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Calculate % by mass of Gold in Gold and Silver Alloy

Submitted by Anonymous (not verified) on Mon, 06/15/2009 - 10:18

I had posted this as a reply to an earlier post, but have not gotten a response.  In Chemistry, the Central Science 10th ed, there is a problem regarding % comp by mass with the following information. 

An alloy of gold and silver, totalling .675 cm3 volume, 9.85g mass.  Density of gold 19.3g/cm3; denisty of silver 10.5 g/cm3.  What is the percent of gold by mass.  The answer key in the book says 61.5% gold by mass, but doesn't give the process for calculating this.  An earlier poster put this problem on the board but the equation received (when I tried it) gave a very different answer. 

I can sort of work back from the answer.  The problem is working forward, not knowing the answer, if that makes any sense.

assuming the volume of gold and silver are additive

you can say

x = vol of Silver

0.675 - x = vol of Gold

mass of allow = mass of gold + mass of silver

9.85 g = V x density of gold  +  V x density of sliver

9.85 =  (.675-x) 19.3  g/mL  +  x ( 10.5 g/ mL)

x will give you the vol of silver

subtract from 0.675 to get vol of Gold

multiply vol of Gold x density of gold

you get ~6 g of Gold

divide by original mass