Boyle’s Law: Definition, Statement, Derivation, Detailed Explanation, Examples

Boyle’s Law comes under the chapter States of Matter and provides the relation between gas and volume. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662. Boyle showed that the volume of air trapped by a liquid in the closed short limb of a J-shaped tube decreased in exact proportion to the pressure produced by the liquid in the long part of the tube. The law states that “at a constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume“.

In this article, we will help you understand Boyle’s Law, its derivation, formula, and how to solve questions using the law.

What is Boyle’s Law in Simple Terms?

The law states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, provided the temperature remains unchanged within a closed system. According to Boyle’s Law, the pressure exerted by a fixed amount of gas (no. of moles) is inversely proportional to the volume, when the temperature is kept constant.

p ∝ 1/V or p ∝ \(\frac{1}{V}\)

p = k1 \(\frac{1}{V}\)

In the above equation, k1 is the proportionality constant. The value of constant k1 depends upon the amount of the gas, the temperature of the gas, and the units in which p and V are expressed.

So the above equation becomes pV = k1.

Boyles Law Derivation

From the above graphs and equations we now know that at a constant temperature, a product of pressure and volume of a fixed amount of gas is constant.

So, if a fixed amount of gas at constant temperature (T) occupying volume (V1) at pressure (p1) undergoes expansion, so that volume becomes (V2) and pressure becomes (p2), then as per Boyle’s law:

p1 V1 = p2 V2 = constant

⇒ \(\mathbf{\frac{p1}{p2}=\frac{V2}{V1}}\).

Density and Pressure Relation Using Boyle’s Law

When Boyle experiments are carried out in a quantitative manner they prove that gases are highly compressible. This is because when a given mass of a gas is compressed, the same number of molecules occupy a smaller space.

Hence we can obtain a relation between density and pressure by using this law.

we know that density = mass per unit volume ⇒ d = m/V.

Putting the value in the equation we get d = (m/k1) p = k′ p. This equation proves that at a constant temperature, pressure is directly proportional to the density of a fixed mass of the gas.

Boyle’s Law Examples

Here we will provide you with some solved questions that require the application of Boyle’s law:

Example 1: A balloon is filled with hydrogen at room temperature. It will burst if pressure exceeds 0.2 bar. If at 1 bar pressure the gas occupies 2.27 L volume, upto what volume can the balloon be expanded?

Solution 1: From Boyle’s Law we have p1V1 = p2V2

• If p1 is 1 bar, V1 will be 2.27 L
• If p2 = 0.2 bar, then we have V2 = (p1V1)/p2
• V2 = (1 bar x 2.27 L ) / (0.2 bar) = 11.35 L
• Since the balloon bursts at 0.2 bar pressure, the volume of the balloon should be less than 11.35 L.

Example 2: A vessel of 120 mL capacity contains a certain amount of gas at 35°C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35°C. What would be its pressure?

Solution 2: Here also we will use Boyle’s Law equation.

• Here V1 = 120 mL, P1 = 1.2 bar and V2 = 180 mL, P2 = ?.
• As temperature is constant, So, P₁V₁ = P₂V₂
• (1.2 bar) x (120 mL) = P2 x (180mL)
• (1.2 x 120)/1000 = (P2 x 180) / 1000
• P2 = 144/180 bar => 0.8 bar.

Example 3: At 0°C, the density of a gaseous oxide at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?

Solution 3: To solve this we will use the expression, d =MP/RT. It is already given that the temperature and density are the same. Therefore,

• M₁P₁ = M₂P₂ (as R is constant) (Gaseous oxide) (N₂) or
• M₁ x 2 = 28 x 5 (Molecular mass of N₂ = 28 u) or M₁ = 70u.

Real Life Examples Of Boyle’s Law

Boyle’s law states that under isothermal conditions, the pressure of a fixed amount of a gas is inversely proportional to its volume. Here are some real-life examples are:

• Pumping a tire tube with gas.
• The air in our lungs
• Syringe
• A scuba diver

FAQs on Boyle’s Law

Here are some questions that students generally search on Boyle’s Law:

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