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Calculate % of Gold in Gold and Silver Alloy

Submitted by melmel465 on Thu, 09/13/2007 - 22:40

Hello -

This is actually my sisters homework problem (junior in highschool)- she spent time trying to figure it out and her teacher gave her some formulas to help her out.  She finally asked big sister for help, and I have no clue where to start for this!  I've been working on it for over an hour.  Here's the prob:

Gold and silver alloy weighs 9.85g, has a volume of 0.675cm3.  Gold has a density of 19.39g/cm3 and silver 10.5g/cm3.  Calculate the percentage of Gold in grams that is contained in the alloy.

Her teacher gave her the following formulas:
9.85g = x(g) + y(g)
0.675cm3 = x(1cm3/19.3g) = y(1cm3/10.5g)

We easily figured out the density of the alloy = 14.59 g/cm3, but we have no idea where to go next.  Could you give us a few ideas to help us along?  Thank you so much!

Thanks,
Melissa


I'll give it a shot here

the mass of the alloy is 9.85 g

this mass is made up of the mass of gold and the mass of silver so we have

mass alloy = mass gold + mass silver

9.85 g = mass gold + mass silver

then mass silver = 9.85 g - mass gold

density of alloy = mass alloy / volume alloy =  (mass gold + mass silver) / volume alloy

density of alloy = (mass gold + mass silver) / volume alloy
                    =  (mass gold + (9.85 g - mass gold )) / volume alloy

solving this should give you the mass of gold

divide by the original amount and multiply by 100


The book shows the answer as 61.5% gold by mass.  I can't get there with these formulas.  What am I doing wrong?

Chemistry Tutor wrote:

I'll give it a shot here

the mass of the alloy is 9.85 g

this mass is made up of the mass of gold and the mass of silver so we have

mass alloy = mass gold + mass silver

9.85 g = mass gold + mass silver

then mass silver = 9.85 g - mass gold

density of alloy = mass alloy / volume alloy =  (mass gold + mass silver) / volume alloy

density of alloy = (mass gold + mass silver) / volume alloy
                     =  (mass gold + (9.85 g - mass gold )) / volume alloy

solving this should give you the mass of gold

divide by the original amount and multiply by 100