Gases and Atmospheric Chemistry In this package you will be working through the main highlights/expectations of the Gases unit for SCH 3U. This content will give you the background necessary to be prepared for the gases component common in most first year university chemistry classes. States of Matter and Kinetic Molecular Theory: The KMT is used to explain the properties of solids, liquids and gases based on the types of motion that they are undergoing. All matter, even solids, are made up tiny particles that are constantly in motion. The freedom and energy of the motion dictates the state that a substance is in. The kinetic molecular theory makes the following assumptions: 1. All matter is made up of very small particles, known as atoms or molecules. 2. There are empty spaces between the particles. The distance between particles is large compared to their size. 3. These particles are in constant motion. a. The particles in a solid are held close together by strong attractive forces; the particles vibrate but cannot move around. b. The particles in a liquid are held together more loosely by weaker attractive forces; the particles can move around, colliding into other particles and into the container. Gravity keeps the liquid in the bottom of the container but they exert enough attractive force to form a bubble (easily seen in drops of liquid mercury). c. The particles in a gas are very loosely held together by much weaker attraction forces; they can move freely around, filling the entire space available in the container. 4. Their collisions are perfectly elastic, meaning that particles do not lose their kinetic energy by colliding with each other. 5. If heat is added to a substance, its particles gain energy and move faster. A solid has a rigid shape
A liquid takes the shape of its container
A gas occupies the entire container
and takes its shape
Points to consider: a) Why do solids have a definite shape and volume? b) Why are gases easily compressible c) Use the KMT to explain how a substance would change from one state to another (ex. Solid to liquid to gas) d) Use the KMT to explain why the scent of perfume would spread more slowly outdoors in winter than it does in the summer. Atmospheric Pressure: Pressure is the force per unit area. When we are talking about a gas, the pressure is the force exerted by the molecules of the gas on its container by the particles colliding with the surface of the container. The smaller the area that the same force is being exerted on the greater the pressure. There are many different units that we can use to represent pressure. Some of the common ones include: Unit Name Pascal Millimetres Mercury Unit Symbol Pa Mm Hg Torr Atmosphers Pounds per square inch Torr Atm Psi Definition/Conversion 1Pa=1N/m2 760 mmHg = 1atm = 101.325 kPa 1 Torr = 1 mm Hg 1 atm = 101.325 kPa 1 psi = 6895 Pa Practice: Convert each of the following measurements of pressure to the units indicated: a) 203 kPa to mm Hg [1520 mmHg] b) 40.0 kPa to Torr [3.00 X 102 torr] c) 717 mmHg to Pa [9.56 X 104 Pa] You have likely noticed your ears pop as you ride up an elevator, drive down a long hill or fly on an airplane. This is due to the pressure changes as your elevation with respect to Earth changes. Each layer of air in the atmosphere is pushing down on all of the layers below it. For this reason, atmospheric pressure is highest at the Earth’s surface and decreases as your elevation increases. This decreased pressure also means that the molecules of air are further apart at elevation, which is why climbers of Everest require oxygen tanks. The pressure at the summit of Everest is so low that the concentration of oxygen gas is too low to meet the needs of the body. Gas Laws: 1) Charles’ Law As the temperature of a gas is increased, the volume of the gas increases proportionally. ***When working with temperatures in gases you should get in the habit of always using Degrees Kelvin. This is often referred to as the absolute temperature*** oK = oC + 273 Eg. What is the absolute temperature of 25oC? oK = 25 +273 = 298 Practice: Convert the following temperatures to Kelvin: a) -­‐78 oC b) 45 oC Convert to degrees Celsius a) 1337 K b) 210 K Example Question: A sample of gas is drawn into a piston. If the sample occupies 0.255L at 25 oC, what with the volume be at 80 oC? The pressure and amount of gas is kept constant. T1 = 273 + 25 = 298K T2 = 273 + 80 = 353K Rearrange to solve for V2 = V1T2/T1 = .255L(353K)/298K = .300L Practice: a. A sample of methane gas occupies an initial volume of 5.25L at an initial temperature of 200 K. The gas is heated to 300 K while the pressure and amount of gas remain constant. Determine the new volume. [7.88L] b. A sample of carbon dioxide is place in a piston. The intitial temperature of the gas is 35 oC and it occupies a volume of 2.2L. Calculate the temperature at which it will occupy 4.4L. [620K] 2) Boyle’s Law As the volume of a gas is decreased, the pressure of the gas increases proportionally. When dealing with pressure you will normally working in kPa or atm at your units and you should feel comfortable converting between them. P1V1 = P2V2 Example question: A weather balloon is filled with 60.0 L of hydrogen gas at sea level pressure (101.3kPa). It then rises to 900 above Earth’s surface. The atmospheric pressure at this altitude is 90.6 kPa. What is the volume of the balloon at this altitude? P1V1 = P2 V2 101.3kPa(60.0L) = 90.6kPa(V2) 67.1 L = V2 Practice: a. Helium gas has a volume of 8.25L at 446 kPa. What pressure must be applied to the gas when it occupies 12 L? [307 kPa] 3) Gay-­‐Lussac’s Law As the temperature of a gas increases, the pressure of the gas increases proportionally. Example question: A sample of gas is stored in a reinforced steel container at -­‐115 oC, at a pressure of 39.9 kPa. If the pressure reaches 60.8 kPa, what is the final temperature in oC? T1 = 273 + (-­‐115) = 158 K Isolate for T2 T2 = P2T1/P1 = 60.8 kPa (158K) / 39.9 kPa = 241 K Convert to oC =243 K – 273 = -­‐32 oC The Combined Gas Law: The Combined Gas Law, as the name would suggest, combines Charles’, Boyle’s and Gay-­‐Lussac’s Laws to deal with systems that may be experiencing changes in Temperature, Pressure or Volume. You will use the same process as the other laws to solve. Make sure that you convert your temperatures to Kelvin, that your volumes are in Litres and that you have your pressure in kPa or atm. Practice: a. A balloon at the top of Mount Logan occupies a volume of 775mL at a temperature of -­‐28oC and a pressure of 92.5 kPa. What is the pressure of the balloon at the bottom of the mountain if the same balloon has a volume of 825 mL at a temperature of 15 oC? [102 kPa] b. A researcher heated a 2.75 L sample of helium gas at 99.0 kPa from 21.0oC to 71.0oC and recorded that the pressure changed to 105 kPa. Calculate the final volume of the gas. [3.03 L] c. A 450 mL sample of propane gas at 253 kPa and 15 oC was compressed to 310 mL at a pressure of 405 kPa. Calculate the final temperature in Celsius. [45oC] Avogadro’s Law and Molar Volume: You may have come across the acronyms STP and SATP when dealing with gases. It is important that you understand what these mean as they give you information that can help you solve gas problems. STP (Standard Temperature and Pressure): conditions of 0oC and 101.325 kPa. SATP (Standard Ambient Temperature and Pressure): conditions of 25oC and 100 kPa. In stoichiometry we learned that molar mass, the mass of exactly 6.02 x 1023 particles of a substance, is equal to the mass on the periodic table. When dealing with gases we find that the volume of a gas is directly related to the number of moles of gas that we have. At STP 1 mole of any gas occupies 22.4L. If we don’t have exactly one mole of gas, or if we know information about the volume of the gas not at STP, we can use the following equation: Example question:
A party balloon has 2.5 mol of helium gas at STP. What is the volume of the balloon.
V2 = V1(n2)/n1
= 22.4L(2.5 mol) /1 mol
= 56 L
Practice:
a. A container of oxygen gas has a volume of 145.6L. If the pressure of the gas is 101.3 kPa and the
temperature is 0 oC, determine the amount of oxygen gas in the container. [6.5 mol]
b. Determine the mass of hydrogen gas collected in a container if the gas occupies 44.8 L at STP.
[4.04 g.]
Ideal Gas Law:
In the Ideal Gas Law, the products of the pressure and volume of the gas is equal to the product of the
amount, the universal gas constant and the absolute temperature.
The Universal Gas Constant (R) has two main values that you will need to work with depending on the
units of pressure that you are dealing with. The key is to ensure that the pressure units in your gas constant
is the same as the pressure units in the question.
R = 8.134 kPa•L/mol•K
Or
R = = 0.08206 atm•L/mol•K
Once again, when dealing with the ideal gas law, make sure that your temperatures are in K, your volume
in L and that the units of your pressure and R match.
Example Questions:
The air in a person’s lungs has 0.177 mol of gas particles at 310 K
with a pressure of 101.3 kPa. What is the volume of air?
Solution
Therefore, the volume of air in the lungs is 4.5 L.
2) Ammonium sulphate, an important fertilizer, can be prepared by the reaction of ammonia with sulphuric
acid according to:
Calculate the volume of NH3 needed at 42°C and 15.6 atm to react with 870 g of H2SO4.
Solution
First, the temperature must be changed to K.
T(K) = T(° C) + 273.15
= 42°C + 273.15
= 315.15 K
Now, you must convert the given mass into moles.
mol (H2SO4) = mass x MM[H2SO4]
= 870 g / 98.0784 g/mol
= 8.87 mol
Find the number of moles of NH3 that will reaction with the H2SO4.
From the balanced equation, each mole of H2SO4 requires 2 mol of NH3.
So, 8.87 mol x 2 = 17.74 mol of NH3 is needed.
Finally, use the ideal gas law to calculate the volume of ammonia that will react.
Therefore, 29.41 L of are needed.
Happy Practicing!!!
Gas Practice Problems Boyle’s Law 1.
If a gas at 25.0°C occupies 3.60 L at a pressure of 1.00 atm, what will be its volume at a pressure
of 2.50 atm?
2. 500.0 mL of a gas is collected at 745.0 mm Hg. What will the volume be at standard pressure?
3. Convert 350.0 mL at 740.0 mm of Hg to its new volume at standard pressure.
4. Convert 77.0 L at 18.0 mm of Hg to its new volume at standard pressure.
5. A gas occupies 4.31 L at a pressure of 0.755 atm. Determine the volume if the pressure is
increased to 1.25 atm.
6. 600.0 mL of a gas is at a pressure of 8.00 atm. What is the volume of the gas at 2.00 atm?
7. 400.0 mL of a gas are under a pressure of 800.0 torr. What would the volume of the gas be at a
pressure of 1000.0 torr?
8. 4.00 L of a gas are under a pressure of 6.00 atm. What is the volume of the gas at 2.00 atm?
9. A gas occupies 25.3 mL at a pressure of 790.5 mm Hg. Determine the volume if the pressure is
reduced to 0.804 atm.
10. A sample of gas has a volume of 12.0 L and a pressure of 1.00 atm. If the pressure of gas is
increased to 2.00 atm, what is the new volume of the gas?
11. You are now wearing scuba gear and swimming under water at a depth of 30.0 m. You are
breathing air at 3.00 atm and your lung volume is 10.0 L. Your scuba gauge indicates that your air
supply is low so, to conserve air, you make a terrible and fatal mistake: you hold your breath while
you surface. What happens to your lungs? Why?
12. A 1.5 L flask is filled with nitrogen at a pressure of 12 atmospheres. What size flask would be
required to hold this gas at a pressure of 2.0 atm?
Charle’s Law:
1.
568 cm3 of chlorine at 25°C will occupy what volume at -25°C while the pressure remains
constant?
2. A sample of nitrogen now occupies a volume of 250 mL at 25°C. What volume did it occupy at
95°C?
3. Oxygen gas is at a temperature of 40°C when it occupies a volume of 2.30 L. To what temperature
should it be raised to occupy a volume of 6.50 L?
4. Hydrogen gas was cooled from 150°C to 50°C. Its new volume is 75.0 mL. What was its original
volume?
5. A sample of neon gas at 50°C and with a volume of 2.50 L is cooled from 25°C. What was its
original volume?
6. Fluorine gas at 300 K occupies a volume of 500 mL. To what temperature should it be lowered to
bring the volume to 300 mL?
7. Helium occupies a volume of 3.8 L at –45°C. What was its initial temperature when it occupied
8.3 L?
8. A sample of argon gas is cooled and its volume went from 380 mL to 250 mL. If its final
temperature was –55°C, what was its original temperature?
9. A container holds 50.0 mL of nitrogen at 25°C and at a constant pressure of 736 mm Hg. What
will be its volume if the temperature increases by 35°C?
10. On hot days, you may have noticed that potato chip bags seem to expand. If a 250 mL bag at a
temperature of 19°C is left inside a car (with windows sealed on a hot summer day) when the
temperature rises to 60°C, what will be new volume of the bag?
11. A plastic pop bottle is flexible enough that the volume of the bottle can change even without
opening it. If you have an empty 2 L pop bottle at a room temperature of 25°C, what will the new
volume be if you put it in the freezer at -4°C?
12. A homemade thermometer is produced so that a piston goes up and down as the temperature
changes. It is calibrated so that at 100°C, the piston is at the 30 L position. If the piston indicates
20 L, should you wear a jacket or a bathing suit before going out? Explain your answer using your
calculations.
Gay-Lussac’s Law:
1.
2.
Explain the relationship between the temperature and pressure of a gas.
A gas container is initially at 47 mm Hg and 77 K. What will the pressure be when the container
warms up to room temperature of 25°C?
3. A gas thermometer measures temperature by measuring the pressure of a gas inside the fixed
volume container. A thermometer reads a pressure of 248 torr at 0.0°C. What is the temperature
when the thermometer reads a pressure of 345 torr?
4. Calculate the final pressure inside a scuba tank after it cools from 1000°C to 25°C. The initial
pressure in the tank is 130.0 atm.
5. A gas is collected at 22°C and 745 mm Hg. When the temperature is changed to 0.0°C, what is the
resulting pressure?
6. Use Gay-Lussac's law to explain what is wrong with the following statement: "I brought a fully
inflated beach ball outside to play volleyball in the snow with my friends, but it exploded before
we could start."
7. The gas pressure in an aerosol can is 151.6 kPa at 25.0°C, what would the pressure be inside the
can at 300.0°C?
8. The temperature of a gas is 6.0°C and 65.3 mbar, what is the pressure at 4.0°C?
9. A tank for compressed gas has a maximum safe pressure limit of 825 kPa. The pressure gauge
reads 388 kPa when the temperature is 24.0°C. What is the highest temperature the tank can
withstand safely?
10. If a helium-filled balloon is at STP. What was its initial temperature if its pressure was 1.62 atm?
11. What information is missing from the following question? "A small ball is inflated to 100 kPa of
pressure. What is the final pressure if the temperature increases by 20°C? "
12. You notice that a sealed bag of potato chips bulges when placed near a sunny window. What can
you hypothesize about the relationship between the temperature and pressure of an enclosed gas?
Combined Gas Law:
1.
2.
3.
4.
5.
6.
7.
8.
9.
A gas is at 135°C and 455 mm Hg in a 2.00 L container. It is cooled down to a temperature of
25°C. If it is kept in the same container, what is its new pressure?
A gas has a volume of 39 L at STP. What will its volume be at 4 atm and 25°C?
A gas, now contained at STP, has a volume of 500 mL. The initial pressure was 0.96 atm at 20°C.
What was the initial volume?
A balloon is filled up with air to a volume of 1.15 L at 296.5 K. What does the volume change to
if the balloon is taken outdoors where the temperature is 278.4 K and the pressure is half of what it
was indoors?
Calculate the pressure in a tire if it starts out filled with 7.54 L of air at 219 kPa and 21.6°C and
gets heated to 65.2°C as the volume increases to 7890 mL.
A 700.0 mL gas sample gas sample at STP is compressed to a volume of 200.0 mL, and the
temperature is increased to 30.00°C. What is the new pressure of the gas in kPa?
A balloon of air now occupies 10.0 L at 25.0°C and 1.00 atm. What temperature was it initially, if
it occupied 9.4 L and was in a freezer with a pressure of 0.939 atm?
6.8 L of a gas is found to exert 97.3 kPa at 25.2°C. If the volume is changed to 12.5 L, what would
be the required temperature to change the pressure to standard pressure?
A cylinder is fitted with a moveable piston. A gas in the cylinder is heated up. If the pressure only
increases slightly, what will happen to the volume of the cylinder? Why?
Ideal Gas Law:
1.
2.
3.
4.
5.
6.
7.
8.
9.
At what temperature will 0.654 moles of neon gas occupy 12.30 L at 1.95 atm?
A sample of argon gas at STP occupies 56.2 L. Determine the number of moles of argon.
A gas is compressed in a 25 L storage tank under a pressure of 150 kPa and a temp of
21°C. How many moles of gas are contained in the tank?
What volume will 45 grams of hydrogen gas occupy at 1.05 atm and 25°C?
At what temperature will 5.00 g of Cl2 exert a pressure of 900 mm Hg at a volume of 750.0 mL?
A 143.03 g sample of a gas is at 1789.7 torr, 256.8 K and occupies 29.1 L. What is the chemical
formula for this gas? (hint: find the molar mass first)
A 28.8 g piece of dry ice (solid carbon dioxide) is allowed to sublime (convert directly from a
solid to a gas) into a large balloon. Assuming that all of the carbon dioxide ends up in the balloon,
what will the volume of the balloon be at a temperature of 22°C and a pressure of 742 mm Hg?
Calculate the density of NO2 gas at 0.97 atm and 35°C.
Ammonium nitrate decomposes explosively upon heating according to the following equation:
2NH4NO3(s)
2N2 (g) + O2 (g) + 4H2O (g)
Calculate the total volume of gas produced at 125°C and 748 mm Hg when 1.55 kg of ammonium
nitrate completely decomposes.
10. Aerosol cans carry clear warnings against incineration because high pressures can develop at high
temperature. Using the ideal gas law, explain the basis for this warning.
11. A yet unknown chemist presents his findings at a news conference on the treatment of a major
disease, stating that: "This process will radically improve the way patients are treated. A small 1
mol dose of the drug is vaporized in a 20 L chamber at a temperature of 300K and pressure of 10
atm. Please invest generously in our company." Should you believe him and invest in his
company? Explain.
12. You are given a sample of an unknown gas. Describe how you can identify the gas in the
laboratory. What measurements will you make? What apparatus might you need?