# Effective atomic number for a mixture (with components concentration)

1. May 20, 2013

### sci_girl

Assume we have a concentration of any specific material (in mg/M). Let's say for example: Ag (Z=47) with concentration 10 mg/M in water (H2O, Z=7.42).

How can I calculate the effective atomic number (Zeff.) for the silver-water mixture if the concentration of silver was 10 mg/M for example?

The only formula I know to calculate Zeff. is the following:

but it uses (fn) the fraction of the total number of electrons associated with each element, not the concentration in mg/M.

Is there any possible way to convert the concentration (in mg/M) into a fraction of total number of electrons for silver then calculate Zeff for the silver-water mixture mentioned above as an example?

source: http://en.wikipedia.org/wiki/Effective_atomic_number (example for H2O provided)

2. May 20, 2013

### I like Serena

Based on the atomic masses of silver, hydrogen, and oxygen, you can convert their masses to atom counts.

Silver has a molar mass of 107.8682 grams.
So for instance 10 mg of Silver is 0.010 / 107.8682 moles.

3. May 20, 2013

### sci_girl

Thanks for the response. that's for my second question..
but how can I apply this to calculate the Zeff for the silver-water mixture using the formula in the original post above (or any other formula) ?

4. May 20, 2013

### I like Serena

What does it mean?
Afaik 1 M = 1 mol/L.

Anyway, if you have 10 mg silver in 1 kilogram water, you have:
0.010 / 107.8682 moles silver
1000 / 18 moles water, consisting of 2000 / 18 moles hydrogen, and 1000 / 18 moles oxygen.

Therefore the number of silver electrons is 47 x 0.010 / 107.8682.
The number of hydrogen electrons is 1 x 2000 / 18.
And the number of oxygen electrons is 8 x 1000 / 18.

From this you can calculate first the fractions, and then the Zeff.

5. May 23, 2013

### sci_girl

sorry, I've been busy with exams.

6. May 23, 2013

### I like Serena

I take it you've already taken the exam on this subject... successfully?

7. May 24, 2013

### sci_girl

not on this subject specifically but it helped me to figure things out... I was not convinced that mg/M is even a concentration unit, it confused me but I think I've got it all clear now. Thank you <3