A given mass of air has a volume of 6.00 L at 101 kPa. At constant temperature, the pressure is decreased to 25.0kPa Calculate the final volume for the gas. 24.21 1201 10.01 30.01

To solve this problem, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, this can be expressed as:<br /><br />\[ P_1V_1 = P_2V_2 \]<br /><br />Given:<br />- Initial pressure, \( P_1 = 101 \, \text{kPa} \)<br />- Initial volume, \( V_1 = 6.00 \, \text{L} \)<br />- Final pressure, \( P_2 = 25.0 \, \text{kPa} \)<br /><br />We need to find the final volume, \( V_2 \).<br /><br />Rearranging the equation to solve for \( V_2 \):<br /><br />\[ V_2 = \frac{P_1V_1}{P_2} \]<br /><br />Substituting the given values:<br /><br />\[ V_2 = \frac{101 \, \text{kPa} \times 6.00 \, \text{L}}{25.0 \, \text{kPa}} \]<br /><br />\[ V_2 = \frac{606 \, \text{kPa} \cdot \text{L}}{25.0 \, \text{kPa}} \]<br /><br />\[ V_2 = 24.24 \, \text{L} \]<br /><br />Therefore, the final volume of the gas is approximately 24.24 L. The closest option to this value is 24.21 L.