CHAPTER 5: GASES - CHEM 1, G-Chem...

CHAPTER 5: GASES

MODEL OF GASES

KINETIC MOLECULAR THEORY (KMT) OF GASES

Postulates for an “Ideal” gas:

• The space taken up by the gas particles themselves is negligible; Vgas = Vcontainer.

• The gas particles don’t interact with one another.

• The gas particles are in constant random motion. The collisions of the particles with a

surface or container walls are the cause of gas pressure.

• The average kinetic energy of the gas particles is proportional to the Kelvin temperature.

MEASURING ATMOSPHERIC PRESSURE

Barometer (designed by Torricelli) Manometer

Pressure Conversions: 1 atm ≡ 101,325 Pascals (Pa) 1 bar ≡ 105 Pa 1 atm = 14.69 psi

Pressure Conversions: 1 atm ≡ 760 mmHg (exact) 1 atm ≡ 760 torr (exact)

GAS LAWS (RELATIONSHIPS)

BOYLES LAW (PUBLISHED IN 1662)

Data from Boyle’s Experiment

Pressure (in Hg)

Volume (in3)

117.5 12.0 87.2 16.0 70.7 20.0 58.8 24.0 44.2 32.0 35.3 40.0 29.1 48.0

Explanation via “Kinetic Molecular Theory”

Sample Problem:

A gas that occupies 125 mL at 2.75 atm is tripled in volume (expanded to 375 mL), without changing the moles or temperature of gas. What is the pressure of the expanded gas?

CHARLES LAW (FORMULATED IN 1787)

Measurements of 0.0446 mol of hydrogen gas at 1 atm:

Volume (L)

Temp (˚C)

0.817 –50.0 –0.0163 1.00 0.0 error 1.18 50.0 0.0236 1.37 100.0 0.0137 1.55 150.0 0.0103


A room temperature balloon of air (T = 22 ˚C) placed into liquid N2 (T = –195 ˚C).

Volume (L)

Temp (K)

0.817 223.2 0.00366 1.00 273.2 0.00366 1.18 323.2 0.00365 1.37 373.2 0.00367 1.55 423.2 0.00366

Sample Problem:

A gas that occupies 250 mL at 25 ˚C is doubled in volume, without changing the moles or pressure of the gas. What is the temperature of the gas?

A. –124 ˚C

B. 12.5 ˚C

C. 50. ˚C

D. 323 ˚C

COMBINED GAS LAW

Boyle’s Law Charles’ Law Combined Laws Combined Gas Law Equation

PV = constant "#

= constant $"#

= constant $%"%#%

= $&"&#&

Sample Problem:

A sample of air at 24.5 ˚C is in a steel cylinder with an easily movable lid. The diameter of the cylinder is 1.20 cm and the lid is at a height of 5.00 cm from the bottom. When the air is heated to 43.0 ˚C, to what height will the lid move to?

d= 1.20 cm

Airh= 5.00 cm

movable lid

AVOGADRO’S LAW

Volume of gas compared to moles:


IDEAL GAS LAW

Avogadro’s Law Previously Combined Laws Ideal Gas Law

"'

= constant $"#

= constant $"'#

= constant

Sample Problems:

R = 0.08206 L·atm/mol·K R = 8.3145 J/mol·K

Two balloons of gas are in the same room. Balloon A contains 0.75 moles of gas, while balloon B has 1.5 moles of gas. Which balloon is larger (has a greater volume)?

A gas in a closed steel cylinder at 3.0 atm and 100 K is warmed to 200 K. What is the new pressure of the gas?

A rigid container contains 1.50 moles of argon gas at 12.0 atm. Gas is allowed to leak out until the container has only 0.50 mole of argon gas (with no change in temperature). What is the pressure inside the container?

GAS CALCULATIONS

MOLAR VOLUME

What volume does exactly 1 mol of helium gas occupy at 0.00 ˚C and exactly 1 atm?

Sample Problem:

A balloon containing air has a volume of 500.0 mL at STP. A steel cylinder of gaseous HCl has a volume of 725.0 mL at STP.

a. Which container has more gas molecules, the balloon or the steel cylinder?

b. Calculate the number of HCl molecules in the steel cylinder.

GAS DENSITY

The density of a gas is related to its molar mass:

MM = (()*

mol = (++

PV = nRT PV = (,#++

MM = (,#$"

MM =

𝒅𝑹𝑻𝑷

MM = molar mass, d = density

Sample Problem:

What is the density of chlorine gas at 720 mmHg and 20.0 ˚C?

Sample Problem:

Rank the following materials in order of increasing density: CO2 (g), H2O (l), He (g), N2 (g). Explain your answer.

GAS STOICHIOMETRY

Sample Problem:

A car airbag needs to inflate to the correct volume so that the bag can cushion properly in the event of a collision. Airbags are inflated with nitrogen gas, formed through the reaction below.

If a passenger-side airbag needs to inflate to 60.0 L at 25 ˚C and 1.04 atm, what mass of NaN3 solid should the airbag contain?

2 NaN3 (s) → 2 Na (s) + 3 N2 (g)

GAS MIXTURES

DALTON’S LAW OF PARTIAL PRESSURES

Sample Problem:

A 5.00 L flask contains 4.8 g Ar (g) and 3.00 mol He (g) at 25.2 ˚C. What is the total pressure inside the flask?

V = 2.0 L; T = 25 ˚C

= CO2P = 0.50 atm

= HeP = 0.38 atm

V = 2.0 L; T = 25 ˚C

P = ?

V = 2.0 L; T = 25 ˚C

COLLECTING GASES OVER WATER

Sample Problem:

A sample of zinc metal (61.4 mg) reacts with excess HCl through the balanced equation below, and hydrogen gas is collected over water at 22 ˚C. The total pressure of the collected gas is 756 torr. The vapor pressure of water at 22 ˚C is 21 torr. Calculate the volume (in mL) of hydrogen gas produced from the reaction.

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

MORE GAS CONCEPTS + CALCULATIONS

AVERAGE PARTICLE SPEED

CORRELATION WITH TEMPERATURE

Sample Problem:

Consider separate 1.0 L gaseous samples of SF6, He, NO2 , and N2, all at STP.

a. Rank the gases in order of increasing average kinetic energy.

b. Rank the gases in order of increasing average velocity.

ROOT MEAN SQUARE VELOCITY

urms = 1𝟑𝑹𝑻𝑴𝑴

urms = “root mean square velocity” (similar to average velocity) R = gas constant, 8.3145 J/mol·K T = temperature in Kelvin MM = molar mass in kg / mol (kg needed to cancel as J = kg·m2/s2)

Mathematical subtly: this equation is derived from KEavg= 45 RT and KE = 6

5 m u2. It turns out KEavg is related to

(u2)average and not (uaverage)2. Thus when the square root is taken in the derivation, you don’t exactly get the average velocity (uaverage). Instead we call it “root mean square” velocity.

Sample Problem:

Calculate the root mean square velocity for a gas particle of water (MM = 18.02) at 25 ˚C.

Root Mean Square Velocities (urms) for gases at 25 ˚C

Gas Molar Mass (g/mol) urms (m/s) urms (mi/hr) MACH

H2 2.02 1918 4291 5.64 He 4.00 1363 3049 4.01

H2O 18.02 642 1437 1.89 N2 28.02 515 1152 1.51

CO2 44.01 411 919 1.21 SF6 146.07 226 505 0.66

Speed of sound (MACH 1): 340 m/s or 761 mi/hr

RATE OF DIFFUSION

Diffusion = the eventual mixing and spreading of materials (gases in our context).

Effusion = the passage of a gas particle through a tiny hole into an evacuated chamber.

Graham’s Law of Effusion

Rate of effusion ∝ 6

√++

MM = molar mass in g/mol

𝒓𝟏𝒓𝟐=

=𝑴𝑴𝟐

=𝑴𝑴𝟏 or 1𝑴𝑴𝟐

𝑴𝑴𝟏

r1 = rate of effusion (gas 1) r2 = rate of effusion (gas 2) MM1 = molar mass (gas 1) MM2 = molar mass (gas 2)

Sample Problem:

Under identical conditions, which gas effuses faster, NH3 (MM = 17.04) or HCl (MM = 36.46)?

What is the rate of effusion for NH3 (g) compared to HCl (g)?

Uranium hexafluoride, UF6, is a solid that can be converted to gas at mild temperatures (55 ˚C). Diffusion of UF6 gases used to be a common method to enrich uranium, and was used to provide uranium for the atomic bomb dropped on Nagasaki, Japan, in 1945 that ended World War II.

Which gas effuses more quickly:

235UF6 (g), (MM = 349.00) or

237UF6 (g), (MM = 352.00)

Sample Problem:

The rate of effusion for a particular gas was found to be 24.0 mL/min. Under the same conditions, the rate of effusion of pure methane gas (CH4) is 47.8 mL/min. What is the molar mass of the unknown gas?

REAL GASES

CHAPTER 5: GASES - CHEM 1, G-Chem...

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