4. A diver has about 0.05L of gas dissolved in his blood while swimming 200 feet underwater (at a
pressure of 7.05atm). He returns too quickly to the surface, quickly reaching a depth of 20 feet (at
a pressure of 1.60atm). What is the new volume within his blood?
a. Identify the law to be used:
b. Solve the problem:
pressure of 7.05atm). He returns too quickly to the surface, quickly reaching a depth of 20 feet (at
a pressure of 1.60atm). What is the new volume within his blood?
a. Identify the law to be used:
b. Solve the problem:
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Boyle's Law
P1V1 = P2V2
where in, P1 = first pressure
V1 = first volume
P2 = second pressure
V2 = second volume
Given: P1 = 7.05atm
V1 = 0.05L
P2 = 1.60atm
Unknown: V2 = ?
Formula: V2 = P1V1 / P2
Note: To get the formula, apply division and cancellation of like terms using the original formula of Boyles Law.
P1V1 = P2V2 ← divide both sides by P2
P1V1 / P2 = P2V2 / P2 ← cancel like terms
P1V1 / P2 = PV ← final formula for V2
Note: Easier method is by Transposition
P1V1 = P2V2 ← transpose P2 to the other
side
P1V1 / P2 = V2 ← final formula for V2
Solution: V2 = P1V1 / P2
= (7.05atm)(0.05L) / 1.60atm
= 0.3525atm•L / 1.60atm
= 0.22L
Note: "atm" is cancelled out, so the unit for volume will remain which is "L"
Reminder: Cancellation of units is applicable when the other same unit is on the denominator.
Final Answer: V2 = 0.22L