A sample of gas occupies 9.0 mL at a pressure of 500 mm Hg. A new volume of the same sample is at 750 mm Hg. Is the new pressure smaller or larger than the original? square Therefore, is the new volume larger or smaller than 9.0 mL? square What is this new volume? square

To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature and the amount of gas are held constant. Mathematically, Boyle's Law is expressed as:<br /><br />\[ P_1 V_1 = P_2 V_2 \]<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 />- Initial pressure (\( P_1 \)) = 500 mm Hg<br />- Initial volume (\( V_1 \)) = 9.0 mL<br />- Final pressure (\( P_2 \)) = 750 mm Hg<br /><br />We need to find the final volume (\( V_2 \)).<br /><br />First, let's determine if the new pressure is smaller or larger than the original:<br />- The new pressure (750 mm Hg) is larger than the original pressure (500 mm Hg).<br /><br />Therefore, the new volume will be smaller than the original volume because pressure and volume are inversely related according to Boyle's Law.<br /><br />Now, let's calculate the new volume using Boyle's Law:<br /><br />\[ P_1 V_1 = P_2 V_2 \]<br /><br />Substitute the known values into the equation:<br /><br />\[ 500 \, \text{mm Hg} \times 9.0 \, \text{mL} = 750 \, \text{mm Hg} \times V_2 \]<br /><br />Solve for \( V_2 \):<br /><br />\[ V_2 = \frac{500 \, \text{mm Hg} \times 9.0 \, \text{mL}}{750 \, \text{mm Hg}} \]<br /><br />\[ V_2 = \frac{4500 \, \text{mm Hg} \cdot \text{mL}}{750 \, \text{mm Hg}} \]<br /><br />\[ V_2 = 6.0 \, \text{mL} \]<br /><br />So, the new volume is 6.0 mL.<br /><br />Summary:<br />- The new pressure is larger than the original.<br />- Therefore, the new volume is smaller than 9.0 mL.<br />- The new volume is 6.0 mL.