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

Relevant 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 I am comfortable converting things like mile/gallon to km/litre but I don't 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 I am 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 I am 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 can't get my head around. I don't 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?

 

[kuruman]

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.

 

[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 I am still getting the wrong units. I know the answer is around 82 but i don't know why my units are still wrong. Is it my algebra? I can't see what's wrong

 

[kuruman]

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

 

[kuruman]

That looks about right.

 

[Mr-Thirty]

That looks about right.

Thank you so much