A 1.50-liter sample of dry air in a cylinder exerts a pressure of 3.0 atmospheres at a temperature of 25^circ C Without change in temperature, a piston is moved in the cylinder until the pressure in the cylinder is reduced to 1.0 atmosphere. What is the volume of the gas?(Be sure to use the correct number of significant figures.) 0.50 L 2.0 L 0.22 L 4.5 L

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 />- \( P_1 = 3.0 \) atm<br />- \( V_1 = 1.50 \) L<br />- \( P_2 = 1.0 \) atm<br /><br />We need to find \( V_2 \).<br /><br />Substitute the known values into the equation:<br /><br />\[ 3.0 \, \text{atm} \times 1.50 \, \text{L} = 1.0 \, \text{atm} \times V_2 \]<br /><br />\[ 4.5 \, \text{L atm} = 1.0 \, \text{atm} \times V_2 \]<br /><br />Now, solve for \( V_2 \):<br /><br />\[ V_2 = \frac{4.5 \, \text{L atm}}{1.0 \, \text{atm}} \]<br /><br />\[ V_2 = 4.5 \, \text{L} \]<br /><br />Therefore, the volume of the gas when the pressure is reduced to 1.0 atmosphere is 4.5 L. The correct answer is 4.5 L.