According to Boyle’s Law, the volume of any given amount of gas held at a constant temperature varies inversely with the applied pressure. In other words, when the pressure increases the volume decreases. When pressure decreases, volume increases. This can be derived from the following equation: P1 V1=P2 V2

The common use of this equation is to predict how a change in pressure or volume will alter the volume/pressure of the gas. Thus, the product of the initial volume and pressure is equal to the product of pressure and volume after a change in either pressure or volume under constant temperature.

Aim:
In this experiment, we will investigate the relationship between the pressure and volume of air. My hypothesis is as we decrease the volume (press down on the syringe) then the pressure measured by the pressure gauge will increase.

Materials:

* Pressure gauge (kPa = ± 2.0) (mmHg = ± 10.0)
* Rubber stopper
* Extender
* Stopcock
* 60.0 mL Syringe (± 0.5)

Figure 1a Figure 1b
Procedure:

1. Obtain all required materials from the teacher.

2. Fill the syringe to its maximum measured capacity of air (60.0 mL ± 0.5) by gradually pulling the syringe extender away from the actual syringe. [See Figure 1a]. Next, carefully attach the syringe to the stopcock, extender, rubber stopper, and pressure gauge accordingly. [See Figure 1b] Make sure the stock cock is opened (test the stock cock and syringe head of time so you know that the left turn allows the air to flow though while the right turn closes the valve and doesn’t let air escape) so that the air from the syringe can enter through the extender to the pressure gauge.

3. Using the 60.0 mL ± 0.5 syringe, for the first trial carefully push the plunger down slightly to a lowered volume of 55.0 mL ± 0.5 and hold this position to record the pressure movement (the inner red numbers represent pressure in units of kilopascals, while the outer numbers in the black font are measured in mmHg or Mercury).

4. Repeat step 3, but instead of lowering the plunger to 55.0 mL ± 0.5, lower the plunger at a constant interval of 5 [so that the next data point is 50.0 mL ± 0.5, and the next 45.0 mL ± 0.5, 40.0 mL ± 0.5, 35.0 mL ± 0.5, 30.0 mL ± 0.5, 25.0 mL ± 0.5, 20.0 mL ± 0.5] each time accurately recording the pressure readings.

5. Graph and interpret data and the relationship between pressure and volume of air at room temperature.

Results:

Summary Data of Volume and Pressure of air (gaseous mixture that mostly includes nitrogen, oxygen, argon and carbon dioxide) at a constant room temperature of 21.0 ± 1.0?C. Volume (mL) (± 0.5)| Pressure (mmHg) (± 10.0)| Pressure (kPa) (± 2.0)| 55.0| 90.5| 12.1|

50.0| 100.1| 13.3|
45.0| 110.0| 14.7|
40.0| 125.0| 16.7|
35.0| 145.0| 19.3|
30.0| 165.5| 22.1|
25.0| 200.0| 26.7|
20.0| 250.1| 33.3|

Data Summary of Pressure and Inverse Volume
1/Volume (1/mL) (±0.001)| Pressure x Volume (mmHg)| Pressure x Volume (kPa)| 0.018| 4977.5| 665.5|
0.020| 5005.0| 665.0|
0.022| 4950.0| 661.5|
0.025| 5000.0| 668.0|
0.029| 5075.0| 675.5|
0.033| 4965.0| 663.0|
0.040| 5000.0| 667.5|
0.050| 5002.0| 666.0|

Theoretical Pressure Calculations:
P1 V1=P2 V2

Using the equation P1 V1=P2 V2, I calculated the actual pressure (the value that I theoretically could produce) and compared it with my experimental value (what I measured during the experiment itself). Both sides of the equation must balance each other.

Trial 1:
P1 V1=P2 V2
(90.5 mmHg ± 10.0)(55.0 mL ± 0.5) = (P2) (50.0 mL ± 0.5)
P2 = 99.6 mmHg ± 10.0%

Trial 2:
(100.1 mmHg ± 10.0)(50.0 mL ± 0.5) = (P2) (45.0 mL ± 0.5) P2 = 111.2 mmHg ± 9.0%

Trial 3:
(110.0 mmHg ± 10.0)(45.0 mL ± 0.5) = (P2) (40.0 mL ± 0.5) P2 = 123.8 mmHg ± 8.1%

Trial 4:
(125.0 mmHg ± 10.0)(40.0 mL ± 0.5) = (P2) (35.0 mL ± 0.5) P2 = 142.9 mmHg ± 7.0%

Trial 5:
(145.0 mmHg ± 10.0)(35.0 mL ± 0.5) = (P2) (30.0 mL ± 0.5) P2 = 169.2 mmHg ± 5.9%

Trial 6:
(165.0 mmHg ± 10.0)(30.0 mL ± 0.5) = (P2) (25.0 mL ± 0.5) P2 = 198.0 mmHg ± 5.1%

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Trial 7:
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(200.0 mmHg ± 10.0)(25.0 mL ± 0.5) = (P2) (20.0 mL ± 0.5) ————————————————-
P2 = 250 mmHg ± 4.0%
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If we compare the experimental and hypothetical pressure values for each trial, we can see that all the values are relatively accurate because the measurement for each are very close (within a ± 3.0 mmHg ranges) to the true or accepted value (theoretical). ————————————————-

Pressure Percent Error calculations:

Trial 1:
% Error = |125.1 ±10.0 –123.8± 10.0%|99.6 ± 10.0% x 100

% Error = 0.50%
Trial 2:
% Error = |110.0 ±10.0 –111.2± 9.0%|111.2 ± 9.0% x 100

% Error = 1.08%

Trial 3:
% Error = |125.0 ±10.0 –123.8± 8.1%|123.8 ± 8.1% x 100

% Error = 0.97%

Trial 4:
% Error = |145.0 ±10.0 –142.9± 7.0%|142.9 ± 7.0% x 100

% Error = 1.47%

Trial 5:
% Error = |165.5 ±10.0 –169.2± 5.9%|169.2± 5.9% x 100

% Error = 2.19%

Trial 6:
% Error = |200.0 ±10.0 –198.0± 5.1%|198.0± 5.1% x 100

% Error = 1.01%

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Trial 7:
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% Error = |250.1 ±10.0 –250.0± 4.0%|250.0± 4.0% x 100
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% Error = 0.04%
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The percent errors for all of these trials (Trial1-Trial7) all support the accuracy and reliability of the data because the percent errors are minimal and small which exemplify that the experimental result was very close to the hypothetical (or theoretical) pressure. This shows a direct inverse correlation between pressure and volume.
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Analysis:
The comparative graph is shown below:

The slope of this graph exemplifies an inverse relationship. As pressure increases, volume decreases. As volume increases, pressure decreases. Figure 2

The slope of this graph exemplifies a direct proportional relationship between pressure and the inverse volume.
Figure 3
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Conclusion:

From this experiment, the relationship between pressure and volume is explored and analyzed. As volume increases, pressure decreases. As volume decreases, pressure increases. Thus, the pressure and volume of air (which is a mixture of several gaseous components such as nitrogen, oxygen, argon, and carbon dioxide) at a constant temperature (in this case, room temperature of 21.0 ± 1.0?C.) have an inverse relationship (as shown in Figure 4 which exemplifies an exponential decay). This is also known as Boyle’s Law, which can be dated back to 1662. Also, from Avogadro’s Law, we can conclude that the pressure of a gas depends on both volume and temperature, but not composition of the gas or whether the gases are all the same or not.

From the inverse volume versus pressure graph (seem in Figure 3), a straight constant line is produced. This reveals that pressure is proportional to the inverse of volume. The reason that pressure and volume are inversely related is because a gas is made up of loosely packed molecules moving in a random motion. When a gas is compressed in a container, the molecules are pushed closer, which results in a smaller volume that air occupies. The molecules now are forced to bounce in a closer proximity, which inevitably exerts more pressure.

During my experiment, when I pressed the syringe down to a volume of 55 mL ± 0.5, the pressure gauge read approximately 90.5 mmHg (± 10.0) or (12.1 kPa ± 2.0). Then, when I pressed the syringe down even further to 45 mL ± 0.5, the pressure increased to 100.1 mmHg (± 10.0) (or 13.3 kPa ± 2.0). Theoretically, using the equationP1 V1=P2 V2, I calculated P2 to be 99.6 mmHg ± 10.0%, resulting in a tiny percent error of 0.50%. Even for all of the other trials, the percent error of all my experimental values didn’t exceed within a ± 3.0% of the theoretical values. Thus, my data is reliable and does not refute my hypothesis in that pressure and volume are inverse relationships of each other.

Boyles Law applies only to ideal and theoretical gases. However this equation is accurate enough for use in practical labs and applications. Thus, the data from this experiment is not exact, but relatively precise and accurate. Since the summary of percent uncertainty was greater than the overall percent error itself, this reveals that most of the errors occurred in the equipment itself (limitations of the equipment). Thus, my data is reliable because the percent error is not higher than my percent uncertainty which would indicate a mistake in the experimenter. However, there are several sources of errors which may have skewed the data. For example, air currents may have altered the volume and pressure of the air when we were compressing the syringe. Furthermore, again, there could have been a design flaw in the equipment of this experiment (such as a hole in the syringe, or broken pressure gauge). Ways to improve this lab is to take more trials with a greater and longer syringe. Furthermore, we could use different types of gases and see the effects of each on pressure and volume.

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[ 2 ]. Gas Experiments. N.d. S17 Science – Science supplies and servicesWeb. 31 Jan 2013. . [ 3 ]. Banner, Ted. Pre – Lab Pressure and Volume Relationships. 2010. Slide Share – Present YourselfWeb. 31 Jan 2013.