# Convert J/mol k into atm cm^3/mol k

#### Mr-Thirty

Homework Statement
Convert the ideal gas constant to atm cm^3/ mol k
Homework Equations
1 J = Nm
1 atm = 101325 Pa
1 m^3 = 1 x 10^6 cm^3
My lecturer asked us to convert the ideal gas law into the units "atm cm^3/ mol k"
I've used conversion brackets before and im comfortable converting things like mile/gallon to km/litre but I dont understand how to do this one.
The way I was taught was to put the units in brackets and take the numerical calculation out to the front. Then find the conversion and place them in the brackets such that they cancel with the original units and leave behind the new units you were after.

i.e. For 3 feet into inches: 3 x [ft x 12 inch/ 1 ft], the ft's cancel and you do 3 x 12 = 36 inches

But for converting J / mol k to atm / mol k im not sure what to do. I know these are the conversion factors:

1 J = Nm
1 atm = 101325 Pa
Pa = N/m^2
1 m^3 = 1 x 10^6 cm^3

But im trying to reconcile how Joules can be expressed in terms of pressure x volume. I know I need to find an expression for Joules which I can place on the bottom of the fraction in order to cancel it. I think its the idea of the volume part of the calculation which I cant get my head around. I dont know how to express force x distance, force x area and pressure x volume.

(8.314) x [ (J / mol k) x (atm / 101325 Pa) x (cm^3 / m^-3) ]

(8.314) x [ (Nm / mol k) x (atm / 101325 Nm^-2) x (cm^3 / m^-3) ]

How can I express this so I can cancel? Whats the best way to write this?

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#### kuruman

Homework Helper
Gold Member
Start from the well known value $R = 8.31~\mathrm{\frac{J}{mol\cdot K}}$. It looks like you need to convert 1 J into some number times $\mathrm{atm \cdot cm^3}$ because the two are dimensionally the same. Express all units in terms of the basic kilograms, meters and seconds. For example, 1 Newton = 1 kg m/s2.

Last edited:

#### Mr-Thirty

Start from the well known value $R = 8.31~\mathrm{\frac{J}{mol\cdot K}}$. It looks like you need to convert 1 J into some number times $\mathrm{atm \cdot cm^3}$ because the two are dimensionally the same. Express all units in terms of the basic kilograms, meters and seconds. For example, 1 Newton = 1 kg m/s2.
Thank you for the reply, so I tried expressing Joules and pascal in terms of their basic units and im still getting the wrong units. I know the answer is around 82 but i dont know why my units are still wrong. Is it my algebra? I cant see whats wrong

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#### kuruman

Homework Helper
Gold Member
Two mistakes
First: 1 Pa = 1 N/m2 not 1 kg/m2. You need to convert the Newton unit into kg - m - s units.
Second: Where does the extra factor $\mathrm{\frac{10^{-6}cm^3}{m^3}}$ come from? Just convert all meters into centimeters after canceling like terms in the numerator and denominator.

#### Mr-Thirty

Ok thanks for your help, I think I may have figured it out. Please check my working below

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#### kuruman

Homework Helper
Gold Member
That looks about right.

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