3. Atmospheric pressure at the top of Mt. Everest is about 150 mm Hg. That
is why climbers always bring oxygen tanks. If a climber carries a
12.0 liter tank with a pressure of 35,000 mm Hg, what volume will the
gas occupy if it is released at the top of Mt. Everest?
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature and the number of particles remain constant.
Boyle's Law equation:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure (35,000 mm Hg)
V1 = initial volume (12.0 liters)
P2 = final pressure (150 mm Hg) at the top of Mt. Everest
V2 = final volume (unknown)
Now, we can rearrange the equation to solve for V2:
V2 = (P1 * V1) / P2
Substituting the given values:
V2 = (35,000 mm Hg * 12.0 liters) / 150 mm Hg
Simplifying the equation:
V2 = 280,000 mm Hg * liters / 150 mm Hg
Canceling out the units:
V2 = 1,866.67 liters
Therefore, the gas will occupy approximately 1,866.67 liters when released at the top of Mt. Everest.