Lab Experience n. 5 Gay-Lussac's Law

Tuesday 12th February 2013

Lab Experience n. 5 Gay-Lussac's Law

Objective/Task:

Test Gay-Lussac's Law, see how the pressure of a gas changes as we change the temperature.

Background Information:

Pressure: The force exerted per unit area of surface, typical pressure units are ATM, mmHg and kPa.

Volume: The measurement of space taken by a substance, it is length cubed, typical units are L, mL and m3.

Temperature: A measure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or degrees designated on a standard scale. Typical units are K, F and C. (1)

Suppose we double the thermodynamic temperature of a sample of gas. According to Charles’s law, the volume should double. Now, how much pressure would be required at the higher temperature to return the gas to its original volume? According to Boyle’s law, we would have to double the pressure to halve the volume. Thus, if the volume of gas is to remain the same, doubling the temperature will require doubling the pressure.This law was first stated by the Frenchman Joseph Gay-Lussac (1778 to 1850). According to Gay-Lussac’s law, for a given amount of gas held at constant volume, the pressure is proportional to the absolute temperature. Mathematically,

                                                               where kG is the appropriate proportionality constant.

Gay-Lussac’s law tells us that it may be dangerous to heat up a gas in a closed container. The increased pressure might cause the container to explode. (2)

Hypothesis:

To start with we should say that what we will say is not a hypothesis, it is a direct conclusion from Gay-Lussac's Law. 
As a direct conclusion from Gay-Lussac Law we state that there is a the pressure of a sample of gas at constant volume, is directly proportional to its temperature in Kelvin, in simpler words, as we increase the temperature of a gas with a constant volume, the pressure will also increase.

Variables:

Independent variable: Temperature (ºC)
Dependent variable: Pressure (hPa)
Controlled variables: Volume of gas. The mass, the amount of gas inside the tube, as it was closed. The nature of the gas (atmospheric gas which is mainly nitrogen). 

Material/Equipment:

- Tripod
- Stand and clamp
- Bunsen burner
- Magnetic stirrer + stir bar (Picture 1)
- Water Container
- Wood squares (Wood planks)
- Gas pressure sensor
- Laptop (including the programme Logger Pro) 

Procedure:

1. Place the water container on top of the tripod. Adjust the height of wood planks so that the magnetic stirrer is at the same level of the tripod. Make one corner of the container be on top of the tripod and the other corner on top of the wood planks.

2.  Arrange the gas tube in the stand with the clamp. Place it inside the water container. (As we want water to circulate, so it must not touch the bottom part).

3. Pour water into the container, just until the elastic band, so that the tube is completely covered except from the plastic tubule. 

4. Set up the bunsen burner and place it under the tripod.

5. Place the stir bar inside the water bath and turn on the magnetic stirrer.

6. Open in your lap top the Logger Pro 3.6.0 computer program to record the data you will obtain.

7. Connect the gas pressure sensor to the plastic tubule, to know the pressure of the gas in the tube, and to the laptop by the USB entrance. 

8. Connect the Temperature Probe (sensor) USB entrance to the laptop and place the other part inside the water bath.

(Picture 2 - how it would like)

9. Put ice inside the water bath to cool down the temperature of the water and consequently the temperature of the gas in the tube. Remove it after 5 minutes.

10. Collect/record the data you have at the moment in the computer program. 

11. Light up the bunsen burner. Once the temperature has increased 3 or 4 degrees remove the bunsen burner from the water container and allow the temperature to stabilize and just then collect the data. 

12. Repeat this last step as many times as you can to record as many data as possible. (try to obtain at least 12)

13. Make a table and a graph with your results.

Results: 

It will be the same for all gases. It is a general law in nature for gases, as you will find the same result for all the gases. It is a general property of matter.

Conversions:
1 K = 273 ºC
1hPa = 0.000986923266716 atm

Explanation of Reyes: How to make a graph using excel?

(At first it was going to be a video, but the programme she was using couldn't produce videos at all, and she couldn't find a better solution)

In Gay Lussac’s Law experiment we need to make a graph using the data we have obtained. In order to do it we have to follow these steps:

Firstly, include the values to do a table. The first column will contain the pressure values and the second column will contain the temperature values. Name the first column P (hPa), and write it at the top of the table. hPa stands for hectopascals. Below it write the values in order. Then, name the second column t (ºC), and fulfill it the same way you did it with the first column.

Secondly, copy the first column and paste it at the right side of the second column, because the temperature has to be the independent variable and the pressure the dependant one in the graph (so, when the temperature rises, the pressure rises too).

Thirdly, make the graph. In order to do it, select the two columns with the mouse, after that click the button “insert” and click in the graphs section “dispersion only with markers”. The most important thing now is to do the best fitting line. Select the points with the mouse and click the right button, and click “add line of tendency”. Click afterwards “lineal” and also “show the equation in the graph” and “show the value R squared in the graph”. These final two are needed to show the error value in the graph. It is called the regression coefficient and it can be 1 maximum. If it reaches 1, the result will be perfect.

Table 1: Table that shows how the temperature affected the pressure of a gas with a determined volume.

P (hPa)	t (ºC)
15,4745423	100,80167
20,74013	102,4353
25,5784592	104,139604
29,4939479	105,413909
33,6073767	106,824685
37,3726825	108,04899
41,0636121	109,336876
45,282456	110,734052
49,227756	112,138357
53,0649118	113,429115
57,1886965	114,889873
60,8728898	116,164178
64,3273836	117,444936

Table 2: Table that shows the conversion from the units obtained of the magnitudes studied to the S.I units of these magnitudes. 

P (hPa)	P (atm) - SI	t (ºC)	T (K) - SI
15,4745423	0,0153198	100,80167	373,80167
20,74013	0,02053273	102,4353	375,4353
25,5784592	0,02532267	104,139604	377,139604
29,4939479	0,02919901	105,413909	378,413909
33,6073767	0,0332713	106,824685	379,824685
37,3726825	0,03699896	108,04899	381,04899
41,0636121	0,04065298	109,336876	382,336876
45,282456	0,04482963	110,734052	383,734052
49,227756	0,04873548	112,138357	385,138357
53,0649118	0,05253426	113,429115	386,429115
57,1886965	0,05661681	114,889873	387,889873
60,8728898	0,06026416	116,164178	389,164178
64,3273836	0,06368411	117,444936	390,444936

Graphs to show how the pressure of the gas studied with constant volume changed as we increased the temperature.

Graph 1: Temperature (ºC) vs Pressure (hPa)

Graph 2: Temperature (K) vs Pressure (atm) - S.I Units

Conclusions:

We are proud to say that we carried out  the experiment really well because the results we obtained were really closed to what would be perfect. As you can see on the graphs there is a value expressed by R, it refers to the regression coefficient. The ideal value for R is 1, meaning that as closer your experimental R gets to one the better the results - less error. The real value we should take for our experimental R is 0,9998 and not 1, because we should take into account that in the values for the second graph there is more rounding.

We have done a very good experiment because we had 0,0002 points of difference only to reach perfection, because our regression coefficient was 0,9998. In this case we can say that our results have been both very accurated and precised.

In this case we knew that the nature of the gas atmospheric gas which is mainly nitrogen. Furthermore you should know by now that if an experience shows a patter, there is some underline, physical reason. In this case the physical reason refers to Gay-Lussac's Law which is the same for all gases, so it is a general law in nature of gases. 

Pictures:

1.

2.

Videos:

Isabel Caro 

Bibliography:

(1)The ChemEd DL (Sunday, 23 August 2009 13:07); 

Gay-Lussac's Law, Retrieved February 15, 2013 from: http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Gay-Lussac-s-Law-952.html

(2)The Columbia Encyclopedia, 6th ed.. 2012."Gay-Lussac's law." Retrieved February 15, 2013 from Encyclopedia.com: http://www.encyclopedia.com/doc/1E1-X-GayLussa.html