Boyle's Law SimulationLab (Just answer the Q's and fill in the stuff)

Introduction:

Boyle's Law describes the relationship between the pressure and the volume of a system of gas when all other variables are unchanged. Mathematically it can be described as P₁V₁=P₂V₂. Your task: Find (or verify) the relationship between the pressure and volume of an enclosed gas. Through a simulation, you will change the volume of a container or gas and see how the pressure changes. Then you will collect several points of data and make a graph of absolute pressure vs. volume.

The condition that "all other variables remained unchanged" is important. If temperature or number of gas molecules change, the equation P₁V₁=P₂V₂ is no longer valid. Even though we are not adding heat to the tube of gas, its temperature WILL rise slightly when it is compressed, so one should wait a few seconds after compressing for thermal equilibrium to be reestablished (wait for the gas in the container to cool).

Procedure:

Use the Phet simulation to record highly accurate data for your graph of pressure vs. volume.

Open the simulation athttps://phet.colorado.edu/en/simulation/gas-properties

Click on the "Measurement Tools" button. Click on the Ruler. This will cause a ruler to appear. The ruler's units are in nanometers (nm), since our box would have to be very small to build up significant pressure with so few gas molecules (the simulation is realistic in this way!). You will use the ruler to measure the width of the box, but we need to use that measurement to give us a measurement of volume. Let's call the length L and the height H. The volume will be W*L*H. For example: initially the box should have a width of 6.6 nm and the volume will be 6.6*L*H nm³. Then you might expand the box to 8.2 nm wide. Since the length and height will not change, you can say the volume is now 8.2*L*H nm³. The volume will always be the number you measure for width times L times H, so, for simplicity's sake, let's just drop the L*H and simply report the width as our volume, although, technically, that is cheating.

First, you need to add a gas to your container.

Boyle's Law looks at the relationship between volume and pressure when there is a constant temperature. You must set your container to constant temperature. Click on the Temperature button in the "Constant Parameters" on the upper right corner. This will cause the temperature to automatically adjust to whatever the initial value is set at. Set your temperature to constant.

You are going to adjust the volume of the container by clicking on the handle on the left side of the container and dragging it to various widths.

Play with the "Gas in Chamber" parameters in the upper right, and get a mix of heavy and light gasses. Notice how their motions differ. According to the Kinetic Molecular Theory, what action causes pressure on the inside of the container? ______________________________________________________________

Fill in the following chart by selecting various Volumes. Measure the volume of the container using the ruler (insert the number on the ruler, although this is cheating, as mentioned earlier).

Calculate the values as indicated in the other columns.

Trials	Volume (V) (nm3)	Pressure (P) (atm)	Calculate k1 =(PxV)	Calculate k2 =
Trial 1
2
3
4
5

Which variable did you control (independent)? ____________________________

Which variable is the dependent variable? ____________________________

Graph Pressure vs. Volume in Excel or submit a photo of your graph on paper.

As the volume gets larger, what happens to the pressure of the gas?

Which value remains consistent in the data table, k₁ or k₂ ?

This k-value is constant; the ratio between volume and temperature of any point on the graph will be the same. Pick any two points from the graph or table:

Point #1 Point #2

V₁ = V₂ =

P₁ = P₂ =

Considering which k value is constant between these two points, show a equation for Boyles's Law:

We can use this formula to predict the pressure (P₂) or volume (V₂) of any gas.Use this formula to complete the following calculation. Show your work: If a gas has a volume of 1.25 L and a pressure of 1.75 atm, what will the pressure be if the volume is changed to 3.15 L?

Marshmallows are full of very small pockets of air. Tell me your hypothesis about what will happen when you put marshmallows in a vacuum, and include WHY:

__________________________________________________________________________________________

Then watch what happens when you DO it (https://www.youtube.com/watch?v=bWd31AefKns ) and compare the observed results to your expectations:

____________________________________________________________________________________

Plunger Experiment:

One could perform an experiment in real life similar to what we did in the simulation by adding weight to a syringe and measuring its volume as it contracts (see picture). Before you add any weight to the plunger (IMMEDIATELY after the tube is sealed), the absolute pressure in the syringe is equal to atmospheric pressure, 1 ATM (101,000 Pa). The pressure you are ADDING by putting weight on the plunger is the gauge pressure. The absolute pressure in the tube is the gauge pressure plus atmospheric pressure.

Finish filling out the third row in this table (work your way from left to right). The first column is for the situation where there is no mass placed on top. The second row is filled out as an example. Something to keep in mind is that the mass of the weight you add to the plunger is NOT the pressure you are adding to the tube. The gauge pressure you are adding is the force applied by the weight divided by the area over which that force is applied (the cross sectional area of the cylinder or the surface area of the circular plunger). The area of a circle is pr² where r is the radius, but it is easier to measure the diameter (let's say you measured the diameter to be 1.5 cm=0.015m), so you could use the formula A = (p/4)d² = 0.000177m²

Mass (kg)	Force (N) (mass* 9.8m/s2)	Cross sectional area of plunger	Gauge pressure (Pa) (Force/area)	Absolute pressure (Pa) (Gauge pressure + 101,000 Pa)	Volume
0	0	0.000177m2	0	101,000	50.0 mL
0.5 kg	4.9 N	0.000177m2	4.9N/0.000177m2= 27,680Pa	128,680	39.2 mL
2.0 kg		0.000177m2			22.1mL

Use the ideal gas equation (PV = nRT) to find the number of moles of gas (n) in the plunger. You could use values from any of the three rows of the table. Use Pa as your unit of pressure, m³ as your unit of volume (convert from mL), and Kelvin as your unit of temperature (assume it is at room temperature). You should use 8.314 J/K*mol as the gas constant R. (In physics we should practice using SI units, so for those who have done chemistry, don't use the 0.082 gas constant that involves L and ATM instead of m³ and Pa.)

Bonus: Looking at Boyle's Law, P₁V₁=P₂V₂, you can see that every time pressure gets decreased by half, the volume must double. Let's use this fact to sketch out a rough graph below that will show us the general shape our experimental graph should have. Set up a graph with P on the y axis and V on the x axis, where each axis goes up to a maximum value of 32 (in some completely random arbitrary units). Start with high pressure, low volume, a data point where the pressure is 32 and the volume is one. Mark this point on your graph. For the next point, cut the pressure in half (divide by 2) and double the volume to two. For the third point, cut the pressure in half AGAIN, and double the volume again to 4. Keep dividing pressure by two and doubling volume, and mark these points on the graph, until your volume gets all the way up to 32. Does this graph look like the previous one?

Bonus 2: Solve the ideal gas equation for pressure and combine n, R, and T into one constant, k (get one numerical value for k). Graph this equation (P = k/V becomes y = k/x) on a graphing calculator, and quickly sketch what it looks like. This is again what your experimental graph should look like.

Link for reference of simulation is https://phet.colorado.edu/en/simulati