Please help me with this!!

Question

Oxygen is composed of three isotopes: oxygen-16, oxygen-17 and oxygen-18 and has an average atomic mass of 15.9980 amu. Oxygen-17 has a mass of 16.992 amu and makes up 0.035% of oxygen. Oxygen-16 has a mass of 15.982 amu and Oxygen-18 has a mass of 17.984 amu. What is the percent abundance of Oxygen-18? 

Answer 1

I'm going to get you started. The first thing I do with these problems is make a table of the known information. Take a moment to draw out a chart with the percentages and masses of each isotope. Since you don't know the mass of oxygen 16, let's give it the variable x. 

 

 Percentages can be represented as decimals, with 100% equalling 1. You might know this, but you just divide the number by 100 to change it. So let's change them to decimals for ease. Now, you know that all of the percents must add to 100%, or 1. Therefore, 1 minus the mass of oxygen 17 is useful information. 1-.00035= 0.99965. Therefore, 0.9965-x must equal the percentage of oxygen 18.

 

You can use this information to make an equation. Solving to find x will give you the percentage of oxygen 16, and then you get oxygen 18 by subtracting that number from 0.99965.

 

How do we make an equation? It should look like this. (average mass of element)= (mass of isotope 1)(percent of isotope 1)+(mass of isotope 2)(percent of isotope 2).. and so on.

 

See if you can come up with an equation, and I will check back to help if you need it.

 

 

 

Answer 2

So I've given you two previous answers now.  This time I'm going to help you set up the problem and let you finish it.

 

we know that

.. relative mass = sum of (atomic mass x relative abundance) over all

.. .. .. ... .. .. . ... .the stable isotopes.

 

we know that relative abundances add to 1. that is

.. abundance of O16 + abundance of O17 + abundance O18 = 1

 

so that IF we let the relative abundance of O18= Z, then

.. relative abundance O16 = (1 - 0.00035 - Z) = (0.99965 - Z)

 

and finally

.. (0.99965 - Z)*15.982 + .00035*16.992 + Z*(17.984) = 15.9980

 

multiply it out and solve for Z.

 

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update

.. Z = (15.9980 - 0.99965*15.982 - 0.00035*16.992) / (17.981 - 15.982)

.. Z = 0.783%