Measuring the Pressure of a Gasand

Gas Laws of Boyle, Charles and Avogadro

Chemistry 142 B

Autumn Quarter, 2004

J. B. Callis, Instructor

Lecture #13

The Three States of Matter for the Element Bromine

Important Characteristics of Gases

1) Gases are highly compressible An external force compresses the gas sample and decreases its volume: removing the external force allows the gas volume to increase.2) Gases are thermally expandable When a gas sample is heated, its volume increases. When it is cooled its volume decreases.3) Gases have low viscosity Gases flow much easier than liquids or solids.4) Most Gases have low densities Gas densities are on the order of grams per liter whereas liquids and solids are grams per cubic cm, 1000 times greater.5) Gases are infinitely miscible

Gases mix in any proportion such as in air, a mixture of many gases.

Helium He 4.0

Neon Ne 20.2

Argon Ar 39.9

Hydrogen H2 2.0

Nitrogen N2 28.0

Nitrogen Monoxide NO 30.0

Oxygen O2 32.0

Hydrogen Chloride HCl 36.5

Ozone O3 48.0

Ammonia NH3 17.0

Methane CH4 16.0

Substances that are Gases under Normal Conditions

Substance Formula MM(g/mol)

Pressure of the Atmosphere• Called “atmospheric pressure,” or the force

exerted upon us by the atmosphere above.• A measure of the weight of the atmosphere

pressing down upon us.

Area

ForcePressure

• Measured using a barometer - A device that can weigh the atmosphere above us.

The Effect of Atmospheric Pressure on objects at the earth’s surface

A Mercury Barometer

Construct a Barometer using Water

Density of water =

Density of Mercury =

Height of water column = Hw

Hw =

Hw =

A Closed End Manometer

An Open ended Manometer

A J-tube similar to the one used by Boyle

Common Units of Pressure

Unit Atmospheric Pressure Scientific Field

pascal (Pa); 1.01325 x 105 Pa SI unit; physics, kilopascal(kPa) 101.325 kPa Chemistry

atmosphere (atm) 1 atm* Chemistry millimeters of mercury 760 mmHg* Chemistry, medicine, ( mm Hg ) biology

torr 760 torr* Chemistry

pounds per square inch 14.7 lb/in2 Engineering ( psi or lb/in2 )bar 1.01325 bar Meteorology, chemistry, physics

Problem 13-1: Converting Units of Pressure

Problem: A chemist collects a sample of Carbon dioxide from the decomposition of limestone (CaCO3) in a closed end manometer, the height of the mercury is 341.6 mm Hg. Calculate the CO2 pressure intorr, atmospheres, and kilopascals.Plan: The pressure is in mmHg, so we use the conversion factors fromThe preceding table to find the pressure in the other units.Solution:

(a) PCO2 (torr) =

converting from mm Hg to torr:

converting from torr to atm:

(b) PCO2( atm) =

converting from atm to kPa:

(c) PCO2(kPa) =

Boyle’s Law : P - V RelationshipPressure is inversely proportional to volume at fixed

temperature and fixed amount:

P = or V = or PV=KKV

KP

Where:

P is the pressure exerted by the sample on the surroundings.

V is the volume occupied by the sample.

K is a constant of proportionality.

Problem 13-2: Applying Boyles LawProblem: A gas sample at a pressure of 1.23 atm has a volume of 15.8 cm3, what will be the volume if the pressure is increased to 3.16 atm?Plan: We begin by converting the volume that is in cm3 to mL and thento liters, then we do the pressure change to obtain the final volume.Solution:

V1 (cm3)

V1 (ml)

V1 (L)

V2 (L)

1cm3 = 1 mL

1000mL = 1L

x P1/P2

P1 = 1.23 atm P2 = 3.16 atmV1 = 15.8 cm3 V2 = unknownT and n remain constant

V1 =

V2 =

Deviations From Boyle’s Law

Extrapolation of PV Data to Zero Pressure Yields Ideal Behavior

Charles’s Law : V - T RelationshipVolume is directly proportional to temperature at

fixed pressure and fixed amount:

V = CT or = CV T

Where:

V is the volume occupied by the sample.

T is the temperature in degrees Kelvin.

C is a constant of proportionality.

Charles’s Law Behavior for Several Gases

Problem 13-3: Charles Law

A sample of carbon monoxide, a poisonous gas, occupies 3.20 L at 125 oC. Calculate the temperature (oC) at which the gas will occupy 1.54 L if the pressure remains constant.

V1 = T1 =

V2 = T2 =

T2 =

T2 = oC =

Problem 13-4: Amonton’s Law

Problem: A copper tank is compressed to a pressure of 4.28 atm at a temperature of 0.185 oF. What will be the pressure if the temperature is raised to 95.6 oC?Plan: The volume of the tank is not changed, and we only have to deal with the temperature change, and the pressure, so convert to SI units, and calculate the change in pressure from the Temp.and Pressure change.Solution:

T1 =

T2 =

P2 =

Avogadro’s Law : V - n RelationshipVolume is directly proportional to moles of gas at

fixed pressure and temperature:

V = Bn or = BV n

Where:

V is the volume occupied by the sample.

n is the number of moles of gas.

B is a constant of proportionality.

Problem 13-5: Avogadro’s Law

Problem: Sulfur hexafluoride is a gas used to trace pollutant plumes in the atmosphere, if the volume of 2.67 g of SF6 at 1.143 atm and 28.5 oC is 2.93 m3, what will be the mass of SF6 in a container whose volume is543.9 m3 at 1.143 atm and 28.5 oC?Plan: Since the temperature and pressure are the same, it is a V - n problem, so we can use Avogadro’s Law to calculate the moles of the gas, then use the molecular mass to calculate the mass of the gas.Solution: Molar mass SF6 = 146.07 g/mol

Standard Temperature and Pressure (STP)

A set of Standard conditions have been chosen to make it easier to understand the gas laws, and gas behavior.

Standard Temperature = 00 C = 273.15 K

Standard Pressure = 1 atmosphere = 760 mm Mercury

At these “standard” conditions 1.0 mole of a gas willoccupy a “standard molar volume”.

Standard Molar Volume = 22.414 Liters = 22.4 L

Answers to Problems in Lecture #13

1. 341.6 torr, 0.4495 atm, 45.54 kPa

2. 0.00615 L

3. -81oC

4. 6.18 atm

5. 496 g SF6