Question

The percentage composition by mass of the less expensive 14-karat gold is typically 58.5 percent gold, 4.0 percent silver, 31.2 percent copper, and 6.3 percent zinc. find the percentage composition by volume of 14-karat gold. the density of zinc is ρzinc=7.14g/cm3. enter four answers as percentages, separated by commas. round each to the nearest integer.

Answer 1

39%, 5%, 45%, 11%
   First, let's look up the density of the metals involved. There's multiple places you can find this data. I've found:
 Gold: 19.30 g/cm^3
 Silver: 10.49 g/cm^3
 Copper: 8.96 g/cm^3
 Zinc: 7.14 g/cm^3
   Now imagine you have enough of each element available to make exactly 100 grams of the desired alloy. That would mean you have 100 * 0.585 = 58.5 grams of gold. And that gold would have a volume of 58.5 g / 19.30 g/cm^3 = 3.031 cm^3
 Let's continue to do that and get the volumes for all 4 elements.
 Gold = 3.031 cm^3
 Silver = 4.0 g / 10.49 g/cm^3 = 0.0381 cm^3
 Copper = 31.2 g / 8.96 g/cm^3 = 3.482 cm^3
 Zinc = 6.3 g / 7.14 g/cm^3 = 0.882 cm^3
   Now sum the individual volumes together to get the total volume:
 Sum = 3.031 cm^3+ 0.0381 cm^3 + 3.482 g/cm^3 + 0.882 cm^3 = 7.776 cm^3
   Now for the percentages:
 Gold = 3.031 cm^3/7.776 cm^3 = 0.389789 = 38.9789% = 39%
 Silver = 0.0381 cm^3/7.776 cm^3 = 0.048997 = 4.8997% = 5%
 Copper = 3.482 cm^3/7.776 cm^3 = 0.447788 = 44.7788% = 45%
 Zinc = 0.882 cm^3/7.776 cm^3 = 0.113426 = 11.3426% = 11%