Chapter 11Gases

The Gas Laws of Boyle, Charles and Avogadro

The Ideal Gas Law

Gas Stoichiometry

The Kinetic Molecular Theory of Gases

Effusion and Diffusion

Collisions of Gas Particles with the Container Walls

Intermolecular Collisions

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States of Matter

SolidLiquid Gas

We start with gases because they are simpler than the others.

Pressure (force/area, Pa=N/m2):

A pressure of 101.325 kPa is needed to raise the column of Hg 76 cm (760 mm).

“standard pressure”

760 mm Hg = 760 torr = 1 atm = 101.325 kPa

V1 / V2 = T1 / T2 (fixed P,n)

P1V1 = P2V2 (fixed T,n)

Boyle’s Law

Charles’ Law

V x P = const

V / T = const

V / n = const (fixed P,T)Avogadro

1662

1787

1811 n = number of moles

Boyle’s Law: Pressure and Volume

The product of the pressure and volume, PV, of a sample of gas is a constant at a constant temperature:

PV = k = Constant

(fixed T,n)

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Pressure and Volume compared in two ways

Directly P α V and Indirectly P α 1 / V

Charles’ Law: T vs VAt constant pressure, the volume of a sample of gas is a linear function of its temperature.

V = bT

T(°C) =273°C[(V/Vo)]

When V=0, T=-273°C

Charles’ Law: T vs V

The Absolute Temperature Scale

Kelvin temperature scale

T (Kelvin) = 273.15 + t (Celsius)

Gas volume is proportional

to Temperature

V = Vo ( 1 + ) t 273.15oC

Charles’ Law: The Effect of Temperature on Gas Volume

V1 / V2 = T1 / T2 (at a fixed pressure and for a fixed amount of gas)

V vs T

Avogadro’s law (1811)

V = an

n= number of moles of gas

a = proportionality constantFor a gas at constant temperature and pressure the volume

is directly proportional to the number of moles of gas.

V1 / V2 = T1 / T2 (at a fixed pressure)

P1V1 = P2V2 (at a fixed temperature)

Boyle’s Law

Charles’ Law

V = kP -1

V = bT

V = an (at a fixed pressure and temperature)Avogadro

V = nRTP-1

n = number of moles

PV = nRT

ideal gas law

an empirical law

Example

At some point during its ascent, a sealed weather balloon initially filled with helium at a fixed volume of 1.0 x 104 L at 1.00 atm and 30oC reaches an altitude at which the temperature is -10oC yet the volume is unchanged. Calculate the pressure at that altitude .

n1 = n2

V1 = V2

P1V 1

n1T 1

=P2V 2

n2T 2

P1

T 1

=P2

T 2

P2 = P1T2/T1 = (1 atm)(263K)/(303K)

STP (Standard Temperature and Pressure)

For 1 mole of a perfect gas at O°C (273K)

(i.e., 32.0 g of O2; 28.0 g N2; 2.02 g H2)

nRT = 22.4 L atm = PV

At 1 atm, V = 22.4 L

STP = standard temperature and pressure

= 273 K (0o C) and 1 atm

The Ideal Gas Law

What is R, universal gas constant?

the R is independent of the particular gas studied

R=8 . 3145 N m mol−1 K−1

R=8 . 3145 J mol−1 K−1

PVR

nT= (1atm)(22.414L)

(1.00 mol)(273.15 K)=

R= 0 .082057 L atm mol -1 K-1

R= (101 . 325 x 10 3 N m -2)(22 . 414 x 10 -3 m 3)(1 . 00 mol )(273 . 15K )

PV = nRT

PV = nRT

ideal gas law constants

R=8 .3145 J mol−1 K−1

R= 0 .082057 L atm mol -1 K-1

Example

What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L, 1.00 atm and 30 8 C?

1) Use PV = nRT; n=PV/RT.

2) Find the number of moles.

3) Use the atomic weight to find the mass.

n = PV/RT =

(1 atm) (10,000 L) (293 K)-1 (0.082 L atm mol-1 K-1)-1

= 416 mol

(416 mol)(1.0 g mol-1) = 416 g

Example

What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L, 1.00 atm and 30 8 C?

Use volumes to determine stoichiometry.

Gas Stoichiometry

The volume of a gas is easier to measure than the mass.

Gas Density and Molar Mass

RearrangemV

=PRT

M

mV

=d=PRT

M

PV=nRT

PV=mM

RT

See that n = m/M which in words is moles (n) equals a given mass (m) divided by the molar mass (M).

Think about the units. Moles = grams / (grams per mole)

Gas Density and Molar Mass

Example

Calculate the density of gaseous hydrogen at a pressure of 1.32 atm and a temperature of -45oC.

RearrangemV

=PRT

M

mV

=d=PRT

M

Remember to use units of Kelvin for the temp!

Density = mass / volume = (pressure*molar mass) / (gas constant R*temperature) = (1.32 atm * 2.016 g/mol for H2) / (0.0821)*(273-45 K)

= 0.142 g/L (grams per liter) Liters is the volume herebecause of the units of the constant R.

2NH4ClO4 (s) → N2(g) + Cl2 (g) + 2O2 (g) + 4 H2 (g)

• The Ideal Gas Law is an empirical relationship based on experimental observations.– Boyle, Charles and Avogadro.

• Kinetic Molecular Theory is a simple model that attempts to explain the behavior of gases.

The Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases1. A pure gas consists of a large number of identical molecules separated by distances that are large compared with their size. The volumes of the individual particles can be assumed to be negligible (zero).

2. The molecules of a gas are constantly moving in random directions with a distribution of speeds. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

3. The molecules of a gas exert no forces on one another except during collisions, so that between collisions they move in straight lines with constant velocities. The gases are assumed to neither attract or repel each other. The collisions of the molecules with each other and with the walls of the container are elastic; no energy is lost during a collision.

4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

Speed Distribution

Temperature is a measure of the average kinetic energy of gas molecules.

Real Gases

• Ideal Gas behavior is generally conditions of low pressure and high temperature

PV = nRT

PV = 1.0

nRT