math help needed

Question

In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 73.5 grams.

I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.

Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?

 %

Answer 1

1st, Calculate the density of the chain: mass of chain/ displaced volume = 73.5 g/5 ml = 12.7 g/ml

2nd: The overall density is obtained from mass of chain/volume of the chain Unfortunately, volume percent is a lot easier to do, but we are asked for mass percent:

overall mass = 73.5

overall volume , we will define the mass fraction of gold as f which means the volume fraction of an ingredient i is mf_i/ρ_i so for gold: 73.5f/19.3 and for others 73.5(1-f)/9.7 The sum of the volumes of the ingredients is the total volume. This leads to the equation:

12.7 = 73.5/(73.5f/19.3+73.5f/9.7)

factoring out the total mass and taking the reciprocal of both sides:

1/12.7 = f/19.3 + (1-f)/9.7

Now solve algebraically for f. (This could have been obtained as a volume balance)

Don't forget to make the fraction a percent by multiplying by 100.