Gases © 2009, Prentice-Hall, Inc. Chapter 5: Gases (Zumdahl) John Bookstaver St. Charles Community College Cottleville, MO Chemistry, The Central Science,

Gases

© 2009, Prentice-Hall, Inc.

Chapter 5: Gases (Zumdahl)

John Bookstaver

St. Charles Community College

Cottleville, MO

Chemistry, The Central Science, 11th editionTheodore L. Brown; H. Eugene LeMay, Jr.;

and Bruce E. Bursten

Gases


Characteristics of Gases

• Unlike liquids and solids, gases– expand to fill their containers;– are highly compressible;– have extremely low densities.

Gases


• Pressure is the amount of force applied to an area.

Pressure

• Atmospheric pressure is the weight of air per unit of area.

P =FA

Gases


Units of Pressure

• Pascals– 1 Pa = 1 N/m2

• Bar– 1 bar = 105 Pa = 100 kPa

Gases


Units of Pressure

• mm Hg or torr–These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.

• Atmosphere–1.00 atm = 760 torr

Gases


Manometer

This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

Gases

Sample Problem: Manometer pressure

# 29, p 232If the open-tube manometer contains a nonvolatile silicone oil (density = 1.30

g/cm3) instead of mercury (density 12.6 g/cm3) what are the pressures in the flask as shown in parts a and b in torr, atm, and Pa?

SOLUTION: If the levels of Hg in each arm of the manometer are unequal, the difference in height in mm will be equal to the difference in pressure in mm Hg between the flask and the atmosphere. Which level is higher will tell us whether the pressure in the flask is less than or greater than atmospheric.

Pflask <Patm; Pflask= 760.-118 = 642 mm Hg= 642 torr.

642 torr x 1 atm = 0.845 atm.

760 torr

0.845 atm x 101.3 x 105 Pa = 8.56 x 104 Pa

1 atm


Gases


Standard Pressure

• Normal atmospheric pressure at sea level is referred to as standard pressure.

• It is equal to– 1.00 atm

– 760 torr (760 mm Hg)– 101.325 kPa– 14.7 psi (pounds per in2)

Gases


Boyle’s Law

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

Gases


As 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

Gases

Boyle’s Law• Since PV=k

• P1V1= k AND P2V2 = k


This equation can be used to solve for a missing value when 3 of the values are known.

THEN

P1V1 = P2V2

Where P1 & V1 are the pressure and volume occurring at the same time

Where P2 & V2 are the pressure and volume occurring at the same time, but a different time than P1 & V1

Gases

Boyle’s Law: Practice Problem

• Consider a 1.53 L sample of gaseous SO2 at a pressure of 5.6 x 103 Pa.

If the pressure is change to 1.5 x 104 Pa at a constant temperature, what will be the new volume of the gas?


V1

P1

P2

V2

(5.6 x 103 Pa) (1.53 L) = V2

1.5 x 104 Pa

V2 = 0.57 L

Gases


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.

• i.e.,VT

= k

Gases

Charles’s Law• Since V= k

T

V1= k AND V2 = k

T1 T2


This equation can be used to solve for a missing value when 3 of the values are known.

THENV1 = V2

T1 T2

Where V1 & T1 are the volume and temperature occurring at the same time

Where V2 & T2 are the volume and temperature occurring at the same time, but a different time than V1 & V2

NOTE: all temperatures for gas law calcs must be in K. (K = 273 + ⁰C)

Gases

Charles’s Law Sample Problem

A sample of gas at 15 C and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38 C and 1 atm?


T1 = 288K P1

V1

T2 = 311K P2

V2

V2 = (2.58 L) (311K)288K

V2 = 2.79 L

Gases


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

Gases


Ideal-Gas Equation

V 1/P (Boyle’s law)V T (Charles’s law)V n (Avogadro’s law)

• So far we’ve seen that

• Combining these, we get

V nTP

Gases


Ideal-Gas Equation

The constant of proportionality is known as R, the gas constant.

Gases


Ideal-Gas Equation

The relationship

then becomes

nTP

V

nTP

V = R

or

PV = nRT

Gases


Densities of Gases

If we divide both sides of the ideal-gas equation by V and by RT, we get

nV

PRT

=

Gases


• We know that– moles molecular mass = mass

Densities of Gases

• So multiplying both sides by the molecular mass () gives

n = m

PRT

mV

=

Gases


Densities of Gases

• Mass volume = density

• So,

Note: One only to know the molecular mass, the pressure, and the temperature to calculate the density of a gas

THIS EQUATION IS NOT ON THE AP FORMULA SHEET.

PRT

mV

=d =

Gases

Sample Problem: density of gases

Uranium hexafluoride is a solid at room temperature, but it boils at 56 C. Determine the density of uranium hexafluoride at 60. C and 745 torr.


T= 333K P = 745torr x 1 atm 760 torr

= 0.90826 atmd= (0.90826 atm) (352 g/mol)(0.08206 L*atm/mol*K)(333K)

d= 12.6 g/L

Gases


Molecular Mass

We can manipulate the density equation to enable us to find the molecular mass of a gas:

Becomes

PRT

d =

dRTP =

Gases


Dalton’s Law ofPartial Pressures

• 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 + …

Gases

Sample problem: partial pressureA mixture of 1.00 g H2 and 1.00 g He is placed in

a 1.00 L container at 27C. Calculate the partial pressure of each gas and the total pressure.

Copy solution from board.


Gases


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.

Gases


Kinetic-Molecular Theory

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

Gases


Main Tenets of Kinetic-Molecular Theory

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

Gases



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

Gases



Attractive and repulsive forces between gas molecules are negligible.

Gases



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.

Gases



The average kinetic energy of the molecules is proportional to the absolute temperature (Kelvin measures absolute temperature.)

Gases


Effusion

Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

Gases


Effusion

The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.

Gases


Diffusion

Diffusion is the spread of one substance throughout a space or throughout a second substance.

Gases


Graham's Law (re: rate of effusion)KE1 KE2=

1/2 m1v12 1/2 m2v2

2=

=m1

m2

v22

v12

m1

m2

v22

v12

=v2

v1

=

Gases

Graham’s Law of Effusion

• “the rate of effusion is equal to the inverse ratio of the masses”


Gases

Graham’s Law of Effusion: Sample Problem

#82, p 236: the rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under identical experimental conditions, the effusion rate of pure methane gas is 47.8 mL/min. What is the molar mass of the unknown gas?

SOLUTION:


Gases


Deviations from Ideal Behavior

The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

Gases


Real Gases

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

Gases


Real Gases

Even the same gas will show wildly different behavior under high pressure at different temperatures.

Gases


Corrections for Nonideal Behavior

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

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

Gases


The van der Waals Equation: predicts behavior of gases at low temps & high pressures

) (V − nb) = nRTn2aV2(P +

Note: the greater the molecular mass and complexity, the greater the deviation from ideal .

Gases

Kinetic Energy• We can calculate the kinetic energy

(KE) of a molecule or a mole of molecules.

• KEmolecule = ½ mv2

• KEmole = RT


2

3

Gases

Sample Problem: Kinetic Energy


Gases © 2009, Prentice-Hall, Inc. Chapter 5: Gases (Zumdahl) John Bookstaver St. Charles Community College Cottleville, MO Chemistry, The Central Science,

Documents

manometer pressure

constant pressure

pressureatmospheric

boyles lawthe volume

units of pressurepascals1

charless lawthe volume

new volume

constant temperature