The original conditions in a container filled with gas at constant temperature are 183 mL and 310 mm Hg. The desired new volume is 906 mL. What pressure should be applied? square - mm Hg

To solve this problem, we can use Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, Boyle's Law is expressed as:<br /><br />\[ P_1 \times V_1 = P_2 \times V_2 \]<br /><br />where:<br />- \( P_1 \) is the initial pressure,<br />- \( V_1 \) is the initial volume,<br />- \( P_2 \) is the final pressure,<br />- \( V_2 \) is the final volume.<br /><br />Given:<br />- \( P_1 = 310 \) mm Hg,<br />- \( V_1 = 183 \) mL,<br />- \( V_2 = 906 \) mL.<br /><br />We need to find \( P_2 \).<br /><br />Using Boyle's Law:<br /><br />\[ 310 \, \text{mm Hg} \times 183 \, \text{mL} = P_2 \times 906 \, \text{mL} \]<br /><br />Solving for \( P_2 \):<br /><br />\[ P_2 = \frac{310 \, \text{mm Hg} \times 183 \, \text{mL}}{906 \, \text{mL}} \]<br /><br />\[ P_2 = \frac{56730}{906} \]<br /><br />\[ P_2 \approx 62.6 \, \text{mm Hg} \]<br /><br />Therefore, the pressure that should be applied is approximately 62.6 mm Hg.