Boyle's Law Formula
Boyle's Law states that the pressure of a given mass of gas is inversely proportional to its volume when the temperature is held constant. The formula is expressed as:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume
Relationship
From Boyle's Law, we can derive the relationship:
- If the volume of a gas decreases (\( V \downarrow \)), the pressure increases (\( P \uparrow \)), assuming temperature remains constant.
- If the volume of a gas increases (\( V \uparrow \)), the pressure decreases (\( P \downarrow \)), assuming temperature remains constant.
This means that the product of pressure and volume for a fixed amount of gas at constant temperature is a constant value.
Example Problem
Problem: A balloon has a volume of 2.0 L at a pressure of 1.0 atm. If the gas is compressed to a volume of 1.0 L, what will the new pressure be?
Given:
- \( V_1 = 2.0 , \text{L} \)
- \( P_1 = 1.0 , \text{atm} \)
- \( V_2 = 1.0 , \text{L} \)
Find:
- \( P_2 \)
Using Boyle’s Law, we can rearrange the formula to solve for \( P_2 \):
\[ P_2 = \frac{P_1 V_1}{V_2} \]
Substituting the known values:
\[ P_2 = \frac{1.0 , \text{atm} \times 2.0 , \text{L}}{1.0 , \text{L}} \]
\[ P_2 = \frac{2.0 , \text{atm} \cdot \text{L}}{1.0 , \text{L}} = 2.0 , \text{atm} \]
Conclusion
Thus, if the balloon is compressed to a volume of 1.0 L, the new pressure will be 2.0 atm.