\[ P_{1} V_{1}=P_{2} V_{2} \] 1. A sample of oxygen gas occupies a volume of 250 mL at 740 torr pressure. What volume \( \begin{array}{l}\text { wilf it occupy at } 800 \text { tom pressure? } \\ \text { (11-2 } 50\end{array} \frac{7401250)}{800} \)

To find the volume the oxygen gas will occupy at 800 torr pressure, you can use the given equation \( P_{1} V_{1}=P_{2} V_{2} \). Let's plug in the values: - Initial pressure \( P_{1} = 740 \) torr - Initial volume \( V_{1} = 250 \) mL - Final pressure \( P_{2} = 800 \) torr Rearranging the formula to find \( V_{2} \): \[ V_{2} = \frac{P_{1} V_{1}}{P_{2}} = \frac{740 \times 250}{800} \] Calculating: \[ V_{2} = \frac{185000}{800} = 231.25 \, \text{mL} \] Thus, the oxygen gas will occupy approximately 231.25 mL at 800 torr pressure. When we explore gas laws, we uncover that they date back to the 17th century, initially framed by scientists like Boyle and Charles. These laws brought clarity to the relationships between pressure, volume, and temperature, forming the basis of modern chemistry and physics. Imagine how these pioneering experiments shaped our understanding of gases; they laid the groundwork for everything from meteorology to the design of hot air balloons! In practical terms, understanding how gases behave under different pressures is invaluable. For instance, when engineers design pressure vessels or dive tanks, they must calculate the changes in volume and pressure to ensure safety and efficiency. Moreover, in medical settings, controlling the pressure and volume of gases in anesthesia machines is critical for patient safety, making this knowledge essential in the real world!