Question

A syringe initially holds a sample of gas with a volume of 285 mL at 355 K and 1.88 atm. To what temperature must the gas in the syringe be heated/cooled in order to have a volume of 435 mL at 2.50 atm?

Answer 1

We know that PV = nRT

Where

T = Temperature ;P = pressure ; n = No . of moles ;R = gas constant ; V= Volume of the gas

As the gas remains the same , n will constant

So PV / T = constant

Thereby PV/T = P'V'/T'

Where

P = initial pressure = 1.88 atm

V = initial volume = 285 mL

T = initial temperature = 355 K

P'= final pressure = 2.50 atm

V' = final volume = 435 L

T' = final temperature = ?

Plug the values we get

PV/T = P'V'/T'

T' = (P'V'T) / (PV)

   = (2.50x435x355)/(1.88x285)

   = 720.5 K

Therefore the temperature increases from 355 K to 720.5 K

Therefore the syringe is heated to 720.5K