Unit IX:Gases

Behavior of GassesThe push or pull particles exert over a particular area is called pressurePressure plays a role in our everyday

livesExamples:

The pascal (Pa) is the SI unit of pressure

A device that measures atmospheric pressure is called the barometerInvented in 1643 by Evangelista Torricelli

(Italian;1608-1647)Student of Galileo’s

Units of Pressure

The SI unit for pressure is the Pascal (Pa)Sample EquationsNote: Solve by dimensional analysis, with the

correct number of significant figures! Not necessarily in standard scientific

notation.

1. 842 mm Hg → Pa2. 12.8 psi → atm3. 1.88 bars → torr4. 1.25 atm → kPa5. .78 atm → mm Hg

Boyle’s LawThe first careful experiments on gases was conduced by Robert BoyleIrish (1627 – 1691)Performed J – Tube experiments

Formula:P1V1 = P2V2

Pressure (before)(Can be in any units)

Volume (before)(Can be in any units)

Pressure (before)(units consistent with P1)

Volume (after)(units consistent with V1)

Gas Law Problem SolvingSet-up an Information MatrixThe abbreviations STP or ST or SP are often

used in place of numbers1st set of

conditions (Before Change)

2nd set of conditions

(After Change)

Pressure

Volume

Temperature

Sample Problem 1: A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. What is the new volume of the container if the pressure decreases to 1.87 atm?

P

V

T

Condition 1

Condition 2

3.54 atm

1.87 atm

23.1 L ?

V2 = P1V1

P2

V2 = (3.54 atm ● 23.1 L)

(1.87 atm)

= 43.7 L

Charles’ LawJacques Charles was the 1st to fill a balloon with H2 gasFrench Physicist (1746 – 1823)Showed the volume of a given gas (at

constant pressure) increases with temperature

Formula:V1T2 = V2T1

Volume (before)(Can be in any units)

Temperature (after)(Kelvin – K)

Volume (after)(units consistent with V1)

Temperature (before)(Kelvin - K)

Sample Problem 2: Your are given 1.2 L of oxygen gas measured at 380 torr and 18°C. What will be the volume when the temperature goes up to 307°C?

P

V

T

Condition 1

Condition 2

380 torr

380 torr

1.2 L ?

V2 = V1T2

T1

V2 = (1.2 L ● 580 K)

(291 K)

= 2.4 L18°C

291 K

307°C

580 K

Combined Gas LawBoyle’s and Charles’ Law can be combinedPressure, Volume, and Temperature are

inter-relatedFormula: P1V1 P2V2

T1 T2

=

OR P1V1T2 = P2V2T1

Sample Problem 3A: A helium balloon with a volume of 410. mL is cooled from 27°C to -27°C. The pressure on the gas is reduced from 110. kPa to 25 kPa. What is the new volume of the gas?

P

V

T

Condition 1

Condition 2

110. kPa

25 kPa

410. mL

?

V2 = P1V1T2

P2T1

V2 = (110 kPa • 410. mL • 246 K)

(25 kPa • 300 K)

= 1.5 x 103 mL27°C

300 K

-27°C

246 K

Sample Problem 3B: A gas sample is originally at STP. If the volume was originally 10.5 L, then what will happen to the pressure when the temperature rises to 109°F?

P

V

T

Condition 1

Condition 2

1.00 atm

?

10.5 L

P2 = P1V1T2

V2T1

P2 = (1.00 atm • 316 K)

(273 K)

= 1.16 atm273 K109°F

316 K

The Ideal Gas LawThe Ideal Gas Law relates the number of particles to pressure, volume, and temperatureBased on Avogadro’s Principle

Equal volumes of gases at the same temperature and pressure contain equal numbers of particles

Formula:

P V = n R T

Pressure (atm)

Volume (L)

Moles (mol)

Temperature (K)

Universal Gas Constant(0.0206 L • atm / K • mol)

There are some limitations to the Ideal Gas Law1. Works well at low pressures & high

temperatures

2. Most gases do not behave ideally at 1 atm

3. Does not work well near the condensation conditions of a gas

Remember the Gas Law Problem Solving Matrix

Condition 1

Condition 2

P

V

n

T

All Gas Law matrices should include mol (n) from this point!

You won’t necessarily know what Gas Law you will be solving!

The Ideal Gas Law will not use Condition 2!

Sample Problem 4A: A 333 g sample of Radon gas has a volume of 2.1 x 104 mL at 33°C. What is the pressure of the gas?

P = n R T

V

P = (1.5 mol • .08206… • 306 K)

21 L

1.8 atm=

Condition 1

Condition 2

P

V

n

T

?2.1 x 104

mL

333 g Rn gas

33°C

21 L

1.5 mol

306 K

Sample Problem 4B: Calculate the volume of hydrogen produced at 1.50 atm and 19°C by the reaction of 26.5 g of Zn with excess hydrochloric acid?

1 Zn (s) + 2 HCl (aq) → 1 ZnCl2 (aq) + 1 H2 (g)

1 2

PVn

T

1.50 atm

?

2.65 g Zn

19°C

?

.405 mol

292 K

1.50 atm

V = n R T

P

V = (.405 mol • .08206… • 292 K)

1.50 atm

6.5 L H2=

The density of a gas can be determined by using the Ideal Gas LawFormula:

D=M P

R T

Density (g/L)

Universal Gas Constant(0.0206 L • atm / K • mol)

Temperature (K)

Pressure (atm)Molar Mass (g)