Ten grams of a gas occupies 12.5 liters at a pressure of 42.0 cm Hg . What is the volume when the pressure has increased to 75.0 cm Hg? none of the above 7.00 L 8.00 L 6.00 L

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 />\[ P_1 \times V_1 = P_2 \times V_2 \]<br /><br />Where:<br />- \( P_1 \) and \( V_1 \) are the initial pressure and volume.<br />- \( P_2 \) and \( V_2 \) are the final pressure and volume.<br /><br />Given:<br />- \( P_1 = 42.0 \) cm Hg<br />- \( V_1 = 12.5 \) L<br />- \( P_2 = 75.0 \) cm Hg<br /><br />We need to find \( V_2 \).<br /><br />Using Boyle's Law:<br /><br />\[ 42.0 \, \text{cm Hg} \times 12.5 \, \text{L} = 75.0 \, \text{cm Hg} \times V_2 \]<br /><br />Solving for \( V_2 \):<br /><br />\[ V_2 = \frac{42.0 \, \text{cm Hg} \times 12.5 \, \text{L}}{75.0 \, \text{cm Hg}} \]<br /><br />\[ V_2 = \frac{525.0}{75.0} \]<br /><br />\[ V_2 = 7.00 \, \text{L} \]<br /><br />Therefore, the volume when the pressure has increased to 75.0 cm Hg is 7.00 liters. The correct answer is:<br /><br />7.00 L