A 100 ml sample of a gas at -73℃ and 2 atm is heated to 123℃ and the pressure is reduced to 0.5 atm.
What will be the final volume ???
Answers
A sample of gas has an initial volume of 26.0 L at a pressure of 1.7 ATM. If the sample is compressed to a volume of 10.7L, what will its pressure be?
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2 ANSWERS
Satya Venugopal
Satya Venugopal, B.Sc. Physics & Minor in Mathematics, Nanyang Technological University (2012)
Answered Jun 19, 2017
Short answer: Depends on what the story is with the sample gas’s temperature.
Long answer:
Assuming we have an ideal gas, the Ideal Gas Law applies, so
PV = nRT
Where P is the pressure of the gas, V its volume, n the number of moles it contains, and T its temperature. R is the ideal gas constant.
From the above law we get PV/nT = R, i.e. PV/nT will always be a constant for an ideal gas. This allows us to compare initial and final conditions of the gas:
(Pi)(Vi)/n(Ti) = (Pf)(Vf)/n(Tf)
Where Pi = Initial pressure, Vi = Initial volume, and Ti = Initial temperature
While Pf = Final pressure, Vf = Final volume, and Tf = Final temperature
Assuming we are dealing with a closed system (i.e. the sample does not lose any gas to the outside of the container, or gain any gas from it), the number of moles of the gas must be constant. So the initial and final values of n are the same, and we can cancel off the n from both sides, to give us:
(Pi)(Vi)/(Ti) = (Pf)(Vf)/(Tf)
From the question, we know (Pi) = 1.7 atm, (Vi) = 26.0 l, (Vf) = 10.7 L, and we are asked to find (Pf) in atm. Substituting these into our above equation:
(1.7)x(26.0)/(Ti) = (Pf)x(10.7)/(Tf)
(Pf) = ((1.7)x(26.0)x(Tf))/((10.7)x(Ti))
As you can see, we lack any information about the initial temperature, Ti, or the final temperature, Tf. So we are unable to solve the problem.
(Unless we assume the temperature remains constant throughout, and Ti and Tf will cancel each other off. Then we can plug the above values into a calculator to obtain our answer for the final pressure, Pf.)