Gases

Chapter 14

Review from Chapter 13

Pressure



Describing gases

: To describe a gas fully, you need to state the 4 measurable quantities: 1. Volume 3. Temperature   2. # of molecules 4. Pressure

Definition:

surface The force per unit of area on a

Equation:

Measuring Pressure

  A

barometer

is a device used to measure atmospheric pressure Introduced by Torricelli with experiments involving mercury (Hg)   He determined the air (atmosphere) could support a column of Hg 760 mm high The height of the Hg depends on the air pressure   What would happen to the height of the column in the mountains? What would happen to the height of the column 100ft under water?

Units of Pressure

     Pressure can be measured in many units

Most common

: mm of Hg

1 mm Hg = 1 torr

(in honor of Torricelli) Atmospheric Pressure at sea level and 0 o C is 760 mm Hg Other units of pressure include: Atmospheres (atm) and Pascal (Pa)

CONVERSIONS

760 mm Hg= = 760 torr = 1 atm = 29.92 in Hg = 14.7 psi = 101325 Pa = 101.325 kPa

Standard Temperature and Pressure (STP)

 To compare volume of gases, it is necessary to know the

pressure

at which the

volume

is measured  For purpose of comparison, scientists have agreed on standard conditions 

STP= 1 atm pressure and 0 o C

Review Calculation

 The atmospheric pressure in Denver is 0.830 atm. Express this in mmHg and kPa.

Boyle’s Law

  Robert Boyle studied the relationship between

pressure

and

volume

Boyle’s Law:

States that the

volume

of a fixed mass of gas varies inversely with the

pressure

at

constant temperature

 Can be written as:

P 1 V 1 = P 2 V 2

Practice Problem

P 1 V 1 = P 2 V 2

 A sample of oxygen gas has a volume of 150. mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the

temperature remains constant

?

    P 1 = V 1 = P 2 = V 2 =

Charles’s Law

  Jacques Charles studied the relationship between volume and temperature

Charle’s Law:

States that the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature .

 Can be written as:

Kelvin Temperature?

  The Kelvin scale is K= 273 + o C -273 o C is the lowest possible temperature to achieve (

absolute zero

)  Absolute zero is given the value of zero on the Kelvin scale

Practice Problem

A sample of neon gas occupies a volume of 752 mL at 25 o C. What will the volume of the gas occupy at 50 o C if the pressure remains constant?     V 1 = T 1 = V 2 = T 2 =

Gay-Lussac’s Law

 Gay-Lussac determined the relationship between temperature and pressure 

Gay-Lussac’s Law:

The pressure of a fixed mass of gas at

constant volume

varies directly with the Kelvin temperature  Can be written as:

Practice Problem

 The gas in an aerosol can is at a pressure of 3.00 atm at 25 o C. Directions on the can warn the user not to keep in a place where the temperature exceeds 52 o C. What would the pressure in the can be at the 52 o C?     P 1 = T 1 = P 2 = T 2 =

The Combined Gas Law

  A gas sample often undergoes changes in temperature, pressure and volume. Combining all three (Boyle’s, Charles’, and Gay-Lussac’s) will give us a valid equation  Can be written as:

Practice Problem

 A helium filled balloon has a volume of 50.0 L at 25 o C and 1.08 atm. What volume will it have at 0.855 atm and 10.

o C?       P 1 = T 1 = V 1 = P 2 = T 2 = V 2 =

Avogadro’s Principal

   Equal volumes of gases at the same temperature and pressure contain equal numbers of particles  From Chapter 11: 1 mole= 6.02 x10 23 particles

Molar volume

for a gas is the volume that one mole occupies at 0.00

o C and 1.00 atm pressure.

(STP conditions)

Avogadro showed experimentally that

one mole

any gas will occupy a volume of

22.4L at STP.

of 

Conversion Factor:

22 .

4 L 1 mol

Practice Problem

 What volume will 0.416 g of krypton gas occupy at STP?

The Ideal Gas Law

 Describes the physical behavior of an ideal gas in terms of pressure, volume, temperature, and the number of moles of gas present

PV=nRT



R

represents an experimentally determined constant that is referred to as the ideal gas constant

(depends on the units used for pressure)

Numerical Values of the Gas Constant, R

Units of R L  atm mol  K L  kPa mol  K L  mmHg mol  K Numerical Value of R 0.0821

8.314

62.4

Units of P atm kPa mm Hg Units of V L L L Units of T K Units of

n

mol K K mol mol

Real vs. Ideal Gas

 An

ideal gas

is one whose particles take up no space and have no intermolecular attractive forces  In the real world, no gas is truly ideal.



Real gases

deviate most from ideal gas behavior at extremely high pressures and low temperatures

Practice Problem

 What is the pressure in atm exerted by a 0.500 mol samples of nitrogen gas in a 10.0L container at 298K?

Applying the Ideal Gas Law

 Rearranging the PV=

n

RT equation allows you to also calculate the molar mass and density of a gas sample if the mass of the sample is known  Recall from Chapter 12-

n

(moles) =

m

(mass)/

M

(molar mass)  D= Density (mass/volume) M  mRT PV D  DRT P  MP RT

Practice Problem

 Calculate the grams of N 2 gas present in a 0.600 L sample kept at 1.00 atm pressure and a temperature of 22.0

o C.

Gas Stoichiometry

Why are we using stoichiometry?

  Suppose we need to determine the volume of something other than our known (the given), we can apply stoichiometry to achieve the desired products/reactants “Plan of Attack”   Start with a

BALANCED

equation. Use stoichiometry first to get into the desired substance  Use the Ideal Gas Law (IGL) to convert into volume of that substance Gas volume A  moles A  moles B  mass B Mass A  moles A  moles B  gas volume B

Practice Problem

 What volume of chlorine gas at 38 o C and 1.63 atm is needed to react completely with 10.4 g of sodium to form NaCl?

(

Cl 2 + 2Na



2NaCl

)