He-LLO - Boyle's Law

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Boyle's Law

[MELC 21] Investigate the relationship between: 1. volume and pressure at a constant temperature of a gas. 2. volume and temperature at a constant pressure of gas; and 3. explain these relationships using the kinetic molecular theory. (S9MT-IIj-20)

Day 3: Plot data and infer the volume-pressure relationship at the constant temperature of a gas.

Day 4: Cite examples/situations where Boyle’s Law is observed.

Day 5: Calculate for each unknown on volume and pressure relationship at a constant temperature of a gas.

Boyle's law, proposed by Anglo-Irish chemist Robert Boyle in 1662, states that for a given mass of gas at a constant temperature, the pressure exerted by the gas is inversely proportional to its volume. In simpler terms, as long as the temperature and the quantity of gas remain constant, an increase in volume results in a decrease in pressure, and vice versa [©].

Examples/situations where Boyle’s Law is observed.

Blowing up a balloon: As you blow air into a balloon, you increase the number of gas molecules inside. To accommodate this increase, the balloon stretches, and its volume expands. This expansion happens because the pressure of the air inside the balloon pushes outwards according to Boyle's Law.

Using a syringe: A syringe works on the principle of Boyle's Law. When you pull the plunger back, you increase the volume inside the barrel. This decrease in pressure allows liquid (or gas) to flow into the syringe. Pushing the plunger down decreases the volume in the barrel, increasing the pressure and forcing liquid (or gas) out.

Mathematical expression: Boyle's law can be expressed by the equation: P₁V₁ = P₂V₂

where:

P₁ is the initial pressure of the gas
V₁ is the initial volume of the gas
P₂ is the final pressure of the gas
V₂ is the final volume of the gas
The product of the initial pressure and volume (P₁V₁) remains constant as long as the temperature stays the same.

Example Problem 1
1. A bicycle pump contains a piston and a cylinder. Initially, the air in the cylinder has a volume of 2.0 liters (L) and a pressure of 1.0 atmosphere (atm). The cyclist pushes the piston down, compressing the air in the cylinder to a volume of 0.50 L. If we assume the temperature remains constant, what is the new pressure of the air in the cylinder?

Given:

(P₁) = 1.0 atm

(V₁) = 2.0 L

(V₂) = 0.50 L
Required:

(P₂)
Equation:

P₁V₁ = P₂V₂

rearrange to P₂ = (P₁V₁) / V₂
Solution

P₂ = (1.0 atm * 2.0 L) / 0.50 L
Answer

P₂ = 4.0 atm

By compressing the air in the cylinder (decreasing the volume), the pressure increases (4.0 atm) to maintain the constant product of pressure and volume according to Boyle's Law.

Example Problem 2

A scuba diver's compressed air tank holds 10 liters (L) of air at a depth of 30 meters underwater. The pressure at this depth is approximately 4 atm (assuming atmospheric pressure is 1 atm). The diver ascends to the surface where the pressure is 1 atm. Assuming the temperature remains constant, what is the new volume of the air in the tank?

Given:

(P₁) = 4 atm

(V₁) = 10 L

(P₂) = 1 atm
Required:

(V₂)
Equation:

P₁V₁ = P₂V₂

rearrange to V₂ = (P₁V₁) / P₂
Solution

V₂ = (4 atm * 10 L) / 1 atm
Answer

V₂ = 40 L

As the diver ascends (pressure decreases from 4 atm to 1 atm), the air expands according to Boyle's Law to maintain the constant product (P₁V₁). The volume increases to 40 liters to compensate for the lower pressure at the surface.

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