Gas laws Review

Boyles’ Law 1) 1.00 L of a gas at standard temperature and pressure is compressed to 473 mL. What is the new pressure of the gas? 2) In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x 106 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion? 3) Synthetic diamonds can be manufactured at pressures of 6.00 x 104 atm. If we took 2.00 liters of gas at 1.00 atm and compressed it to a pressure of 6.00 x 104 atm, what would the volume of that gas be? 4) The highest pressure ever produced in a laboratory setting was about 2.0 x 106 atm. If we have a 1.0 x 10-5 liter sample of a gas at that pressure, then release the pressure until it is equal to 0.275 atm, what would the new volume of that gas be? 5) Atmospheric pressure on the peak of Mt. Everest can be as low as 150 mm Hg, which is why climbers need to bring oxygen tanks for the last part of the climb. If the climbers carry 10.0 liter tanks with an internal gas pressure of 3.04 x 104 mm Hg, what will be the volume of the gas when it is released from the tanks? 6) Part of the reason that conventional explosives cause so much damage is that their detonation produces a strong shock wave that can knock things down. While using explosives to knock down a building, the shock wave can be so strong that 12 liters of gas will reach a pressure of 3.8 x 104 mm Hg. When the shock wave passes and the gas returns to a pressure of 760 mm Hg, what will the volume of that gas be? 7) Submarines need to be extremely strong to withstand the extremely high pressure of water pushing down on them. An experimental research submarine with a volume of 15,000 liters has an internal pressure of 1.2 atm. If the pressure of the ocean breaks the submarine forming a bubble with a pressure of 250 atm pushing on it, how big will that bubble be? 8) Divers get “the bends” if they come up too fast because gas in their blood expands, forming bubbles in their blood. If a diver has 0.05 L of gas in his blood under a pressure of 250 atm, then rises instantaneously to a depth where his blood has a pressure of 50.0 atm, what will the volume of gas in his blood be? Do you think this will harm the diver?

Boyles’ Law ANSWERS 1) 2.11 atm 2) 2.0 x 10­5 L 3) 72.7 L 8) V = 0.25 L, yes

Charles’ Law Worksheet 1) The temperature inside my refrigerator is about 40 ºCelsius. If I place a balloon in my fridge that initially has a temperature of 220 ºC and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? 2) A man heats a balloon in the oven. If the balloon initially has a volume of 0.4 liters and a temperature of 20 ºC, what will the volume of the balloon be after he heats it to a temperature of 250 ºC? 3) On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they have not been opened. If I have a 250 mL bag at a temperature of 19 ºC, and I leave it in my car which has a temperature of 600 ºC, what will the new volume of the bag be? 4) A soda bottle is flexible enough that the volume of the bottle can change even without opening it. If you have an empty soda bottle (volume of 2 L) at room temperature (25 ºC), what will the new volume be if you put it in your freezer (-4 ºC)? 5) Some students believe that teachers are full of hot air. If I inhale 2.2 liters of gas at a temperature of 180 ºC and it heats to a temperature of 380 ºC in my lungs, what is the new volume of the gas? 6) How hot will a 2.3 L balloon have to get to expand to a volume of 400 L? Assume that the initial temperature of the balloon is 25 ºC. 7) I have made a thermometer which measures temperature by the compressing and expanding of gas in a piston. I have measured that at 1000 ºC the volume of the piston is 20 L. What is the temperature outside if the piston has a volume of 15 L? What would be appropriate clothing for the weather?

Charles’ Law Worksheet ANSWER KEY 3) 285 mL 4) 1.81 L 5) 2.35 L 6) 51,800 K 7) The temperature is 298.5 K, which corresponds to 0.50 ºC. A jacket would be appropriate clothing for this weather.

The Ideal Gas Laws 1) If four moles of a gas at a pressure of 5.4 atmospheres have a volume of 120 liters, what is the temperature? 2) My car has an internal volume of 2600 liters. If the sun heats my car from a temperature of 200 ºC to a temperature of 550 ºC, what will the pressure inside my car be? Assume the pressure was initially 760 mm Hg. How many moles of gas are in my car? 3) A toy balloon filled with air has an internal pressure of 1.25 atm and a volume of 2.50 L. If I take the balloon to the bottom of the ocean where the pressure is 95 atmospheres, what will the new volume of the balloon be? How many moles of gas does the balloon hold? (Assume T = 285 K)

The Ideal Gas Laws ANSWERS 1) 1973 K 2) 840 mmHg; 67 moles 3) 0.033 L; 0.13 moles

Conceptual Question 1 Air is contained in a sealed tank of fixed volume. The air in the tank is initially at 20 °C and 1 atm (101.3 kPa). It is then heated to 250 °C. What will happen to the density of the air in the container? a. Density will decrease b. Density will not change c. Density will increase d. Insufficient information

Conceptual Question 1 ANSWER b. Density will not change

Conceptual Question 2 In a cryogenics (extreme cold) demonstration, a scientist takes a small, partially inflated balloon out of liquid nitrogen (at a very low temperature). As the balloon rests on the table, it begins to grow in size. Explain this phenomenon.

Conceptual Question 2 ANSWER Volume vs. temperature relationship Direct, when one increases so does the other Specifically, gas particles are moving faster and spreading out farther from one another

Conceptual Question 3 Huge weather balloons partially filled with helium are sent high into the earth’s atmosphere to examine the air. As a balloon rises into the air, the air pressure outside the balloon decreases rapidly. If the atmospheric pressure becomes one-third of its original pressure, what will happen to the balloon volume? Explain.

Conceptual Question 3 ANSWERS Pressure vs. volume relationship Indirect, when one increases, the other decreases and vice versa Balloon will grow to 3 times the size Less pressure on gas molecules in balloon. They have the freedom (and energy) to move more and take up more space

Conceptual Question 4 Use the kinetic molecular theory to explain why on a cold autumn morning a camper’s air mattress may appear to be somewhat flatter than it was when blown up the afternoon before. Assume no leaks.

Conceptual Question 4 ANSWERS Volume vs. temperature relationship Direct When temp decreases so does volume As temp cools, gas particles move slower = take up less space

Conceptual Question 5 What is the effect of increasing temperature on the volume of a gas? Increase Decrease Stays the Same

Conceptual Question 5 ANSWERS Volume increases Direct relationship

Conceptual Question 6 What is the effect of increasing temperature on the density of a gas? Increase Decrease Stays the Same

Conceptual Question 6 ANSWERS Since volume increases when temp increases, density will decrease Same mass of gas taking up more space

Conceptual Question 7 360 kPa = __ atm = __ mmHg

Conceptual Question 7 ANSWERS 360 kPa = 3.55 atm = 2700 mmHg

Conceptual Question 8 Sketch what a graph of : volume vs. temperature would look like for any gas. pressure vs. volume would look like for any gas. pressure vs. temperature would look like for any gas.

Conceptual Question 8 ANSWERS Sketch what a graph of : volume vs. temperature would look like for any gas. pressure vs. volume would look like for any gas. pressure vs. temperature would look like for any gas.

Conceptual Question 9 (not really conceptual – more like mathematical Calculate the number of liters that 0.730 mole of CO2 occupies at STP.

Conceptual Question 9 ANSWERS 0.730 moles CO2 x 22.4 L = 16.4 L 1 mole

Conceptual Question 10 At a birthday party a child sits on a partially filled balloon, decreasing its volume by 1/2. What is the new pressure inside the balloon?

Conceptual Question 10 ANSWERS Pressure vs. volume relationship Indirect = when 1 increases the other decrease 2 times the pressure inside the balloon since gas particles can occupy ½ the amount of space