Uniform Units

[Iota]

In chemistry lessons I was taught that the positive units are followed by the inverse units. My teachers didn't use the term 'inverse' to describe them, but that's what they are, I think?

 

So anyway, an example:

 

(moldm^-3) (moldm^-3)

-------------------------- = dm³mol^{-1 <--- So as seen here cubic decimetres comes before mole.}

(moldm^-3)²(moldm^-3)

 

So it becomes Cubic decimetres per mole, as opposed to moles per cubic decimetre.

 

However, in my physics textbooks I frequently see SI units like km h^-1, and others presented with the inverse units coming last.

 

As I'm writing this I'm having ideas as to why this may be; i.e. hour per kilometres doesn't make sense.

 

My question is, does that rule only apply to the process of deriving units? Such as that for k_c (equilibrium constant), or is it simply convention to display them the common way?

[hypervalent_iodine]

This could just be me, but I'm really not seeing the difference in the two examples you cite? Both place the 'inverse unit' (mol^-1 and hr^-1) last when describing them.

 

In any case, it's really just convention. For instance, grams per mole is used to describe g mol^-1 (or g/mol); that is to say, for every mole of substance X, we have Y number of grams (which is what we mean when we say per). That brings me on to something I wanted to comment on in your OP:

 

So it becomes Cubic decimetres per mole, as opposed to moles per cubic decimetre.

 

Well yes, because moles per cubic dm (mol dm^-3 or mol/dm³) is vastly different to cubic dm per mole (dm³ mol^-1 or dm³/mol). Similarly:

 

However, in my physics textbooks I frequently see SI units like km h^-1, and others presented with the inverse units coming last.

 

As I'm writing this I'm having ideas as to why this may be; i.e. hour per kilometres doesn't make sense.

 

It doesn't make sense if your describing km h^-1 (i.e. you travel X km in 1 hour), as hours per kilometer (i.e. it takes you X hours to travel 1 km) would be stated as h km^-1 and as such, does not correspond to the same thing.

[Iota]

Ah I see, cheers for clearing this up.

 

This could just be me, but I'm really not seeing the difference in the two examples you cite? Both place the 'inverse unit' (mol^-1 and hr^-1) last when describing them.

 

The difference was between the units shown in the cancellation process and the SI units. moldm^-3 is changed to dm³mol^-1 when the units are transferred from bottom to top of the equation. SI units are displayed like that of dm³mol^-1 automatically. My amazing observational skills at work again. No, you're right I've been confusing myself on many levels over something simple, as per usual.

 

Since then I've worked out how the unit ms^-1 is probably derived through calculation; it does make sense and doesn't happen as automatically as I previously thought. Both common sense and a simple calculation have now shown me this.

 

Thanks.

Edited July 30, 2012 by Iota

[hypervalent_iodine]

Not a problem! My common sense gets the better of me on a daily basis.