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 volume of a gas is inversely proportional to its pressure when temperature is constant.
Boyle's Law equation:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume
Let's assign the given values from the problem:
P1 = 35,000 mm Hg
V1 = 12.0 liters
P2 = 150 mm Hg (pressure at the top of Mt. Everest)
V2 = ?
Now, we can plug in the values and solve for V2:
35,000 mm Hg * 12.0 liters = 150 mm Hg * V2
(35,000 mm Hg * 12.0 liters) / 150 mm Hg = V2
V2 = (4,200,000 mm Hg⋅liters) / 150 mm Hg
V2 ≈ 28,000 liters
Therefore, if the gas is released at the top of Mt. Everest, it will occupy a volume of approximately 28,000 liters.
To find the volume the gas will occupy when released at the top of Mt. Everest, we can use the principle of Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is constant.
Boyle's Law equation: P₁V₁ = P₂V₂
Where:
P₁ = initial pressure (in mm Hg)
V₁ = initial volume (in liters)
P₂ = final pressure (in mm Hg)
V₂ = final volume (unknown)
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 (at the top of Mt. Everest).
Now, we can rearrange the equation to solve for V₂:
V₂ = (P₁ * V₁) / P₂
Substituting the values into the equation:
V₂ = (35,000 mm Hg * 12.0 liters) / 150 mm Hg
V₂ = 2,800 liters
Therefore, the gas will occupy a volume of 2,800 liters when released at the top of Mt. Everest.