Question

A student measures the pressure and volume of an empty water bottle to be 1.4 atm

and 2.3 L. She then decreases the pressure to 0.65 atm. What is the new volume?

Answer 1

The new volume is 4.95 L

Step-by-step explanation:

Pressure and volume are related by Boyle's law:

"The volume occupied by a given gas mass at constant temperature is inversely proportional to the pressure"

Boyle's law is expressed mathematically as:

Pressure * Volume = constant

o P * V = k

If you have a certain volume of gas V1 that is at a pressure P1 at the beginning of the experiment and you vary the volume of gas to a new value V2, then the pressure will change to P2, and it will be true:

P1 * V1 = P2 * V2

In this case, you know:

• P1: 1.4 atm
• V1: 2.3 L
• P2: 0.65 atm
• V2: ?

Replacing:

1.4 atm* 2.3 L=0.65 atm* V2

Solving:

`V2=(1.4 atm*2.3 L)/(0.65 atm)`

V2=4.95 L

The new volume is 4.95 L

Answer 2

`V_2=5.0L`

Step-by-step explanation:

Hello,

In this case, we use the Boyle's law which allows us to understand the volume-pressure behavior as an inversely proportional relationship:

`P_1V_1=P_2V_2`

Hence, solving for the final volume we obtain:

`V_2=(P_1V_1)/(P_2) =(1.4atm*2.3L)/(0.65atm)\\\\V_2=5.0L`

Best regards.