Final answer:
To find the volume a gas at 89 atm and 6.75 L will occupy at 68.55 mmHg, Boyle's Law was applied after converting pressures to the same units. The final volume was calculated to be approximately 6648.4 L.
Step-by-step explanation:
Calculating Gas Volume After Pressure Change
A student is tasked to determine what volume a gas that occupies a volume of 6.75 L at 89 atm will occupy at a pressure of 68.55 mmHg. This problem can be solved using Boyle's Law, which states that for a given mass of an ideal gas at constant temperature, the pressure and volume are inversely proportional to each other.
To start, we need to ensure that the pressures are in the same units. We know that 1 atm is equivalent to 760 mmHg. Thus, the initial pressure in mmHg is 89 atm × 760 mmHg/atm = 67640 mmHg.
At this point, we can apply Boyle's Law, which is:
P1 × V1 = P2 × V2
where,
By substituting the known values:
67640 mmHg × 6.75 L = 68.55 mmHg × X L
Solving for X, we get:
X = (67640 mmHg × 6.75 L) / 68.55 mmHg
X ≈ 6648.4 L
The gas will occupy a volume of approximately 6648.4 L at a pressure of 68.55 mmHg.