Question

A balloon that contains 9.5 L of air at 13.0 atm is taken underwater to a depth atwhich the pressure is 7.4 atm. Calculate the new volume of the balloon?

Answer 1

16.7 L.

Step-by-step explanation:

What is given?

Volume 1 (V1) = 9.5 L.

Pressure 1 (P1) = 13.0 atm.

Pressure 2 (P2) = 7.4 atm.

What do we need? Volue 2 (V2).

Step-by-step solution:

This is a Boyle's Law problem. Boyle's law states that the volume of a given mass of gas varies inversely with the pressure when the temperature is kept constant. An inverse relationship is described in this way. As one variable increases in value, the other variable decreases.

The formula of this law is:

`P_1V_1=P_2V_2.`

Where P is pressure and V s volume. We want to find the new volume, BV2, so let's clear for this unknown value and replace the given data that we have, like this:

`V_2=(P_1V_1)/(P_2)=\frac{13.0\text{ atm}\cdot9.5\text{ L}}{7.4\text{ atm}}=16.69\text{ L}\approx16.7\text{ L.}`

The new volume of the balloon would be 16.7 L.