Question

Boyles law, formula, relationship, example problem

Answer 1

### 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**:
1. **Given:**
- \( V_1 = 2.0 \, \text{L} \)
- \( P_1 = 1.5 \, \text{atm} \)
- \( V_2 = 1.0 \, \text{L} \)
- \( P_2 = ? \)

2. **Using Boyle's Law formula:**
\[
P_1 V_1 = P_2 V_2
\]

3. **Substituting the known values:**
\[
(1.5 \, \text{atm})(2.0 \, \text{L}) = P_2 (1.0 \, \text{L})
\]

4. **Calculating:**
\[
3.0 \, \text{atm} \cdot \text{L} = P_2 (1.0 \, \text{L})
\]

5. **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**.