Given a gas is at 1 atm and 20 L, what is the volume of the gas when pressure changes to 3 a 6.7 L 7.6 L 3.0 L 21.0 L

To solve this problem, we can use Boyle's Law, which states that the volume of a gas is inversely proportional to the pressure, provided the temperature remains constant. Mathematically, this can be expressed as:<br /><br />\[ P_1 \times V_1 = P_2 \times V_2 \]<br /><br />Where:<br />- \( P_1 \) is the initial pressure (1 atm)<br />- \( V_1 \) is the initial volume (20 L)<br />- \( P_2 \) is the final pressure (3 atm)<br />- \( V_2 \) is the final volume (unknown)<br /><br />Rearranging the equation to solve for \( V_2 \):<br /><br />\[ V_2 = \frac{P_1 \times V_1}{P_2} \]<br /><br />Substituting the given values:<br /><br />\[ V_2 = \frac{1 \text{ atm} \times 20 \text{ L}}{3 \text{ atm}} \]<br /><br />\[ V_2 = \frac{20 \text{ L}}{3} \]<br /><br />\[ V_2 \approx 6.7 \text{ L} \]<br /><br />Therefore, the volume of the gas when the pressure changes to 3 atm is approximately 6.7 L.