- #1

Mr-Thirty

- 6

- 1

- 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?

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?