Question

The initial volume of a gas cylinder is 750.0 ml. if the pressure of a gas inside the cylinder changes from 840.0 mm hg to 360.0 mm hg, what is the final volume the gas occupies?

Answer 1

It should be 1.750 L
Hope this helps.

Answer 2

`V_2=1.75L`

Explanation:

Use the Boyle's law which states that the pressure of a gas in a closed container is inversely proportional to the volume of the container, when the temperature is constant. Mathematically this is:

`P_1*V_1=P_2*V_2` (1)

Where:

`P_1=Initial\hspace{3}pressure\\P_2=Final\hspace{3}pressure\\V_1=Initial\hspace{3}volume\\V_2=Final\hspace{3}volume`

Before attempting to solve the problem, let's do the pertinent conversions:

`840mmHg*(1torr)/(1mmHg) *(1Pa)/(133.32torr) =6.3Pa`

`360mmHg*(1torr)/(1mmHg) *(1Pa)/(133.32torr) =2.7Pa`

`750ml*(1L)/(1000ml)=0.75L`

So, we got:

`P_1=6.3Pa\\P_2=2.7Pa\\V_1=0.75L`

Now, let's isolate
`V_2` from (1) in order to find the final volume:

`V_2=(P_1*V_1)/(P_2) \\\\V_2=(6.3*0.75)/(2.7) = 1.75L`