[Boxxxed]

We are given

Atomic weight of 12C = 12.011 u
Mass of 13C             = 13.003355 u

How do I calculate the % abundance of 13C?



A1=Abundance of  Carbon 13
M1=Mass of Carbon 13

A2=Abundance of Carbon 12
M2=Mass of Carbon 12


m=(A1M1)+(A2M2)

12.011=(A1*13.003355)(A2*12.011)

What do I do now?

[Jorriss]

The atomic mass of carbon-12 is 12 by definition. The averaged mass of carbon is 12.011, this includes its isotopes.

[V]

I just learned how to do this type of problem yesterday. The answer would be a percent for each isotope.

Set up like
Mass isotope A (x) + Mass Isotope B (1 - x) = Periodic Table Mass

However, it won't work with this data because the weighted average (Periodic table mass) is outside the values range. So... I'm not sure if the question was just typed wrong or if there is something wrong with the given data or if I'm totally misunderstanding...

... but that is how I learned to calculate the abundance of isotopes.

[Boxxxed]

We were given this question without ever seeing that formula before. How is it deduced?

The next step in the problem is 12.011=(x)(13.005533u)+(12.011u)(x-1)

I have no idea how that is derived, it is correct though.

[sjb]

We were given this question without ever seeing that formula before. How is it deduced?

The next step in the problem is 12.011=(x)(13.005533u)+(12.011u)(x-1)

I have no idea how that is derived, it is correct though.

A simple weighted average of the constituents, so if e.g. 1 apple weighs 100g, and 2 apples weigh 115g each, then the average would be ^{[(1 x 100) + (2 x 115)]}/₍₁₊₂₎, x in your formula is the ratio, e.g ¹/₍₁₊₂₎. As previously mentioned, however, the data you've provided are misleading. Where have you got the atomic weight of ¹²C from?

[V]

Hi there,

You have to solve for two unknowns, but as they are percentages... they are parts of 1.0
So you solve for x and once you know x, you subtract x from 1 and you have the percentage for the other isotope (the one that was attached to (1-x)).

So, just look at it as algebra... (which I stink at) but first you have to take distribute the value that is times (1-x) to separate things out.. and then combine like terms and solve for x.

Hope that helps.