The percent by mass of gold in the mixture will be 34.5%.
The following information can be deduced based on the information given:
Density of gold = 19.3 g/cm³.
Density of sand = 2.94 g/cm³
Density of mixture = 4.17 g/cm³
It should be noted that when we find the volume fo gold on a 1cm³ sample, then we can be able to find that mass. The volume of gold will be calculated thus:
4.17 = [(19.3x + 2.95(1 - x)]
4.17 = 19.3x + 2.95 - 2.95x
4.17 = 16.35x + 2.95
x = 0.0746cm³
The mass of gold will be:
= 0.0746 × 19.3
= 1.44
The percent by mass of gold in the mixture will be:
= 1.44/4.17 × 100
= 34.5%
In conclusion, the percent by mass of gold in the mixture will be 34.5%.
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