Which of these expressions are correct variations of the Combined Gas Law? both of the above P_(1)V_(1)T_(2)=P_(2)V_(2)T_(1) P_(2)=P_(1)((T_(2))/(T_(1)))((V_(1))/(V_(2)))

The Combined Gas Law is expressed as:<br /><br />\[<br />\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}<br />\]<br /><br />To determine if the given expressions are correct variations of the Combined Gas Law, let's analyze each one.<br /><br />1. \( P_{1}V_{1}T_{2}=P_{2}V_{2}T_{1} \)<br /><br />Starting from the Combined Gas Law:<br />\[<br />\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}<br />\]<br />Multiplying both sides by \( T_1 T_2 \) to eliminate the denominators:<br />\[<br />P_1 V_1 T_2 = P_2 V_2 T_1<br />\]<br />This matches the first expression, so it is correct.<br /><br />2. \( P_{2}=P_{1}\left(\frac {T_{2}}{T_{1}}\right)\left(\frac {V_{1}}{V_{2}}\right) \)<br /><br />Starting again from the Combined Gas Law:<br />\[<br />\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}<br />\]<br />Rearranging to solve for \( P_2 \):<br />\[<br />P_2 = P_1 \left(\frac{V_1}{V_2}\right) \left(\frac{T_2}{T_1}\right)<br />\]<br />This matches the second expression, so it is also correct.<br /><br />Therefore, both expressions are correct variations of the Combined Gas Law. The correct answer is:<br /><br />**both of the above**