# How can you do all individual gas law problems with pv=nRT?

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I think you mean this..

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.. PV = nRT

and rearrange

.. PV / (nT) = R

and note that R is a universal constant.. so that ALL.. PV/(nT)'s must equal each other... you can readily write..

.. P1V1 / (n1T1) = P2V2 / (n2T2)

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now.. if we start holding some of those variables constant.. say n1=n2.. so they cancel out... we can generate these variations of that equation

0 variables held constant...

.. (1).. [P1V1 / (n1T1) = P2V2 / (n2T2)]...nothing constant... not named

1 variable held constant...

.. (2).. [V1 / (n1T1) = V2 / (n2T2)]...P held constant... not named

.. (3).. [P1 / (n1T1) = P2 / (n2T2)]...V held constant... not named

.. (4).. [P1V1 / T1 = P2V2 / T2].......n held constant... "combined gas law"

.. (5).. [P1V1 / n1 = P2V2 / n2].......T held constant... not named

2 variables held constant...

.. (6).. [n1T1 = n2T2]..... .... .P, V held constant... not named

.. (7).. [V1 / T1 = V2 / T2]... .P, n held constant... "Charles Law"

.. (8).. [V1 / n1 = V2 / n2]... .P, T held constant... "Avogadro's Law"

.. (9).. [P1 / T1 = P2 / T2]... .V, n held constant... not named.

.. (10).. [P1 / T1 = P2 / T2]...V, T held constant... not named.

.. (11).. [P1V1 = P2V2]... .... .n, T held constant... "Boyles Law"

and the trivial ones with 3 and 4 variables constant.. you can write those out.

notice #9 is not named? Some teachers will insist that is "Gay Lussac's Law".. but that is not correct. Gay Lussac never studied constant volume constant mole gas laws.

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anyway... instead of memorizing all those variations, their names, and for what conditions they apply and praying to God during exams that you choose the write equation.. do this

(1) start with the equation P1V1 / (n1T1) = P2V2 / (n2T2)

(2) rearrange for your desired unknown

(3) identify and cancel anything held constant

(4) plug in the data and chug out the result

.... remember to convert T to an absolute scale.. R or K.. never °F nor °C

example...

1L of H2 gas @ 25°C and 2 atm was allowed to example to 2L at 0°C. After which the moles of gas in the container was doubled while temperature held constant. What is the final pressure?

.. P1V1 / (n1T1) = P2V2 / (n2T2)

rearrange for P2

.. P2 = P1 x (V1 / V2) x (n2 / n1) x (T2 / T1)

nothing is held constant.. so we can't cancel any of the variables.

solving.. we're given that

.. P1 = 2atm

.. V2 = 2L

.. V1 = 1L

.. n2 = 2 x n1

.. T2 = 273.15K

.. T1 = 298.15K

so..

.. P2 = 2atm x (1L / 2L) x (2 x n1 / n1) x (273.15 / 298.15) = 1.83 atm

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example..

.. 2L of a gas at a pressure of 2atm and temperature of 0°C was allowed to expand and warm until the pressure was 1atm and temperature was 25°C. What is the new volume

starting with

.. P1V1 / (n1T1) = P2V2 / (n2T2)

rearranging

.. V2 = V1 x (P1 / P2) x (n2 / n1) x (T2 / T1)

since moles.. n... isn't mentioned, we assume it's held constant.. so n2/n1 cancels out leaving

.. V2 = V1 x (P1 / P2) x (T2 / T1)

solving

.. V2 = 2L x (2 atm / 1 atm) x (298.15K / 273.15K) = 4.37L

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notice in the first case example.. NOTHING is held constant.. So if you just memorized "Charles law", "combined gas law", "boyles law" and the erroneously named "Gay Lussac's Law", you would not be able to solve this problem!

notice in the 2nd example... because moles was constant, it dropped out leaving this

.. P1V1 / T1 = P2V2 / T2

which was rearranged a bit.. that is "combined gas law"

that combined gas law came about naturally just by starting with P1V1 / (n1T1) = P2V2 / (n2T2) and canceling the variables held constant. .

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see how that works?

you can use that 1 equation and that logic to solve ALL those pesky 2 state gas law problems.

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more examples

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