Question

Part A

Pure gold crystallizes in a face-centered cubic unit cell with an edge length of 4.08 Å. The alloy called 18-karat gold consists of 75% Au, 9.0% Ag. and 16% Cu by mass. What am
subscripts in the empirical formula of 18-karat gold (Au-Ag,Cuz) to two significant digits?
Express the subscripts to two significant figures separated by commas.

Answer 1

The empirical formula of 18-karat gold (Au-Ag,Cuz) to two significant digits is Au3-Ag1,Cuz1.

Step-by-step explanation:

To determine the subscripts in the empirical formula of 18-karat gold (Au-Ag,Cuz), we need to consider the mass percentages of each element in the alloy. Given that the alloy consists of 75% Au, 9.0% Ag, and 16% Cu, we can assume a 100g sample. This means we would have 75g of Au, 9g of Ag, and 16g of Cu.

Now, we can calculate the moles of each element by dividing the mass of each element by its molar mass. The molar mass of Au is 197 g/mol, Ag is 108 g/mol, and Cu is 63.5 g/mol.

By dividing the moles of each element by the smallest mole value obtained, we can determine the empirical formula of 18-karat gold. In this case, the subscripts to two significant digits are Au3-Ag1,Cuz1.

Answer 2

The empirical formula subscripts for 18-karat gold, which consists of 75% gold, 9% silver, and 16% copper by mass, are calculated to be Au4.6, Ag1, Cu3.0, rounded to two significant digits.

Step-by-step explanation:

The question asks for the empirical formula subscripts for 18-karat gold based on its constituent metal percentages by mass. To find the empirical formula, you should first determine the mole ratio of the metals based on their percentage composition.

Let's imagine we have 100 grams of 18-karat gold. This means we would have 75 grams of gold (Au), 9 grams of silver (Ag), and 16 grams of copper (Cu). Next, we find the moles of each metal using their atomic masses (Au: 196.97, Ag: 107.87, Cu: 63.55).

• Moles of Au = 75 g / 196.97 g/mol ≈ 0.381 mol
• Moles of Ag = 9 g / 107.87 g/mol ≈ 0.0834 mol
• Moles of Cu = 16 g / 63.55 g/mol ≈ 0.252 mol

To find the empirical formula subscripts, you divide each molar amount by the smallest number of moles which is 0.0834 moles of Ag:

• Au: 0.381 / 0.0834 ≈ 4.57
• Ag: 0.0834 / 0.0834 ≈ 1
• Cu: 0.252 / 0.0834 ≈ 3.02

After rounding to two significant digits, we get the empirical formula subscripts for 18-karat gold: Au4.6Ag1Cu3.0.