Given a gas is at 23 L and 333 K, what is the volume of the gas when temperature changes to 310 K? Round to one decimal place. square

To solve this problem, we can use the ideal gas law, which states that the volume of a gas is directly proportional to its temperature, provided the pressure and the amount of gas remain constant.<br /><br />The formula for the ideal gas law is:<br /><br />\[ V_1/T_1 = V_2/T_2 \]<br /><br />where:<br />- \( V_1 \) is the initial volume of the gas<br />- \( T_1 \) is the initial temperature of the gas<br />- \( V_2 \) is the final volume of the gas<br />- \( T_2 \) is the final temperature of the gas<br /><br />Given:<br />- \( V_1 = 23 \) L<br />- \( T_1 = 333 \) K<br />- \( T_2 = 310 \) K<br /><br />We need to find \( V_2 \).<br /><br />Rearranging the formula to solve for \( V_2 \):<br /><br />\[ V_2 = V_1 \times \frac{T_2}{T_1} \]<br /><br />Substituting the given values:<br /><br />\[ V_2 = 23 \times \frac{310}{333} \]<br /><br />Now, calculate the value:<br /><br />\[ V_2 \approx 21.8 \]<br /><br />Therefore, the volume of the gas when the temperature changes to 310 K is approximately 21.8 L.