To Verify Boyle's Law Experimentally

29th Oct 2019 @ 4 min read

Boyle's law is a famous gas law studied in physics and chemistry. It relates pressure and volume of gas keeping other parameters (amount of gas and temperature) constant. There are several ways to verify the law. The article covers a standard laboratory method to verify the law by studying the relation between pressure and volume.

Experiment: Air column

Objective

To verify Boyle's law i.e. for a given amount of gas, absolute pressure is inversely proportional to volume at a constant temperature.

Apparatus

Air column with measuring scale, Bourdon pressure gauge, oil reservoir, hand air pump, barometer

The air column is connected to the oil reservoir such that the air in the column is completely sealed off by the oil.

Boyle's law experiment — Experimental diagram for the verification of Boyle's law

Nomenclature

V_i is the volume reading of the gas in the air column.
P_i is the pressure reading in the pressure gauge.

Procedure

Connect the apparatus as shown in the above diagram.
The connection of the oil reservoir to the air column must be such that there is no leakage and the air is completely sealed off by the oil.
The hand air pump is attached to the oil reservoir.
After assembling all the types of equipment, open the air tap and start pumping air through the air pump.
Keep pumping the air until the oil is reached in the upper part of the column. As the air flows in the oil reservoir, the pressure inside the system increases. This can be observed in the pressure gauge.
Close the air tap once the oil no longer rises and the pressure gauge reading is constant (i.e. reached its peak).
Wait for two to three minutes to cool down the compressed air and note the pressure reading and the volume reading.
Now, slightly open and then quickly closed the air tap to let some air escape the system. This will lower the oil in the column.
After two to three minutes, note the pressure and volume reading.
Repeat the above two steps such that seven to eight observations are recorded.
Prepare the observation table and follow the calculations as shown below.
Plot pressure vs volume and pressure vs inverse volume graph
Finally, conclude the experiment based on the graphs.

Precaution

The air in the column should be completely sealed off by the oil.
The air pump is tightly connected to the oil reservoir.
Each reading must be taken after two to three minutes of closing the air tap.
The volume readings must be taken by levelling the eyes to the meniscus of the oil.

Observation

A sample observation table is provided below.

Sample observation table
Pressure reading (kPa)	Volume reading (cm³ or ml)
650	25
450	33
290	48
230	57
195	64
160	72
110	89

Calculation

Pressure and volume are the two parameters are measured throughout the experiment. The experiment is performed at a constant temperature which is room temperature. The amount of the gas in the column is also constant. Thus, the conditions of Boyle's law are satisfied.

The volume readings are in cm³ and the pressure readings are in kPa. The pressure measured is gauge pressure, not absolute. So, we need to add the atmospheric pressure to the readings to obtain absolute pressure. The atmospheric pressure is obtained from a barometer, but it is considered as 1 atm i.e. 101.325 kPa.

For example, a gauge pressure of 650 kPa is an absolute pressure of 650 + 101.325 = 751.325 kPa. The table below lists absolute pressure.

Gauge pressure to abosolute pressure
Pressure reading (kPa)	Absolute pressure (kPa)
650	751.325
450	551.325
290	391.325
230	331.325
195	296.325
160	261.325
110	211.325

The final table consists of absolute pressure (kPa), volume (cm³), inverse volume (cm⁻³), and pressure-volume (kPa cm³).

Calculation table
Absolute pressure (kPa)	Volume (cm³)	Inverse volume^† (cm⁻³)	Pressure-volume^† (kPa cm⁻³)
751.325	25	0.040	19 000
551.325	33	0.030	18 000
391.325	48	0.021	19 000
331.325	57	0.017	19 000
296.325	64	0.016	19 000
261.325	72	0.014	19 000
211.325	89	0.011	19 000
Note: † rounded off to two significant figures.

As observed from the table above, pressure-volume nearly remains constant i.e. PV = k.

Result

The graph of pressure vs volume and pressure vs inverse volume are plotted.

Boyle's law experiment graph (pressure vs volume) — As pressure decreases, volume increases exponentially. The graph is an exponential curve.

As expected, the above graph (pressure vs volume) is an exponential curve. As observed from the graph, pressure decreases with rise in volume or vice versa.

Boyle's law experiment graph (pressure vs inverse volume) — The graph of pressure vs inverse volume is a straight line passing through the origin.

The graph of pressure to inverse volume is a straight line and follows the equation y = mx.

Conclusion

The experiment is successfully studied, and the system obeys Boyle's law. From the graphs, it can be concluded that the pressure of the gas in the column is inversely proportional to the volume of the gas at a constant temperature for a fixed amount of gas.