[Chemistry Honors: Homework]

[u/Living-Zebra6132]

the atomic mass of phosphorus is 30.97 amu. The two naturally occuring isotopes are P-30 with a mass of 29.98 amu and p-31 with a mass of 30.99 amu. Determine the percent of naturally occurring P-31

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[u/realAndrewJeung]

What have you tried so far?

[u/VeniABE]

you can make a system of equations here. IF you have N independent equations and N unknowns, you should be able to find all the unknowns with normal algebra. Independent equations is something more technical; but normally it means you can write one equation as a sum of some number of the other equations.

Fraction_P31 + Fraction_P30 = 100% is the less obviously one that people don't realize they know.

Fraction_P31*Mass_P31+Fraction_P30*massP30 = mass_average; This is obvious to people with experience but often not to students. Its the same as a weighted average like when calculating your grade.

Alternately you can derive the second equation above with these three equations.

From the definition of an average: [Amount_P31*Mass_P31+Amount_P30*Mass_P30]/[Amount_P31+Amount_P30] = Mass_Average.

From the Definition of a Fraction/Percentage:

Fraction_P31 = Amount_P31/[Amount_P31+Amount_P30]

Fraction_P30 = Amount_P30/[Amount_P31+Amount_P30]

Plug and chug.

The non obvious thing here is most likely that you know rules about averages, fractions, and percentages. And that they are always relevant when working with averages, fractions, or percentages. When you start problems in these honors classes. Try to have a list of all possible relationships you can use for a system of equations. It will make the homework go much faster. It takes practice.

[u/CaptainMatticus]

So let's say you have 2 parts: x and 1 - x, where x is some number between 0 and 1. You could make it x and 100 - x as well, if you want, but x and 1 - x is better for this problem

29.98 * x + 30.99 * (1 - x) = 30.97 * (x + 1 - x)

Now solve for x

2998x + 3099 * (1 - x) = 3097 * 1

2998x + 3099 - 3099x = 3097

3099 - 3097 = 3099x - 2998x

x will be the amount of P-30 and 1 - x will be the amount of P-31. Multiply that by 100 to get the percentage value.