A scuba diver ascends too quickly and develops the bends. A nitrogen bubble has formed in the patient's elbow. At a depth of 64 ft, where the pressure is 2.94 atm, the bubble had a volume of 0.026 mL. Assuming a constant temperature and number of moles of nitrogen in the bubble, what volume did the bubble increase to at the surface, where the pressure is 1.00 atm?
P1V1 = P2V2
P1 = 2.94 Atm
V1 = 0.026 mL
P2 = 1.00 atm
V2 = ?
Solve for V2
To solve this problem, we can use Boyle's Law, which states that the product of the pressure and volume of a gas is constant at a constant temperature.
According to Boyle's Law, we have:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure = 2.94 atm
V1 = initial volume = 0.026 mL
P2 = final pressure = 1.00 atm
V2 = final volume (what we want to find)
Let's plug in the values into the formula and solve for V2:
P1 * V1 = P2 * V2
2.94 atm * 0.026 mL = 1.00 atm * V2
Now, we can calculate V2:
(2.94 atm * 0.026 mL) / 1.00 atm = V2
V2 = 0.07644 mL
Therefore, the volume of the bubble at the surface, where the pressure is 1.00 atm, is approximately 0.07644 mL.
To solve this problem, we can use Boyle's Law, which states that the volume of a gas is inversely proportional to the pressure if temperature and moles of gas remain constant. Boyle's Law can be represented by the equation:
P1V1 = P2V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, we are given the initial volume V1 (0.026 mL) and pressure P1 (2.94 atm) at a depth of 64 ft, and we need to find the final volume V2 at the surface pressure P2 (1.00 atm).
Let's substitute the given values into the equation:
(2.94 atm)(0.026 mL) = (1.00 atm)(V2)
Now we can solve for V2:
V2 = (2.94 atm * 0.026 mL) / (1.00 atm)
= 0.07644 mL
Therefore, the bubble increased to a volume of 0.07644 mL at the surface.