The pressure of the gas would be 9.0 atm if the piston is pushed down hard to a volume of 36.0 ml.
To solve this problem, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume at constant temperature.
First, we need to set up the equation: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given that the initial volume (V1) is 144.0 ml and the initial pressure (P1) is 2.25 atm, and the final volume (V2) is 36.0 ml, we can plug in the values into the equation:
2.25 atm * 144.0 ml = P2 * 36.0 ml
Next, we can solve for P2 by dividing both sides of the equation by 36.0 ml:
2.25 atm * 144.0 ml / 36.0 ml = P2
P2 = 9.0 atm
Therefore, the pressure of the gas would be 9.0 atm if the piston is pushed down hard to a volume of 36.0 ml.
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