So I'm learning quantitative chemistry right now, and we just went over relative atomic mass, defined as,
the ratio between the average mass of all naturally occurring isotopes of an element to 1/12th the mass of C-12.
Bit wordy, but it makes sense. Then we learnt that relative atomic mass is dimensionless which also makes sense since it's a ratio between two
physical quantities that have the same unit, so the units will cancel out.
But if you think about it aren't all measurements relative? For example, take the meter. We take a certain length, define that as 1 meter, and then
measure everything relative to that. If something is 5m, it means it's five times that standard length. For mass, we take the mass of the
platinum-iridium cylinder, define that as 1kg and measure everything relative to that. Isn't this the exact same thing? We take 1/12 the mass of a
carbon atom, define that as 1 unit and then measure everything relative to that. So then why does it not have units while everything else does?
[Edited on 15-10-2013 by r15h4bh.c]Oscilllator - 15-10-2013 at 02:33
amu = atomic mass unit. I believe thats the unit you were looking for?
Often chemists don't put the unit at the end, because "amu" isn't particularly helpful, and mass units (kg, g etc) are more helpful. For example,
H2SO4 has a mass of 98.07 amu, but we usually don't write that since in the experiment we would just weigh out 98.07g of H2SO4.
Does that make sense?r15h4bh.c - 15-10-2013 at 03:52
Yeah, that makes sense and I read about the atomic mass unit, but on the definition everywhere, including Wikipedia, it is stated that it's a
dimensionless quantity. That's what I don't understand. What's the point of naming a unit and all that if in the definition you say it's
dimensionless? On another note, why does Avogadro's constant have units of 1/mol?bfesser - 15-10-2013 at 04:03
<a href="http://en.wikipedia.org/wiki/Metrology" target="_blank">Metrology</a> <img src="../scipics/_wiki.png" />woelen - 15-10-2013 at 04:07
There are more quantities which are dimensionless. E.g. if we have an angle between two lines, then that angle is specified in radians (or in
degrees), but the quantity itself is dimensionless.
The reason for this is that dimensionless quantities are ratios where units cancel out (radians are ratios of length of arc of circle and length of
radius of circle, the meters cancel out). A true dimensional quantity has a reference unit value. E.g. for distance, the reference unit value is 1
meter and a distance is expressed in the number of unit values, and hence we need to specify this in meters. r15h4bh.c - 15-10-2013 at 05:55
Yes, so for relative atomic mass, we define 1/12 the mass of C-12 as a reference unit, right? That's 1amu. Then why do we call it a dimensionless
quantity?
[Edited on 15-10-2013 by r15h4bh.c]watson.fawkes - 15-10-2013 at 06:18
Yes, so for relative atomic mass, we define 1/12 the mass of C-12 as a reference unit, right? That's 1amu. Then why do we call it a dimensionless
quantity?
Because there are dimensionless units. As woelen pointed out, radians is a perfectly good example.
Its true units are "distance-1/distance-2" (circumference over diameter), but these two lengths are not the same kind of length. Degrees of angle, for
example, are equally dimensionless, but isn't the same unit. A more complicated example is the measurement of "head" in a pipe, a unit of (at the end
of the day) friction that results in pressure loss. The units of head are the same as that of length, but that doesn't mean you can multiply a head
measurement by another length and end up with the area of a rectangle; it doesn't make sense. So cancelling out the primitive units (meters, seconds,
grams, ...) gives an reduced unit that can be used to distinguish measurements, but not all reduced units that are the same reflect the same
measurement. Dimensionless units are simply another example where this phenomenon happens.
