Gas Notes (Chapter 10)

Gases are made up of atoms and molecules just like all other compounds, but because they are in the form of a gas we can learn a great deal more about these molecules and compounds. It might seem a bit confusing because we can’t see most gases, but we know they exist. We will be doing many demos and lab activities to explain and understand gases!

I. Let’s look at some of the Nature of Gases:

• 1. Expansion – gases do NOT have a definite shape or volume.

• 2. Fluidity – gas particles glide past one another, called fluid just like a liquid.

• 3. Compressibility – can be compressed because gases take up mostly empty space.

• 4. Diffusion – gases spread out and mix without stirring and without a current. Gases mix completely unless they react with each other.

IV. Volume, Pressure, Temperature, Number of Moles (Descriptions of Gases)

• 1. Volume – refers to the space matter (gas) occupies. Measured in liters (L).

1L = 1000mL

Film Canister Demo

• 2. Pressure – the number of times particles collide with each other and the walls of the container (force exerted on a given area). Measured in atmospheres (atm).

http://chemmac1.usc.edu/bruno/java/pressure.html

1atm = 760 millimeters Hg ( Barometers use Hg)

1atm = 760 torr (Named after Torricelli for the invention of the barometer)

1atm = 101.3 kPa - kilopascals

• 3. Temperature – as temperate increases gas particles move faster, as temperature decreases gas particles move slower. Measured in Kelvin (K).

K = 273 + C

A. Boyle’s Law - Pressure and Volume (when temperature remains constant)

V1 = initial or old volume

V1P1 = V2P2 V2 = final or new volume

P1 = initial or old pressure

P2 = final or new pressure

Inverse Relationship (As pressure increases, volume decreases and as pressure decreases, volume increases.)

Boyle’s Law

Robert Boyle(1627-1691)

• Boyle was born into an aristocratic Irish family

• Became interested in medicine and the new science of Galileo and studied chemistry. 

• A founder and an influential fellow of the Royal Society of London

• Wrote extensively on science, philosophy, and theology.

Graph of Boyle’s Law

Boyle’s Law says the pressure is inverse to the volume.

Note that when the volume goes up, the pressure goes down

Pressure and Volume (Boyle’s Law) Gas Demonstrations

• Bell Jar – Shaving Cream

As pressure decreases the volume of the gas increases.

• Bell Jar – Balloon

• Bell Jar – Marshmallow

• Cartesian Diver

1a. A gas occupies 3.00L at 1.00atm of pressure. What volume does it occupy at 5.00atm?

   2a. What is the new pressure when 80.0mL of gas at

500.mmHg is moved to a 100.mL container?   3a. A gas at 800.torr of pressure has a volume of

5.00L. What volume does this gas occupy at 1.00X103torr of pressure?

 

B. Charles’ Law -Volume and Temperature (when pressure is constant) Figure 10-11 page 316

V1 = V2 T1 = initial or old temperature

T1 T2 T2 = final or new temperature

Direct Relationship (As temperature increases, volume increases and as temperature decreases, volume decreases.)

Jacques Charles (1746-1823)• French Physicist• Part of a scientific

balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humans

• This is how his interest in gases started

• It was a hydrogen filled balloon – good thing they were careful!

Temperature and Volume (Charles’ Law) Gas Demonstrations

• Balloon on Flask (hot and cold)

As temperature of the gas increases the volume the gas occupies increases.

• Root Beer Float

1b. A gas has a volume of 500.mL at 298K. What volume does it have at 373K?

  2b. A gas had a volume of 250.mL and a temperature

of 125C. What is the final temperature (in K) if the volume is changed to 100.mL?

   3b. This initial volume of a gas is 250.mL at 30.0C.

What is the temperature of the gas with a new volume of 667mL?

C. Gay-Lussac’s Law - Pressure and Temperature (when volume is constant)

• P1 = P2

• T1 T2

• Direct Relationship (As temperature increases, pressure increases and as temperature decreases, pressure decreases.)

Joseph Louis Gay-Lussac (1778 – 1850) French chemist and

physicist Known for his studies on the physical properties of gases. In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

Temperature and Pressure (Gay-Lussac’s Law) Gas Demonstrations

• Inverted Fountain

As the temperature of the gas increases the pressure of the gas increases. (Inverting the flask into the water showed that the pressure increased because water was pulled into the flask.)

1c. The gas in an aerosol can is at 3atm of pressure at 298K. What would the gas pressure in the can be at 325K?

2c. At 120.C the pressure of a sample of nitrogen gas is 769torr. What will the pressure be at 205C?

3c. A gas at 32.0C has a pressure of 0.0400atm. If the temperature increases to 44.0C what is the new pressure of the gas?

The pressure of each gas in a mixture is called the partial pressure of that gas. Daltons Law of Partial Pressure states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

E. Daltons Law of Partial Pressures

PT = P1 + P2 + P3 + ……. PT = total pressure

P# = the partial pressures of the individual gases

• If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3:

2 atm + 1 atm + 3 atm = 6 atm

1 2 3 4

• 1e. A mixture of gases has the following partial pressure for the component gases at 20.0C in a volume of 2.00L: oxygen 180.torr, nitrogen 320.torr, and hydrogen 246torr. Calculate the pressure of the mixture.

• 2e. What is the final pressure of a 1.50L mixture of gases produced from 1.50L of neon at 0.3947atm, 800.mL of nitrogen at 150.mmHg and 1.2oL of oxygen at 25.3kPa? Assume constant temperature. (Hint use Boyle’s law.)

Daltons Law applied to Gases Collected by Water Displacement

Ptotal = Pgas + PH2O

Daltons Law applied to Gases Collected by Water Displacement

Ptotal = Pgas + PH2O

Daltons Law applied to Gases Collected by Water Displacement

Ptotal = Pgas + PH2O

Daltons Law applied to Gases Collected by Water Displacement – Figure 10-15 page 324

Patm or PT= Pgas + PH2O

Patm or PT = barometric pressure or total pressure

Pgas = pressure of the gas collected

PH2O = vapor pressure of water at specific temperature (Found on page 899 of you textbook.)

• 3e. Oxygen gas from the decomposition reaction of potassium chlorate was collected by water displacement at a pressure of 731torr and a temperature of 20.0C. What was the partial pressure of the oxygen gas collected?

• 4e. Solid magnesium and hydrochloric acid react producing hydrogen gas that was collected over water at a pressure of 759mmHg and measured 19.0mL. The temperature of the solution at which the gas was collected was 25.0C. What would be the pressure of the dry hydrogen gas? What would be the volume of the dry hydrogen gas at STP?

F. Ideal Gas Law (PV = nRT) – to use this law, all units must be as follows:

• P = pressure in atm• V = volume in liters• n = number of moles• T = temperature in Kelvin• R = (0.0821L) (1atm)

(1mol) (1K)• R is the ideal gas constant (page 342 in book

describes where this constant came from.)

• 1f. How many moles of CH4 gas are there in 85.0L at STP?

• 2f. What volume will be occupies by 1.50grams of nitrogen monoxide gas at 348K and pressure of 300.mmHg?

• 3f. A volume of 11.2L of a gas at STP has how many moles?

G. Solving for Density and /or Molar Mass of a gas using the Ideal Gas Law

1. Density (units are g/L) Use the Ideal Gas Law to find moles (n), convert n to grams OR use the Ideal Gas Law to find the volume. Divide n (in grams) by the volume.

• 1g. What is the density of a sample of ammonia gas, NH3, if the pressure is 0.928 atm and the temperature is 63.0C?

• 2g. What is the density of argon gas at a pressure of 551 torr and a temperature of 25.0C?

2. Molar Mass (units are g/mol) If density is given, use the density of the gas to determine the molar mass (use 1 L at the volume and solve for n). If a mass is given, use the Ideal Gas Law to solve for n and then find the molar mass.

• 3g. The density of a gas was found to be 2.00g/L at 1.50atm and 27.0C. What is the molar mass of the gas?

• 4g. What is the molar mass of a gas if 0.427g of the gas occupies a volume of 125mL at 20.0C and 0.980atm?

H. Molar Volume of Gases

Recall that 1 mole of a compound contains 6.022 X 1023 molecules of that compound – it doesn’t matter what the compound is. One mole of any gas, at STP, will occupy the same volume as one mole of any other gas at the same temperature and pressure, despite any mass differences. The volume occupied by one mole of a gas at STP is known as the standard molar volume of a gas. It has been found to be 22.4liters. We can use this as a new conversion factor 1mol of gas/22.4L of same gas. (Avogadro’s Law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

1 mol = 22.4L (molar volume of any gas at STP)

• 1h. What volume, in L, is occupied by 32.0 grams of oxygen gas at STP?

I. Stoichiometry of Gases

Just like mole ratios can be written from an equation so can a volume ratio-same concept!

• 2CO(g) + O2 (g) 2CO2 (g)

• 1i. Using the above equation, what volume of oxygen gas is needed to react completely with 0.626L of carbon monoxide to form carbon dioxide?

• 2i. How many grams of solid calcium carbonate must be decomposed to produce 5.00L of carbon dioxide gas at STP?

• 3i. How many liters of hydrogen gas at 35.0C and 0.980atm are needed to produce 8.75L of gaseous water according to the following equation?

• WO3(s) + 3H2(g) W(s) + 3H2O(g)

J. Graham’s Law IV. Effusion and Diffusion

• Effusion is the process whereby the molecules of a gas confined in a container randomly pass through a tiny opening in the container. (onions on page 352)

J. Graham’s Law IV. Effusion and Diffusion

• Graham’s Law states that the rates of diffusion/effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

•Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

•Molecules move from areas of high concentration to low concentration.

Effusion: a gas escapes through a tiny hole in its container

-Think of a nail in your car tire…

Diffusion and effusion are explained by the next gas law: Graham’s

• Rate of diffusion/effusion of A = √(MB/MA) Rate of diffusion/effusion of B

MA or B = molar mass of that compound Gas A is the lighter, faster gasRate of diffusion/effusion is the same as the velocity (or speed) of the gas.

After the rates of diffusion/effusion for two gases are determined, the gas with the lower molar mass will be the one diffusing/effusing fastest.

• 1j. Compare the rates of effusion for hydrogen and oxygen at the same temperature and

• pressure. (Which one effuses faster and how much faster is it effusing?)

• 2j. A sample of hydrogen effuses through a porous container about 9 times faster than an unknown gas. Estimate the molar mass of the unknown gas.

Graham’s Law and Time

Graham’s Law and Time – the time it takes a gas to effuse is directly proportional to its molar mass.

tA = MA t = time

tB MB

• 3j. A sample of an unknown gas flows through the wall of a pours cup in 39.9 minutes. An equal volume of helium (under same temperature and pressure) flows through in 9.75 minutes. What is the molar mass of the unknown gas?