To determine which gas sample would have a new volume of 3.00 liters when the pressure is decreased from 3.000 ATM to 1.00 ATM at constant temperature, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional when temperature is held constant.
The equation for Boyle's Law is:
P1V1 = P2V2
Where: P1 = Initial pressure V1 = Initial volume P2 = Final pressure V2 = Final volume
Let's analyze the options:
Sample 1: Initial pressure (P1) = 3.000 ATM Initial volume (V1) = Unknown Final pressure (P2) = 1.00 ATM Final volume (V2) = 3.00 liters
Using the Boyle's Law equation, we can rearrange it to solve for the initial volume (V1):
V1 = (P2 * V2) / P1 V1 = (1.00 ATM * 3.00 liters) / 3.000 ATM V1 = 1.00 liters
Therefore, for Sample 1 to have a new volume of 3.00 liters when the pressure is decreased from 3.000 ATM to 1.00 ATM at constant temperature, the initial volume must be 1.00 liter.
The correct option is Sample 1.