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What is Boyle’s law?
In 1662, the Anglo-Irish chemist Robert Boyle proposed Boyle’s law. Boyle’s law says that the pressure exerted by gasses (of a given mass and temperature) is inversely proportional to the volume occupied by the gas. In other words, as long as the temperature and amount of gas remain constant, the pressure and volume of a gas are inversely proportional.
The connection between volume and pressure in a gas may be stated as Boyle’s law mathematically as follows (at constant mass and temperature).
P ∝ (1/V)
The pressure exerted by the gas is P, and the volume occupied by it is V. By adding a constant, k, to this proportionality, we can convert it into an equation.
P = k*(1/V) ⇒ PV = k
When the pressure exerted by the gas (P) is shown on the Y-axis, and the inverse of the volume occupied by the gas (1/V) is plotted on the X-axis, a straight line is formed.
Derivation and Boyle’s law formula
According to Boyle’s law, any change in the volume filled by a gas (at constant quantity and temperature) results in a difference in its pressure. Put another way, the product of a gas’s initial pressure and initial volume equals the product of the gas’s final pressure and final volume (at constant temperature and number of moles). This law can be mathematically represented as follows:
P1V1 = P2V2
Here,
P1 refers to the gas’s starting pressure.
V1 is the gas’s initial volume of occupancy.
P2 refers to the gas’s ultimate pressure.
The final volume filled by the gas is V2.
Boyle’s law formula suggests a pressure-volume connection, which may be used to get this phrase. PV = k for a certain quantity of gas at constant temperatures. Therefore,
P1V1 = k (initial pressure * initial volume)
P2V2 = k (final pressure * final volume)
∴ P1V1 = P2V2
When a gas’s container volume decreases, the equation can be used to predict the increase in pressure exerted by the gas on the container walls (and its quantity and absolute temperature remain unchanged).
Boyle’s Law Examples
When you compress an inflated balloon, the volume occupied by the air inside the balloon shrinks as a result of Boyle’s law temperature; this is accompanied by an increase in the pressure imposed by the air on the balloon. The pressure builds up until it explodes as the balloon is pressed tighter.
The drop in pressure caused by a scuba diver ascending quickly from the deep to the surface of the sea might cause the gas molecules in their body to expand. The gas bubbles can harm a diver’s organs and possibly cause death. A further example of Boyle’s law temperature is the increase in the gas created by scuba divers as they ascend. Another comparative example may be seen in deep-sea fish that die after reaching the water’s surface (due to the expansion of dissolved gasses in their blood).
Our lungs use Boyle’s law during breathing. Inhaling causes the lungs to expand because they are filled with air. As the volume grows, the pressure level decreases. Similarly, when the lungs are emptied of air, they contract, reducing the volume and increasing the pressure. The change in pressure and volume is both instantaneous and periodic.
Flat tires are weak and lack good form, making it difficult for a vehicle to move appropriately. The air molecules get closely packed when air is forced into flat tires with the aid of an air pump. The pressure exerted on the tire walls increases as the number of air molecules in the tire increases. Therefore, inflating flat tires is yet another application of Boyle’s rule in the real world.
One of the most notable instances of Boyle’s law is a soda bottle filled with a combination of carbon dioxide and water. It is difficult to compress a soda can or container that has been sealed. This is because the air molecules within the container are densely packed and have little room to move. When you open a can or a bottle, some air molecules leave, allowing more air molecules to move about and compress the bottle.
A syringe is a piece of medical equipment used to inject or remove fluids. It comprises a cylinder that holds the liquid and a plunger that controls the pressure. The volume of the fluid decreases as the plunger is pushed down, increasing the pressure. Similarly, raising the plunger increases the volume while lowering the pressure. As a result, Boyle’s law governs the operation of a syringe.
Solved exercises on Boyle’s law
Exercise 1: When a human breathes, his lungs can contain up to 5.5 liters of air at 37°C body temperature and 1 atm = 101 kPa ambient pressure. The oxygen content of this air is 21%. Calculate how many oxygen molecules there are in the lungs.
Answer: The air inside the lungs can be treated as an ideal gas. The perfect gas law may be used to calculate the number of molecules.
PV = NkT
Here volume is given in the Litre. 1 Liter is volume occupied by a cube of 10 cm. 1 Liter = 10cm × 10cm × 10cm = 10-3 m3
N = PV/ kT
= 1.01× 105Pa × 5.5 × 10-3 m3 / 1.38× 10-23 JK-1× 310 K
= 1.29 × 1023 Molecules
Only 21% of nitrogen is oxygen. The total number of oxygen molecules in the atmosphere.
= 1.29 × 1023 × 21/100
The number of oxygen molecules is 2.7 × 1022 molecules.
Exercise 2: Calculate the volume of air in your classroom using NTP. Normal temperature (room temperature) and one atmospheric pressure are denoted as NTP.
Answer: A typical class is 6 meters long, 5 meters wide, and 4 meters tall. The room’s volume is V = 6 × 5 × 4 = 120m3. The number of moles may be determined. The volume of a gas occupied by any gas is equivalent to 24.6L at 300K room temperature.
The amount of moles is equal to
μ =120m3 / 24.6 x 10-3m3
≈ 4878 mol.
Air combines around 20% oxygen, 79% nitrogen, and 1% argon, hydrogen, helium, and xenon. Air has a molar mass of 29 g mol-1.
The total air mass in the room is thus m = 4878 × 29 = 141.4kg.
Conclusion
Boyle’s law only applies to ideal gasses. The rule applies only at high temperatures and low pressures. At high pressures, the law breaks down. At high pressures, the ratio of pressure and volume does not remain constant but shows a slight rise. The volume growth is due to repelling interactions between molecules.
