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?
0.5
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
The equation for Boyle's Law is:
P₁V₁ = P₂V₂
Where:
P₁ = initial pressure
V₁ = initial volume
P₂ = final pressure
V₂ = final volume
In this case, the initial pressure (P₁) is 35,000 mm Hg, the initial volume (V₁) is 12.0 liters, and the final pressure (P₂) is 150 mm Hg.
Now, let's solve for the final volume (V₂):
P₁V₁ = P₂V₂
35,000 mm Hg * 12.0 liters = 150 mm Hg * V₂
Divide both sides of the equation by 150 mm Hg:
(35,000 mm Hg * 12.0 liters) / 150 mm Hg = V₂
Now, calculate the final volume:
V₂ = (35,000 mm Hg * 12.0 liters) / 150 mm Hg
V₂ = 2,800 liters
Therefore, if the gas is released at the top of Mt. Everest, it will occupy a volume of 2,800 liters.