https://file.aiquickdraw.com/mathbot/file/1726742864086jbk9lt37.jpg

The problem in the image can be solved using **Boyle's Law**, which states that for a gas at constant temperature, the pressure and volume are inversely proportional:

\[
P_1 V_1 = P_2 V_2
\]

### Given:
- Initial pressure: \( P_1 = 900 \, \text{mm Hg} \)
- Final pressure: \( P_2 = 900 + 300 = 1200 \, \text{mm Hg} \)
- Final volume: \( V_2 = 2700 \, \text{mL} \)

We are asked to calculate the initial volume \( V_1 \).

### Applying Boyle's Law:

\[
P_1 V_1 = P_2 V_2
\]

Rearranging the equation to solve for \( V_1 \):

\[
V_1 = \frac{P_2 V_2}{P_1}
\]

Now, substitute the values:

\[
V_1 = \frac{1200 \, \text{mm Hg} \times 2700 \, \text{mL}}{900 \, \text{mm Hg}}
\]

Let's calculate that.

\[
V_1 = \frac{1200 \times 2700}{900} = 3600 \, \text{mL}
\]

### Final Answer:
The initial volume of the gas is **3600 mL**.

Would you like more details or further clarifications?

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Here are 5 related questions to deepen your understanding:
1. How does Boyle's Law apply to real gases under high pressure?
2. What happens to the volume of gas if the temperature is not constant?
3. Can you derive Boyle's Law from the ideal gas equation?
4. How would the volume change if the pressure is halved instead of increased?
5. What other gas laws interact with Boyle's Law in complex systems?

**Tip:** Boyle's Law only holds true for ideal gases at constant temperature and low pressure; deviations occur at higher pressures.

A certain volume of a gas is under a pressure of 900 mm of Hg. When the pressure is increased by 300 mm, the gas occupies 2700 mL. If this change occurs at a constant temperature, calculate the initial volume of the gas.

Explore how Boyle's Law is applied to calculate the initial volume of a gas when its pressure is increased. This guide offers a detailed solution to understanding the inverse relationship between pressure and volume of gases, suitable for high school physics.

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