Boyle's Law
Definition: Boyle's Law states that the pressure (P) of a gas is inversely proportional to its volume (V) when the temperature is kept constant. This means that if the volume of a gas decreases, the pressure increases, and vice versa, provided the temperature does not change.
Formula: The mathematical representation of Boyle's Law can be written as: \[ P_1 V_1 = P_2 V_2 \] where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.
Relationship
- As volume increases, pressure decreases (and vice versa), assuming constant temperature.
- This relationship can be visualized as a hyperbolic curve on a graph plotting pressure versus volume.
Example Problem
Problem: A gas occupies a volume of 2.0 liters at a pressure of 1.5 atm. If the volume is reduced to 1.0 liter, what will be the new pressure of the gas?
Solution:
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Given:
- \( V_1 = 2.0 , \text{L} \)
- \( P_1 = 1.5 , \text{atm} \)
- \( V_2 = 1.0 , \text{L} \)
- \( P_2 = ? \)
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Using Boyle's Law formula: \[ P_1 V_1 = P_2 V_2 \]
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Substituting the known values: \[ (1.5 , \text{atm})(2.0 , \text{L}) = P_2 (1.0 , \text{L}) \]
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Calculating: \[ 3.0 , \text{atm} \cdot \text{L} = P_2 (1.0 , \text{L}) \]
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Solving for \( P_2 \): \[ P_2 = \frac{3.0 , \text{atm} \cdot \text{L}}{1.0 , \text{L}} = 3.0 , \text{atm} \]
Answer: The new pressure of the gas when the volume is reduced to 1.0 liter is 3.0 atm.
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