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Boyle’s Law

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The English chemist Robert Boyle (1627–1691), widely regarded as one of the pioneers of the modern experimental science of chemistry, is commonly credited with this development. He found that increasing the pressure of a sample of contained gas by two times while holding its temperature constant reduced the gas volume by half. According to Boyle’s law, a gas’s volume changes inversely with pressure when the temperature is held constant. This is an illustration of an inverted relationship. The second variable drops when one variable rises in value.

What is Boyle’s Law?

It is one of the chemistry rules that govern how gases behave. A gas occupies less space while it is under pressure; the greater the pressure, the smaller the volume. The image added below shows how the increase in pressure decreases the volume of the gas.

Graphical Explanation of Boyle's law

 

It explains the link between a gas’s volume and pressure at a fixed temperature. It states that if the temperature of a mass is constant, the pressure of a given mass is inversely proportional to the volume of the given mass. It is also called a pressure-volume relationship.

P ∝ 1/V  (at constant temperature (T))

PV = k   where ‘k’ represents the Boyle’s constant)

PV = constant

If P1 , V1 be the initial pressure and volume of the given sample gas and P2 , V2 be the final pressure and volume of the given sample gas, then we can write as:

P1V1 = P2V2

Another way of defining Boyle’s Law, states that if the temperature of a mass is constant, the product of the pressure and volume of the given mass of a gas is constant.

Formula and Derivation of Boyle’s Law

Here, ‘P‘ represents the pressure exerted by the gas, ‘V‘ represents the volume of the gas, ‘m‘ represents the mass of each molecule of the gas, ‘n‘ represents the total number of molecules present in volume V  and, ‘u‘ represents the root mean square speed of the gas

The kinetic gas equation is written in the form of PV=\frac{1}{3}mnu^2

Rewrite the above equation.

PV=\frac{2}{3}\cdot \frac{1}{2}\cdot mnu^2

Total mass of the gas (M) is the product of mass (m) of each molecules of the gas and total number of molecules (n) present in volume V.

PV=\frac{2}{3}\cdot \frac{1}{2}\cdot Mu^2

The kinetic energy of the gas (K.E) is calculated by K.E=\frac{1}{2} Mu^2

PV=\frac{2}{3}\cdot K.E

Since the molecules are moving with different velocities, they possess different kinetic energies. However, the average kinetic energy of the molecules of a gas is directly proportional to the absolute temperature of the gas.

K.E ∝ absolute temperature of the gas (T)

K.E = kT

Therefore,

PV=\frac{2}{3}kT

Here, 2/3 is a constant, k is called as constant of proportionality.

If Temperature (T) is kept constant then \frac{2}{3}kT       is constant.

Hence, PV = constant 

This is the Boyle’s Law

Density and Pressure Relation using Boyle’s Law

Density is mass (M) per unit volume (V).

D=M/V

Solve for V.

V=M/D

According to Boyle’s Law,

PV = k   (where ‘k‘ represents Boyle’s constant)

\frac{PM}{D}=k

According to Boyle’s Law, gases are compressible because when a given mass is compressed, the same number of molecules occupy the smaller space.

P=\frac{k}{M}D

P = k’D

where 
k‘ represents k/M

P ∝ D

Hence, at a constant temperature, the pressure of the gas is directly proportional to the density of the fixed mass of the gas.

Graphical representation of Boyle’s Law

  • The graph of 1/V vs P represents a straight line passing through the origin (0,0). This graph is shown in the image added below,
P vs 1/V graph

 

  • The graph of V vs P represents a hyperbola. This graph is shown in the image added below,
P vs V graph

 

  • The graph of PV vs P represents a horizontal straight line.

Examples of Boyle’s Law

Various examples of Boyle’s Law are,

Breathing

Respiration involves the application of Boyle’s law in the lungs. When we inhale, air fills the lungs causing them to expand, resulting in an increase in volume and a decrease in pressure. Conversely, when we exhale, the lungs contract, causing a reduction in volume and an increase in pressure. These changes in pressure and volume occur periodically and temporarily during the breathing process.

Soda Bottle

Boyle’s law can be effectively demonstrated using a soda bottle filled with a mixture of carbon dioxide and water. When the bottle is sealed, it becomes difficult to compress because the air molecules inside are tightly packed and have limited space to move. However, upon opening the bottle, some of the air molecules escape, creating more room for the remaining molecules to move. This results in the bottle becoming easier to compress, and the relationship between the change in pressure and volume can be readily observed.

Spray Paint

Boyle’s law is evident in the operation of spray paints. These paints operate by exerting a considerable amount of pressure on the can in which they are stored. When the can’s top is pressed, the volume inside the can decreases, and the paint is expelled with significant force. As Boyle’s law states an inverse relationship between pressure and volume, the effects of the law can be observed in the operation of spray paints.

Scuba Driving

When diving underwater, it’s crucial to balance the relationship between volume and pressure to avoid illness or injury. As a person descends or approaches greater depths, they experience increased pressure, which enhances the solubility of gases in their bloodstream. As the diver ascends or moves towards the surface, the pressure decreases, and the gases in the blood begin to expand. Therefore, the diver must ascend gradually to avoid injury. The relationship between pressure and volume described in this scenario illustrates Boyle’s law.

Spacesuits

As there is a vacuum in space, there is no air or atmosphere and, hence, zero pressure. According to Boyle’s law, when a pressurized gas enters a vacuum, it expands indefinitely. This is why astronauts require specially designed spacesuits to survive in space. If an astronaut’s spacesuit were to rupture, their blood and bodily fluids would begin to boil due to the vacuum, resulting in serious injury.

Significance of Boyle’s Law

Boyle’s law establishes the crucial fact that gases are particularly compressible. The same number of molecules occupy less space when a given amount of gas is compressed by increased pressure.

As a result, the gas’s density rises due to an increase in mass per unit volume. For instance, the air is dense at sea level, but as height increases, both density and pressure decrease. For instance, Mount Everest has a low air pressure of only 0.5 atm. As a result, there is no longer enough oxygen in the air to support regular breathing. This results in symptoms that are typically associated with altitude sickness, such as overall unease, a sluggish sensation, headaches, etc. 

In order to prepare their bodies for the low oxygen pressure, mountain climbers and jawans in high altitudes like Ladakh either undergo lengthy training or carry oxygen cylinders for emergencies.
Similar to this, the cabins of jet aircraft that fly at extremely high altitudes (about 10,000 m) are artificially kept at normal pressure to provide adequate oxygen for breathing. In case of pressure drops, they also have emergency oxygen supplies.

Solved Examples on Boyle’s Law

Example 1: Find the pressure required to compress 600 dm3 of air at 1 Bar to 200 dm3 at 30oC.

Solution:

At constant temperature of 30oC

V1  = 600 dm3, P1 = 1 bar, V2  = 600 dm3 and P2 = ?

Using Boyle’s Law, P1V1 = P2V2

1 Bar × 600 dm3 = P2 × 200 dm3

P2 = 600/200

P2 = 3 Bar

Example 2: Calculate the pressure required to reduce 400 mL of gas at 700 mm pressure to 300 mL at the same temperature.

Solution:

At constant temperature

V1  = 400 mL, P1 = 700 mm, V2  = 300 mL and P2 = ?

Using Boyle’s Law, P1V1 = P2V2

700 mm × 400 mL = P2 × 300  mL

P2 = 280000/300

P2 = 933.33 mL

Example 3: A gas is expanded, at a constant temperature, from a volume of 500 mL to a volume of 1.5 litre, where its final pressure is 150 mm of Hg. What was the original pressure?

Solution:

At constant temperature,

V1  = 500 mL, P2 = 150 mm of Hg, V2  = 1.5 L and P1 = ?

Convert 1.5 L to mL.

1 L = 1000 mL

1.5 L = 1.5 × 1000 mL = 1500 mL

Using Boyle’s Law, P1V1 = P2V2

P1 × 500 mL = 150 mm × 1500  mL

P1 = 225000/500

P1 = 450 mL

Example 4: Find the volume of a sample of nitrogen at a pressure of 1.50 atm, if its volume is 3.15 L at 1.00 atm and the temperature is constant.

Solution:

At Constant Temperature,

V1  = 3.15 L, P1 = 1 atm, P2  = 1.5 atm and V2 = ?

Using Boyle’s Law, P1V1 = P2V2

1 atm × 3.15 L = 1.5 atm × V2

V2 = 3.15/1.5

V2 = 2.1 L

FAQs on Boyle’s Law

Q1: What is Boyle’s Law?

Answer:

An Irish scientist of the 17th century, Robert Boyle, established Boyle’s Law, which affirms that, under constant temperature and amount of gas, the pressure and volume of a gas exhibit an inverse relationship to each other.

Q2: What is the formula for Boyle’s Law?

Answer:

The formula for Boyle’s Law is 

P1V1 = P2V2

where 
P1 is the initial pressure
V1 is the initial volume
P2 is the final pressure
V2 is the final volume

Q3: What is the significance of Boyle’s Law?

Answer:

Boyle’s Law has great significance as it explains the behavior of gases and serves as a fundamental principle for the study of thermodynamics. Additionally, it has numerous practical applications, including the design of engines and the compression of gases.

Q4: How is Boyle’s Law used in everyday life?

Answer:

The applications of Boyle’s Law is very evident in our everyday life, ranging from the inflation of balloons, working of the bicycle pump, and the functioning of scuba diving regulators all works on the principal of Boyle’s Law.

Furthermore, it finds extensive use in the compression of gases for various industrial and medical purposes.

Q5: How does temperature affect Boyle’s Law?

Answer:

An alteration in temperature affects Boyle’s Law due to the rise in the kinetic energy of gas particles leading to an increase in pressure. However, the validity of Boyle’s Law remains unaffected as long as the temperature is constant.

Q6: How does the amount of gas affects Boyle’s Law?

Answer:

Boyle’s Law is independent of the quantity of gas and holds true regardless of the amount of gas present, provided the temperature and volume remain constant.



Last Updated : 01 May, 2023
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