Answer:
1) See below for percentages
2) 1.33g of silver (Ag)
3) Cu is 4g and Zn is 1.67g
Explanation:
Au:Cu:Zn:Ag
9: 12: 5: 2
Total parts = (9+12+5+2) = 28
We can calculate a percentage composition by dividing an element's "parts" by the total parts.
a) This might be considered "this ratio in simplest form," at least for many. "Simplest form is a judgement.
The percentages may be used to calculate the masses of each element in a defined mass of alloy. The first column is an example calculation
for a 3 gram alloy sample.
b) To determine the mass of silver (Ag) required for an alloy containing 6 grams of gold (Au), first enter 6g for the gold. This can be used to calculate to total mass of the alloy by dividing the 6g by the percentage of gold in the alloy, which is 32.1%. [(6g/0.321) = 18.67 grams for the final alloy mass. Enter the 18,67 grams in the table and then multiply that times each element's percent composition to arrive at the masses required for each. (E.g., for silver (Ag) the calculation would be (7.1%)*(18.67g) = 1.33 grams of silver needed for an alloy containing 6 grams of gold.
c) Do the same for copper (Cu) and zinc (Zn) in an alloy containing 3 grams of gold. This is done in the third column. Assign 3 grams for the gold entry, divide that by the percent gold to arrive at an alloy mass of 9.33 grams. Use the other element's percentages to convert the 9.33 grams into individual element masses. Cu and Zn masses are 4g and 1.67g, respectively.
Mass (g)
Percentage 3g alloy 6g Au 3g Au
Au = (9/28) or 32.1% 0.964 6 3
Cu = (12/28) or 42.9% 1.286 8 4
Zn = (5/28) or 17.9% 0.536 3.33 1.67
Ag = (2/28) or 7.1% 0.214 1.33 0.67
100% 3 grams 18.67g 9.33g