Question

A diver exhales a bubble with a volume of 250 ml at a pressure of 2.42 atm and a temperature of 15 degrees c. What is the volume of the bubble when it reaches the surface where the pressure is 1.00 atm and the temperature is 27 degrees c?

Answer 1

To find the volume of a bubble as it ascends to the surface, the Combined Gas Law is used, resulting in a final volume of approximately 621 ml.

Step-by-step explanation:

The student's question is about calculating the change in volume of a gas bubble as it moves from underwater to the surface, taking into account changes in pressure and temperature. To solve this, the Combined Gas Law, which relates pressure, volume, and temperature of a gas, will be employed.

Using the formula P1V1/T1 = P2V2/T2, where:

• P1 is the initial pressure (2.42 atm)
• V1 is the initial volume (250 ml or 0.250 L)
• T1 is the initial temperature in Kelvin (15°C + 273.15 = 288.15 K)
• P2 is the final pressure (1.00 atm)
• T2 is the final temperature in Kelvin (27°C + 273.15 = 300.15 K)

First, convert volumes to liters if they are not already, and temperatures to Kelvin by adding 273.15 to the Celsius value. Then, rearrange the formula to solve for V2:

V2 = P1V1T2 / (P2T1)

Plugging in the values:

V2 = (2.42 atm * 0.250 L * 300.15 K) / (1.00 atm * 288.15 K)

V2 = 0.621 L

The volume of the bubble when it reaches the surface will be approximately 621 ml.