Student Exploration: Boyle’s Law and Charles’s Law

Name:‬ ‭Date:‬ ‭Student Exploration: Boyle’s Law and Charles’s Law‬ ‭ irections: Follow the instructions to go through the simulation. Respond to the questions and‬ D ‭prompts in the orange boxes.‬ ‭Vocabulary‬‭:‬‭absolute zero, Boyle’s law, Charles’s‬‭law, Gay-Lussac’s law, Kelvin scale, pressure‬ ‭ small helium tank measures about two feet (60 cm) high. Yet it can fill over 50 balloons! How can such a‬ A ‭small tank contain enough helium to fill so many balloons?‬ ‭It can fill a lot of balloons because the helium is pressurized‬ ‭ izmo Warm-up‬ G ‭The Boyle’s Law and Charles’s Law Gizmo shows a container of gas. Inside, small purple spheres represent‬ ‭gas molecules.‬ ‭1.‬ ‭Observe the particles. Are they all moving at the same speed?‬ ‭no, some particles are faster than others‬ ‭2. How do the particles interact with the walls and lid of the container?‬ ‭particles collide with container and other particles.‬ ‭ hese interactions contribute to the‬‭pressure‬‭on the‬‭walls of the container. Pressure is defined as force per‬ T ‭unit area. The SI units of pressure are newtons per square meter (N/m‬‭2‭)‬ , or pascals (Pa).‬ ‭2.‬ S ‭ lowly drag the temperature (‬‭T‬‭) slider back and forth.‬‭(Note: In this Gizmo, the‬‭Kelvin scale‬‭is used to‬ ‭measure temperature. On the Kelvin scale, 0 degree s is‬‭absolute zero‬‭, the coldest possible temperature.‬ ‭Absolute zero is equal to -273.15 °C or -459.67 °F)‬ ‭A.‬ ‭How does the change in temperature affect the speed of the molecules?‬ t‭he particles move according to their temperature. (hot = faster, opposite‬ ‭for colder)‬ ‭B.‬ ‭How does the change in temperature affect the volume of the container?‬ I‭f the temperature goes up, the particles will have more space and the‬ ‭volume will increase.‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭Activity A:‬ ‭Boyle’s law‬ ‭Get the Gizmo ready‬‭:‬ ‭‬ S ● ‭ et the temperature (‬‭T‬‭) to 300 K.‬ ‭●‬ ‭Check that the mass (‬‭m‬‭) is set to 0 kg.‬ ‭Question: How does pressure affect the volume of a gas?‬ ‭1.‬ F ‭ orm hypothesis‬‭: In this experiment, you will pile‬‭weights on the lid of the container of gas. What do you‬ ‭think will happen as more weight is added to the lid?‬ ‭When you put weights on top of the container's lid, the pressure will increase.‬ ‭2.‬ ‭Notice‬‭: Look at the DESCRIPTION pane. What is the‬‭mass of the lid?‬‭.10 kg‬ ‭How much pressure does the lid exert on the gas?‬‭98.1‬‭N/M^2‬ ‭3.‬ C ‭ ollect data‬‭: With the temperature held constant at‬‭300 K, use the‬‭Select mass‬‭slider to place weights‬‭on‬ ‭the lid. Record the pressure and volume of the gas for each added mass.‬ ‭Added mass‬ ‭on the lid‬ ‭Total mass‬ ‭(lid + added mass)‬ ‭Pressure*‬ ‭Volume‬ ‭0 kg‬ ‭10 kg‬ ‭98.1‬ ‭2.54‬ ‭10 kg‬ ‭20 kg‬ ‭196.2‬ ‭1.27‬ ‭20 kg‬ ‭30 kg‬ ‭294.3‬ ‭0.85‬ ‭30 kg‬ ‭40 kg‬ ‭392.4‬ ‭0.64‬ ‭*This model does not include atmospheric pressure, which is 101,325 N/m‬‭2‬‭.‬ ‭4.‬ ‭Analyze‬‭: As the pressure increases at constant temperature,‬‭what happens to the volume of the gas?‬ ‭pressure increases, volume decreases‬ ‭This relationship is called‬‭Boyle’s law‬‭.‬ ‭5.‬ ‭Calculate‬‭: Compare the pressure and volume values‬‭in your data table.‬ ‭A.‬ ‭How did doubling the pressure change the gas volume?‬ ‭divided V by 2‬ ‭B.‬ ‭How did tripling the pressure change the gas volume?‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭divided V by 3‬ ‭C.‬ ‭How did quadrupling the pressure change the gas volume?‬ ‭divided V by 4‬ ‭6.‬ P ‭ redict‬‭: If the added mass on the lid was 50 kg, a‬‭total mass of 60 kg would exert pressure on the gas‬ ‭inside the container. What will be the volume of the gas?‬ ‭0.40 m^3‬ ‭7.‬ ‭Test‬‭: Test your prediction using the Gizmo. What is‬‭the volume of the gas?‬ ‭Was your prediction correct?‬ ‭0.42m^3‬ ‭no but close‬ ‭8.‬ C ‭ reate a graph‬‭: On the GRAPH tab, select‬‭V‬‭vs.‬‭P‬‭.‬‭Set‬‭m‬‭to 0 kg, and click‬‭Record‬‭to plot a point on‬‭the‬ ‭graph. Plot a point for each possible mass to create a graph showing the relationship between pressure‬ ‭and volume.‬ ‭ hen your graph is completed, click the‬‭camera‬‭(📷)‬‭icon to take a snapshot. Right-click the image, and‬ W ‭click Copy Image. Paste the image into the space below, and label the graph “Volume vs. Pressure.”‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭📷‬ ‭A.‬ ‭What is the shape of the graph?‬ ‭Exponential decay‬ ‭B.‬ H ‭ ow does this graph illustrate‬ ‭Boyle’s law?‬ ‭as the volume decreases, the pressure increases‬ ‭C.‬ H ‭ ow do you think the graph might change if the temperature was held constant at a higher‬ ‭temperature, say 400 K?‬ ‭Pressure would increase faster, and volume would decrease faster.‬ ‭9.‬ A ‭ pply‬‭: Think about a small helium tank that can fill‬‭50 balloons. What must be true about the helium in the‬ ‭tank compared to the helium in the balloons?‬ ‭The pressure in the tank must be greater than the pressure in the balloon.‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭Activity B:‬ ‭Charles’s law‬ ‭Get the Gizmo ready‬‭:‬ ‭●‬ O ‭ n the SIMULATION pane, set‬‭T‬‭to 100 K and‬‭m‬ ‭to 0 kg.‬ ‭Question: How does temperature affect the volume of a gas?‬ ‭1.‬ ‭Form hypothesis‬‭: How do you think the volume of a‬‭gas will change as the temperature rises and falls?‬ I‭f the temperature goes up the volume will as well. If the temperature goes down, the volume will‬ ‭decrease.‬ ‭2.‬ C ‭ ollect data‬‭: Without changing the mass on the lid,‬‭record the pressure and volume of the gas at each of‬ ‭the given temperatures.‬ ‭Temperature‬ ‭Pressure*‬ ‭Volume‬ ‭100 K‬ ‭98.10 N/M^2‬ ‭0.85‬ ‭200 K‬ ‭98.10 N/M^2‬ ‭1.70‬ ‭300 K‬ ‭98.10 N/M^2‬ ‭2.54‬ ‭400 K‬ ‭98.10 N/M^2‬ ‭3.39‬ ‭500 K‬ ‭98.10 N/M^2‬ ‭4.24‬ ‭*This model does not include atmospheric pressure, which is 101,325 N/m‬‭2‬‭.‬ ‭3.‬ ‭Analyze‬‭: As the temperature increases at constant‬‭pressure, what happens to the volume of the gas?‬ ‭the volume increases at a constant rate.‬ ‭This relationship is called‬‭Charles’s law‬‭.‬ ‭4.‬ E ‭ xplain‬‭: Based on the motions of the gas molecules,‬‭why do you think the volume changed as it did when‬ ‭the temperature was increased?‬ ‭ ith higher temperatures, the molecules move around more and therefore are under the same‬ w ‭amount of pressure at a higher volume.‬ ‭5.‬ ‭Think about it‬‭: Why do you think the pressure was‬‭the same in each test?‬ ‭Because the weight on the tank every test was the same.‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭6.‬ ‭Calculate‬‭: Compare the pressure and volume values‬‭in your data table.‬ ‭A.‬ ‭How did doubling the temperature affect the gas volume?‬ ‭double‬ ‭B.‬ ‭How did tripling the temperature affect the gas volume?‬ ‭triple‬ ‭C.‬ ‭How did quadrupling the temperature affect the gas volume?‬ ‭quadruple‬ ‭7.‬ ‭Predict‬‭: Suppose the temperature was 50 K. What will‬‭be the volume of the gas?‬ ‭0.42‬ ‭8.‬ ‭Test‬‭: Test your prediction using the Gizmo. What is‬‭the volume of the gas?‬ ‭0.42‬ ‭Was your prediction correct?‬ ‭yes‬ ‭9.‬ C ‭ reate a graph‬‭: On the GRAPH tab, select‬‭V‬‭vs.‬‭T‬‭.‬‭Set‬‭T‬‭to 50 K, and click‬‭Record‬‭to plot a point on‬‭the‬ ‭graph. Plot a point every 50 degrees to create a graph showing the relationship between temperature and‬ ‭volume.‬ ‭ hen your graph is completed, click the‬‭camera‬‭icon‬‭to take a snapshot. Paste the image into the space‬ W ‭below, and label the graph “Volume vs. Temperature.”‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭📷‬ ‭D.‬ ‭What is the shape of the graph?‬ ‭linear growth‬ ‭E.‬ H ‭ ow does this graph illustrate‬ ‭Charles’s law?‬ t‭emperature is proportional to volume if pressure is‬ ‭constant.‬ ‭10.‬‭Apply‬‭: Based on what you learned, what would happen‬‭to a balloon placed in the freezer?‬ ‭It would shrink.‬ ‭What would happen to a balloon placed in a warm oven? (Assume it doesn’t pop.)‬ ‭it would grow‬ ‭11.‬‭Think and discuss‬‭: Consider temperature, pressure,‬‭and volume. How does the mathematical relationship‬ ‭in Boyle’s law compare to that in Charles’s law?‬ ‭ oyle's Law describes an inverse relationship, which means that when the pressure goes up, the‬ B ‭volume goes down, provided the temperature remains constant. Charles's Law shows a direct‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ r‭ elationship. if the temperature rises, the volume also increases, as long as the pressure remains‬ ‭constant.‬ ‭Activity C:‬ ‭Gay-Lussac’s Law‬ ‭Get the Gizmo ready‬‭:‬ ‭●‬ O ‭ n the SIMULATION pane, set‬‭T‬‭to 300 K and‬‭m‬ ‭to 15 kg.‬ ‭●‬ ‭Turn on the‬‭Constant volume‬‭checkbox.‬ ‭Question: How does temperature affect the pressure of a gas when volume is constant?‬ ‭1.‬ F ‭ orm hypothesis‬‭: If the volume of a gas is held constant,‬‭how do you think the pressure will change as‬ ‭temperature increases?‬ ‭temp rises and volume and pressure decrease.‬ ‭2.‬ C ‭ ollect data‬‭: Select the TABLE tab. Record the pressure‬‭when‬‭T‬‭= 100 K, 200 K, and so forth up to 500 K.‬ ‭(Note: The volume will remain constant at 1.02 m‬‭3‬‭.)‬ ‭Pressure‬ ‭Temperature‬ ‭Pressure‬ ‭100 K‬ ‭196.20‬ ‭1.962 Pa/K‬ ‭200 K‬ ‭392.40‬ ‭1.962 Pa/K‬ ‭300 K‬ ‭588.60‬ ‭1.962 Pa/K‬ ‭400 K‬ ‭784.80‬ ‭1.962 Pa/K‬ ‭500 K‬ ‭981.06‬ ‭1.962 Pa/K‬ ‭Temperature‬ ‭3.‬ A ‭ nalyze‬‭: Divide the pressure by the temperature to‬‭fill in the last column of the table. Since 1 N/m‬‭2‬ ‭is equal‬ ‭to 1 pascal (Pa), write the units of the ratio as Pa/K.‬ ‭A.‬ ‭When the volume is held constant, how does the pressure change as temperature increases?‬ ‭temp increases pressure increases‬ ‭B.‬ ‭What do you notice about the ratio of pressure to temperature, when volume is constant?‬ ‭always 1.926 Pa/K‬ ‭ ay-Lussac’s law‬‭states that, at constant volume,‬‭the ratio of pressure to temperature is constant.‬ G ‭As temperature increases, pressure increases as well.‬ ‭4.‬ E ‭ xplain‬‭: Based on the motions of the gas molecules,‬‭why do you think the pressure changed as it did when‬ ‭the temperature was increased?‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭ s temp increase the molecules move faster making the number of collisions between the molecules‬ A ‭and the walls increase‬ ‭5.‬ ‭Calculate‬‭: Compare the pressure and temperature values‬‭in your data table.‬ ‭A. How did doubling the temperature affect the pressure?‬ ‭double‬ ‭B. How did tripling the temperature affect the pressure?‬ ‭triple‬ ‭C. How did quadrupling the temperature affect the pressure?‬ ‭quadruple‬ ‭1.‬ C ‭ reate a graph‬‭: Record the pressure for temperatures‬‭of 50 K, 150 K, 250 K, 350 K, and 450 K. On the‬ ‭GRAPH tab, select‬‭P vs. T‬‭. Click the‬‭camera‬‭icon to‬‭take a snapshot. Paste the image into the box below,‬ ‭and label the graph “Pressure vs. Temperature.”‬ ‭📷‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved‬ ‭F.‬ ‭What is the shape of the graph?‬ ‭linear, flat‬ ‭G.‬ H ‭ ow does this graph illustrate‬ ‭Gay-Lussac’s law?‬ ‭ hows that if volume stays the same when the temp‬ s ‭increases, the pressure does too.‬ ‭2.‬ A ‭ pply‬‭: Based on what you learned, what do you think‬‭would happen if you placed a sealed container of gas‬ ‭into a fire?‬ ‭As the temp. rises, the pressure will as well.‬ ‭3.‬ C ‭ hallenge‬‭: Combine Boyle’s law, Charles’s law, and‬‭Gay-Lussac’s law into a single proportional‬ ‭relationship between pressure (‬‭P‭)‬ , volume (‬‭V‭)‬ , and‬‭temperature (‬‭T‭)‬ . Use the symbol “∝” to represent‬‭“is‬ ‭proportional to.”‬ ‭Explain your reasoning.‬ ‭ harles's Law states that if the pressure remains constant, an increase in volume will lead to an‬ C ‭increase in temperature.‬ ‭ ay-Lussac's Law explains that if the volume stays the same, an increase in temperature will‬ G ‭increase pressure. This shows that the result of pressure and volume is directly proportional to‬ ‭temperature.‬ ‭ oyle's Law supports this idea by showing that if the temperature is kept constant, an increase in‬ B ‭pressure will cause the volume to decrease.‬ ‭Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved