Sterling silver is a mixture of silver and copper having a mole ration of silver to copper equal to 7.8 what is the mass percent composition of this mixture?

Ok I know the answer to this and I know how its done: 1 mol Cu weighs 63.5 g
7.8 mol Ag weigh 7.8(107.87)= 841g what i don't understand is why is the 7.8 multiplied with grams of Ag and not Cu?

mol ratio Ag/Cu = 7.8 which means

Ag = 7.8*Cu which means
that the Ag is whatever the Cu is times 7.8 (Ag is the larger component). OR, said another way,
7.8 mols Ag to 1 mol Cu; then
7.8(107.87)g Ag to 63.546 g Cu.
I get %Ag = almost 93% and Cu slightly more than 7%
I think Sterling silver is supposed to be 92.5% Ag to 7.5% Cu.

To determine the mass percent composition of the mixture, we need to calculate the mass of both silver (Ag) and copper (Cu) in the mixture.

You correctly determined that the mole ratio of silver to copper is 7.8. This means that for every 7.8 moles of silver, there is 1 mole of copper.

To calculate the mass of silver in the mixture, we need to use its molar mass, which is 107.87 g/mol. Since we know that 7.8 moles of silver are present, we can multiply this by the molar mass to get the mass of silver:

Mass of silver = 7.8 mol Ag × 107.87 g/mol = 841 g

Now, to calculate the mass of copper in the mixture, we use the molar mass of copper, which is 63.5 g/mol. Since we have a 1:7.8 ratio, we can multiply the mass of silver by this ratio to obtain the mass of copper:

Mass of copper = 841 g Ag × (1 mol Cu/7.8 mol Ag) × 63.5 g/mol = 841 g

From the calculations, we can see that the mass of silver and copper in the mixture is the same, which is 841 g.

The reason we multiplied the mole ratio (7.8) by the grams of silver and not copper is because we wanted to find the mass of silver in the mixture, as stated in the question. We then used this mass to find the mass of copper, based on the mole ratio of 1:7.8. Both masses are equal, indicating that the percentage composition of silver and copper in the mixture is 50% each.

So, the mass percent composition of sterling silver in this mixture is 50% silver and 50% copper.