A 1.50-liter sample of dry air in a cylinder exerts a pressure of 3.00 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 1.00 atmosphere. The volume of the gas is: V=((1.50)(1.00))/((3.00)(298))=0.0016TL V=((1.50)(1.00))/(3.00)=0.50L V=((1.50)(25)(3.00))/((1.00))=113L V=((1.50)(3.00))/((1.00))=4.50L

To find the new volume of the gas when the pressure is reduced to 1.00 atmosphere, we can use Boyle's Law. Boyle's Law states that for a given amount of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, it 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 (3.00 atm),<br />- \( V_1 \) is the initial volume (1.50 L),<br />- \( P_2 \) is the final pressure (1.00 atm),<br />- \( V_2 \) is the final volume.<br /><br />We need to solve for \( V_2 \):<br /><br />\[ V_2 = \frac{P_1 \times V_1}{P_2} \]<br /><br />Substitute the known values into the equation:<br /><br />\[ V_2 = \frac{3.00 \, \text{atm} \times 1.50 \, \text{L}}{1.00 \, \text{atm}} \]<br /><br />\[ V_2 = \frac{4.50 \, \text{atm} \cdot \text{L}}{1.00 \, \text{atm}} \]<br /><br />\[ V_2 = 4.50 \, \text{L} \]<br /><br />Therefore, the volume of the gas when the pressure is reduced to 1.00 atmosphere is 4.50 liters. The correct answer is:<br /><br />\[ V = \frac {(1.50)(3.00)}{(1.00)} = 4.50 \, \text{L} \]