Abstract
The experiment aimed at monitoring the change in volume of a gas in a confined container as the pressure on the gas was being increase. The experiment successfully demonstrated that volume decreases as the pressure on gas is increased.
Introduction
Boyle’s Law involves the relationship that exists between volume and pressure of an ideal gas, assuming that the mass and temperature of the gas is held constant. The law is stated that for a fixed ideal gas amount kept at a fixed temperature, pressure (P) and volume (V) are inversely proportional. This means that when one parameter is increased, the other one decreases. The relationship deducted from the experiment between the pressure and gas volume was
PV = k
There is much open space that exists between the gas molecules and are compressed when pressure is applied. Some of the applications of Boyle’s Law include when a balloon is squeezed decreasing the volume and increasing the pressure inside and when the balloon exceeds the one the balloon can withstand it bursts. The other application is when deep sea fish are come to the surface of the ocean they experience a decrease in the pressure on their body causing death. This occurs following an increase in the volume of air trapped within their body leading to rupturing of bladders, cells and membranes.
In this experiment, the pressure on a gas confined in a syringe was increased and the changes that result in the volume of the gas observed. Although air is made up of a mixture of gases primarily nitrogen, carbon dioxide and oxygen, the data obtained in the experiment was treated as data from a single gas. The collected data was then used to find the atmospheric pressure as well as determining how closely the results agreed with Boyle,s Law.
Methods
Materials
Several hardback text books of approximately equal weight
Bathroom scale
Small marshmallow
Two caps-60cc syringe
Wood blocks- top and bottom
Procedure
Five large hard-bound books of roughly equal weight were selected from a test book collection. The weight weight was confirmed using the bathroom scale. The end cap of the syringe spout was removed, and the piston pulled approximately to the 60mL position. The end cap was placed onto the syringe spout, and the syringe pushed down on the piston with the hand slowly and steadily until the volume of the trapped gas was reduced to about 20mL. The piston was released, and return to the initial volume noted. The test was performed several times and the position to which the piston returned each time became the starting position.
The volume at Volume Trial 1 at zero books was recorded. The base board of the Boyle’s Law apparatus was placed on a flat, steady surface, and the syringe placed onto the base support board so that the syringe spout points downward. The base board had been drilled to accommodate the shape of the pointed end of the syringe spout. The other wooden board was placed onto the top of the piston while supporting the apparatus with one hand. One book was placed onto the board above the piston and the resulting gas volume at Volume Trial 1 at 1 book was recorded. The readings were done on the side of the piston that touched the gas. The second book was placed onto the first book, and the book allowed to settle on the piston. The change in gas volume was recorded. Adding booked was continued and the resulting volume recorded until all the five books were resting on the board. All the books were removed from the piston, and the apparatus reset to the initial volume recorded. The experiment was repeated twice.
Results
The average volume recorded was recorded in Table 1 below from the zero books to five books.
The inverse 1/Average volume was calculated and the results recorded in Table 1. A graph of pressure in the number of books against volume in mL was plotted as in Figure 1 below.
Figure 1: A graph of pressure in number of books against volume in mL
A second graph of weight of books against the inverse of the volume was plotted as shown in Figure 2 below and the equation of the graph determined.
Figure 2: A graph of weight of books against 1/volume in mL-1
The graph passes below the origin meaning there was pressure on the gas even when there was no book on the piston. The position where the line intersects the y-axis roughly represents the atmospheric pressure in the units used on the pressure axis. From the equation the y intercept, at x=0 was calculated as follows
y = 838.06x - 14.032
y=838.06×0-14 .032
y=-14.032
The atmospheric pressure was, therefore, 14.032lbs.
This pressure was added to the initial readings to give the total pressure as in Table 1. Since 1 lb is equal to 0.453592Kg, the weight was converted to Kilogram using this conversion factor. The total pressure was converted to force (N) using the formula F=m×a where a=9.83N/Kg and the resulted recorded in Table 1 above. Pressure is defined as the force exerted on a unit area. The area of the piston in square meters using the diameter of 2.7 cm as below
A=πr2
A=3.14×0.01352
=5.73×10-4M2
Using this area pressure exerted on the piston can be calculated using the formula P=FA. The results were recorded in the Table 1 above.
Discussion and Conclusion
The Boyle’s Law is one of the main Laws that are used to study the behavior of gases. The law states that an increase in pressure would lead to a decrease in the volume of a confined gas. The experiment clearly demonstrated this phenomenon, and through the experiment the Boyle’s constant was found to be around 6400236pamL. The experiment may have various sources of errors such as in the reading the volumes which may have resulted in varying results. The setup may, therefore, be concluded to successfully have demonstrated the Boyle’s Law.
Questions
- The graph of pressure against volume results into a hyperbolic curve. As the pressure increases, the volume is reduced at a faster rate initially, but the reduction in volume is reduced even with the addition of more pressure. This is usually due to the difficulties in compressing the gas.
- The graph of pressure against 1/volume was a linear graph where increase in pressure increased the inverse of the volume. This was as a result of the reduction in volume as pressure increased.
- When gas is put in a confined place, an increase in pressure results in a decrease in temperature until no more compression can be done.
- The results obtained in the experiment would not be different if a different gas like CO2 was used. This is because the gases would behave almost the same way.
- The assumption for constant temperature was not valid since the movement of the piston may result in an increase in temperature.
- The last column in Table 1 gave the constant k in the Boyle’s Law.
- The values were close to one another, and this is a confirmation for the support of the Boyle’s law. This value is similar to the 838.06pamL in Figure 2 above which is the slope of the curve.
