UNIT 6 Gases and Thermochemistry Gas Laws. Properties of Gases One of the three physical states of matter Expand spontaneously to fill the container We.

UNIT 6

Gases and Thermochemistry

Gas Laws

Properties of Gases

• One of the three physical states of matter• Expand spontaneously to fill the container• We live in a homogeneous mixture of gases called

the atmosphere.

• Characterized by minimal intermolecular attractions: each gas molecule pretty much behaves as if there are no other gas molecules around.

• Spontaneously form homogeneous mixtures with other gases

• Characterized by pressure (P), volume (V), temperature (T), and amount (n) but not (much) by chemical identity

Properties of Gases

Pressure• Pressure is force per unit area. • Depending on our use of gas, we will use one of

several units of pressure. • Standard Atmospheric Pressure is the typical pressure

at sea level:

1 atmosphere (atm) 14.7 pounds per sq. in. (psi)

101325 pascal (Pa) - (The pascal is the SI unit of Pressure = 1 N/m2) 1.01325 bar 1013 mbar 29.92 inches of Hg 760 mm of Hg 760 torr

Pressure

http://www.weather.com/maps/maptype/currentweatherusnational/uscurrentweather_large.html

The white curves are isobar lines, lines of constant atmospheric pressure.

• Atmospheric pressure is measured with a barometer (a must when collecting gases over water).

• The weight of the atmosphere pressing on the mercury forces it up the evacuated tube until its weight equals the weight of the atmosphere (hence the unit of pressure called the mm of Hg). Blood pressures (120/80) are measured in mm of Hg.

• Pressures of contained gases (in cylinders or in vacuum systems) are measured with gauges suited to the specific purpose.

Pressure

Mercury barometer

Converting between Units of Pressure

• Use the equivalents to 1 atm (in the back of your text) to convert from one unit of pressure to another.

The pressure in a scanning electron microscope is 5.0 x 10 -5 torr. What is the pressure in atm? In pascal?

These are just dimensional analysis problems:

5.0 x 10-5 torr x 1 atm = 6.6 x 10-8 atm 760 torr

5.0 x 10-5 torr x 1 atm x 101325 Pa = 6.7 x 10-3 Pa 760 torr 1 atm

Gas Laws

Boyle’s Law: PV = constantVolume is inversely proportional to the pressure of a gas if its quantity and temperature are fixed.

Gas Laws

Boyle’s Law: PV = constant

Boyle’s Law: P1V1 = P2V2

Applications of Boyle’s Law: A fixed quantity of gas at 23°C exhibits a pressure of 748 torr and occupies a volume of 10.3 liters. What volume will the gas occupy at 23°C if the pressure is increased to 1.88 atm?

P1V1 = P2V2: 748 torr (10.3 L) = (1.88 atm x 760 torr) (?) 1 atm

? = 748 torr (10.3 L) = 5.39 L1.88 atm x 760 torr/atm

Pressure was increased, so the volume had to decrease.

Gas Laws

Charles’ Law: V = kT (where k is a constant)

Volume is directly proportional to the temperature of a gas IF its quantity and pressure are fixed.

The volume of an ideal gas at 0K is zero!

Gas LawsCharles’ Law: V = kT

Charles’ Law : V1 = V2

T1 T2

Applications of Charles’ Law: A fixed quantity of gas at 23°C exhibits a pressure of 748 torr and occupies a volume of 10.3 liters. What volume will the gas occupy if the pressure is held constant and the temperature is increased to 125°C?T1 = 23°C + 273 = 296 K T2 = 125°C + 273 = 398 K

V1 = V2: 10.3 L = ? LT1 T2 296 K 398 K

? = 398 K (10.3 L) = 13.8 L 296 K

Temperature was increased, so the volume had to increase.

ALWAYS EXPRESS THE TEMPERATURE IN KELVIN FOR GAS LAW CALCULATIONS!!!

The Combined Gas Law (CGL)

PV = constant T or

P1V1 = P2V2

T1 T2

Gas Laws

Avogadro’s Law: V = kn (where k is a constant and n is the number of moles of gas)

Volume is directly proportional to the quantity of a gas IF its temperature and pressure are fixed.

Avogadro’s hypothesis: Equal volumes of gases at the same T and P contain equal

numbers of gas molecules.

Gas Laws

Avogadro’s Law: V = kn

Avogadro’s Law : V1 = V2

n1 n2

Applications of Avogadro’s Law: One mole of a gas occupies a volume of 22.4 L at standard temperature and pressure (STP). What is the volume of 3.00 x 10-2 moles of that same gas at STP?

V1 = V2: 22.4 L = ? Ln1 n2 1 mol 3.00 x 10-2 mol

? = 22.4 L (3.00 x 10-2 mol) = 0.672 L 1 mol

The number of gas molecules decreased, so the volume had to decrease.

STP is standard temperature and pressure.

Standard temperature is 273 K

Standard pressure is 1 atm

Gas Laws

Boyle’s Law, Charles’ Law, and Avogadro’s Law can be combined into one gas law, the

Ideal Gas Law: PV = nRTThe constants from the previous laws have been combined to form the gas constant R.An ideal gas is any gas that obeys the ideal gas law.

STP is standard temperature and pressure.

• Standard temperature is 273 K (0°C).• Standard pressure is 1 atm.• 1 mole of an ideal gas occupies 22.4 L at STP. This is

the standard molar volume of an ideal gas.

The Ideal Gas Law Contains the Other Gas Laws

Ideal Gas Law: PV = nRT

Boyle’s Law: PV = k when the quantity and temperature of a gas are constant.

PV = constant, so PV = k.nRT

Charles’ Law: V = kT when the quantity and pressure of a gas are constant.

V = T, so V = kT.

constant

nR P

The Ideal Gas Law

Ideal Gas Law: PV = nRT (know!!!)The ideal gas equation can be used with reasonable success for a number of gases under a fairly large spectrum of conditions.The value for the gas constant R depends on the other units used in the ideal gas equation:

R = 0.08206 L-atm / mol-K= 8.314 J / mol-K

= 1.987 cal / mol-K

= 8.314 m3-Pa / mol-K

Working Ideal Gas Law Problems - I

What volume would 2.0 moles of He at 298 K and 1.5 atm occupy?

PV=nRT

(1.5 atm) V = (2.0 mol)(0.08206L-atm/mol-K)(298 K)

V = (2.0 mol)(0.08206L-atm/mol-K)(298 K) = 33 L1.5 atm

Working Ideal Gas Law Problems - I

How many moles of nitrogen are in a 5.00 L container held at 100°C and 715 torr?

PV = nRT(715 torr)(5.00 L) = n(0.08206L-atm/mol-K)(373 K) 760 torr/atm

n = (0.941 atm)(5.00 L) = 0.154 mol N2

(0.08206L-atm/mol-K)(373 K)

Working Ideal Gas Law Problems - II

A 2.35 L container at 25°C is pressurized to 1.2 atm with carbon dioxide. What would the pressure in the container be if its temperature is raised to 95°C?

PV=nRT is not helpful in this form. Use the combined gas law

P1V1 = P2V2

T1 T2 In this problem, V1 = V2 (because the container does not change size) and the moles of gas are constant (because there is no indication that any gas was let in or out of the container). The equation then reduces to

P1 = P2 1.2 atm = P2

T1 T2 298 K 368 K

P2 = 1.2 atm (368 K) = 1.5 atm 298 K

Working Ideal Gas Law Problems - II

A 2.35 L piston/cylinder arrangement at 25°C is pressurized to 1.2 atm with carbon dioxide. To what temperature in °C must the cylinder be raised for the CO2 pressure to reach 2.5 atm and the volume to be 4.00 L?

Use the combined gas law

P1V1 = P2V2

T1 T2 1.2 atm (2.35 L) = 2.5 atm (4.00 L) 298 K T2

T2 = 2.5 atm (4.00 L) (298 K) = 1057 K = 800°C 1.2 atm (2.35 L)