Final answer:
To determine how many 400 cc gas jars can be filled from a cylinder containing 30 liters of oxygen at 50 atm pressure when the filling pressure is 750 mmHg, we use the ideal gas law. By converting mmHg to atm, then applying P1*V1 = P2*V2, we find the total volume at the new pressure and then divide by 400 cc to get the number of jars.
Step-by-step explanation:
A cylinder of oxygen contains 30 liters of gas at 50 atm pressure, and you need to know how many 400 cc (cm³) gas jars can be filled from this cylinder at 750 mmHg pressure. The relationship between the amount of gas, pressure, and volume is governed by the ideal gas law and Boyle's Law, assuming the temperature is constant. We can use these laws in a combined form to determine the volume of gas at the new pressure.
First, we need to convert 750 mmHg to atm since the initial pressure is given in atm. 1 atm is equivalent to 760 mmHg. Therefore, 750 mmHg can be converted to atm by dividing by 760 mmHg/atm.
Then, we apply the ideal gas law in its combined form:
P1 * V1 = P2 * V2
Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
50 atm * 30 L = (750 mmHg / 760 mmHg/atm) * V
We can then solve for V2, which gives us the total volume that can be delivered at 750 mmHg. Lastly, we divide this volume by 400 cc (or 0.4 L, since 1 L = 1000 cc) to determine the number of jars we can fill
Please note that the temperature should remain constant for this calculation to be valid and the gas should behave ideally. Actual results may vary due to non-ideal gas behaviors at high pressures.