Gas Notes

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.

II. Kinetic Molecular Theory of Gases Particles of matter (any type) are in constant motion! Because we know this we have a few assumptions that we make about gases, called the Molecular Theory of Gases:

1. Particles of a gas are in constant, straight-line motion, until they collide Gases consist of a large number of tiny particles; these particles are very far apart, therefore gas is mostly empty space. 3. Collisions between particles of a gas and the container wall are elastic. Which means there is no loss of energy.

4. There are no forces of attraction or repulsion between particles of gases The average kinetic energy of gas particles depends on the temperate of the gas. KE=1/2 mv 2 (m=mass in kg and v=velocity is m/sec)

III. Ideal VS Real Gases Ideal gases always obey the kinetic theory. (Closest to ideal would be the noble gases.) Real gases vary from the kinetic theory at various temperatures and pressures.

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

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). 1atm = 760 millimeters Hg ( Barometers use Hg) 1atm = 760 torr (Named after Torricelli for the invention of the barometer) 1atm = kPa - kilopascals

Practice: Convert 4.40 atm to mmHg. Convert 212.4kPa to mmHg.

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

Practice: Convert 32.0°C to K. Convert 400. K to °C.

4. Number of Moles – tells you how much of a certain gas you have 1 mole = number of grams of the compound or element (molar mass)

STP – “standard temperature and pressure” which is 0  C and 1.00 atm.

V. Gas Laws - How do all of pressure, temperature, volume, and amount of a gas relate to each other? Rules for solving gas law problems: 1 st write down what is given and what is unknown, 2 nd identify the gas law you want to use, and 3 rd rearrange the formula to solve for the unknown and then solve the problem. (If temperature is involved, it MUST be converted to Kelvin! K =  C)

A. Boyle’s Law - Pressure and Volume (when temperature remains constant) V 1 = initial or old volume V 1 P 1 = V 2 P 2 V 2 = final or new volume P 1 = initial or old pressure P 2 = final or new pressure Inverse Relationship (As pressure increases, volume decreases and as pressure decreases, volume increases.)

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 1.00X10 3 torr of pressure?

B. Charles’ Law -Volume and Temperature (when pressure is constant) Figure page 316 V 1 = V 2 T 1 = initial or old temperature T 1 T 2 T 2 = final or new temperature Direct Relationship (As temperature increases, volume increases and as temperature decreases, volume decreases.)

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 125  C. 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 30.0  C. 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) P 1 = P 2 T 1 T 2 Direct Relationship (As temperature increases, pressure increases and as temperature decreases, pressure decreases.)

1c. The gas in an aerosol can is at 3.00atm 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 205  C? 3c. A gas at 32.0  C has a pressure of atm. If the temperature increases to 44.0  C what is the new pressure of the gas?

D. Combined Gas Law - Pressure, Temperature, and Volume (None of the variables are constant) V 1 P 1 = V 2 P 2 T 1 T 2

1d. A helium filled balloon has a volume of 50.0mL at 298K and 1.08atm. What volume will it have at 0.855atm and 203K? 2d. Given 700.mL of oxygen at 7.00  C and 7.90atm of pressure, what volume does is occupy at 27.0  C and 4.90atm of pressure? 3d. A gas has a volume of 1.140L at 37.0  C and 620.mmHg. Calculate its volume at 0  C and 760.mmHg.

Gas Worksheet #1 is due next class!

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

1e. A mixture of gases has the following partial pressure for the component gases at 20.0  C 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 atm, 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 – Figure page 324 P atm or P T = P gas + P H2O P atm or P T = barometric pressure or total pressure P gas = pressure of the gas collected P H2O = 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 20.0  C. 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 25.0  C. 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.)

R =.0821 L atm/mol K R = 62.4 L mmHg/mol K

1f. How many moles of CH 4 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 atm and the temperature is 63.0  C? 2g. What is the density of argon gas at a pressure of 551 torr and a temperature of 25.0  C?

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 27.0  C. 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 20.0  C and 0.980atm?

H. Molar Volume of Gases 1 mole of any gas = 22.4 L 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) + O 2 (g)  2CO 2 (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 35.0  C 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)