energy of the molecules is given by


Total kinetic energy of n moles of a gas is given by


A rigid container holds both hydrogen gas (H2)

and nitrogen gas (N2) at 100ºC. Which statement

describes their rms speeds?

A. vrms of H2 < vrms of N2

B. vrms of H2 = vrms of N2

C. vrms of H2 > vrms of N2

QuickCheck


A rigid container holds both hydrogen gas (H2) and

nitrogen gas (N2) at 100ºC. Which statement

describes the average translational kinetic energies

of the molecules?

A. Ktr of H2 < Ktr of N2

B. Ktr of H2 = Ktr of N2

C. Ktr of H2 > Ktr of N2

QuickCheck


Example 5

A container holds helium at a pressure of 200 kPa and a

temperature of 60.0ºC. What is the rms speed of the helium

atoms?


Consider two specimens of ideal gas at the same temperature.

Specimen #1 has the same total mass as specimen #2, but the

molecules in specimen #1 have greater molar mass than the

molecules in specimen #2. In which specimen is the total

translational kinetic energy of the entire gas greater?

A. specimen #1

B. specimen #2

C. The answer depends on the particular mass of gas.

D. The answer depends on the particular molar masses.

E. Both C and D are correct.

QuickCheck


Example 6

What is the average translational kinetic energy of an ideal-

gas molecule at 27ºC? What is the total random translational

kinetic energy of the molecules in 1 mole of this gas?


In-class Activity #2

What is the total translational kinetic energy of the molecules

in 1.0 mol of gas at STP?

Atomic Mass and Atomic Mass Number · 2019-08-25 · the gas temperature is 27ºC. You double the...

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