A 16.5 cm3 bubble under the ocean at 2.1 atm and 12.5oC surfaces to 1.0 atm and 22.1oC. What is the new volume (in cm3)?

i used (p1)(V1)/T1=(P2)(V2)/T2

(2.1)(.0165)/285.65=(1)(V2)/295.25
THE ANSWER I GOT IS .0335

i changed 16.5 to liters which is why its .0165

To solve this problem, you correctly used the ideal gas law equation:

(P1)(V1)/T1 = (P2)(V2)/T2

Where:
P1 = initial pressure in atm
V1 = initial volume in cm3
T1 = initial temperature in Kelvin
P2 = final pressure in atm
V2 = final volume (what we need to find)
T2 = final temperature in Kelvin

First, let's convert the initial volume given as 16.5 cm3 to liters, as you did. Since 1 liter = 1000 cm3, the initial volume would be 16.5 cm3 / 1000 = 0.0165 L.

Plug in the given values into the ideal gas law equation:

(2.1 atm)(0.0165 L) / (12.5 + 273.15 K) = (1 atm)(V2) / (22.1 + 273.15 K)

Now, solve for V2, the final volume:

(2.1)(0.0165) / (12.5 + 273.15) = (1)(V2) / (22.1 + 273.15)

Cross-multiply:

(2.1)(0.0165)(22.1 + 273.15) = (12.5 + 273.15)(V2)

Multiply the two values on the left side and the two values on the right side:

V2 = (2.1)(0.0165)(22.1 + 273.15) / (12.5 + 273.15)

Calculate this expression to find the final volume:

V2 = (0.058185)(295.25) / 285.65

V2 = 0.033536 L

Finally, convert this answer back to cm3 by multiplying by 1000:

V2 = 0.033536 L * 1000 cm3/L

V2 ≈ 33.536 cm3

Therefore, the new volume after the bubble surfaces is approximately 33.536 cm3.