The karat scale used to describe gold alloys is based on
mass per...

Question

The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is 50 mol% silver and 50 mol% gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy.

Accepted Answer

Hello everyone today, we have the following problem. The composition of gold alloys is used to describe is described using the carrot scale based on the mass percentages, determine the carrot number of an alloy made of 47.7% mold gold and 52.3% silver, predict the color of the alloy using the figure below. So we want to assume that we're using one mole and so if we do that, we can say that we have for our moles of gold, we can say that we have 40 .477 moles and foreign molds of silver. We have 0.5-3 moles. And so next we have to find our masses of each one. So our massive gold is going to simply be found using our molds that we have and multiplying by our molar mass and per the periodic table, One mole of gold Is equal to 196.7 g of gold. And that's gonna give us 93.95 g of gold. Next we do that with our silver. So we take the most that we have .5- moles of silver. We multiply that by its molar mass. So we have one mole of silver Is equal to 107.67 g per the periodic table. And that gives us 56.31 g of silver to work with. We then must find the mass percentages for each one. And so we'll start with our gold. So the mass percentage is going to be equal to the number of grams that we found. Which was 93.95 g. We're gonna divide that by the total mass that we have. So we have 93.95 g from the gold. And we have 56.31 g from our silver. And so we multiply that by 100%. This gives us about 62.5%. And by default our mass percent of our silver has to be 100% minus r 62.5% giving us 37. Silver. So we have these two values to work with our 62.5% for gold and our 37.5% silver. So what we're gonna do is we're gonna take our chart here. We're gonna draw a line intersecting where these two meet. And so for our gold here, our au we have 62.5%. And so that's gonna be right about here, we're gonna straw line across. And then for our silver, would you have 37.5. And that's going to be roughly here. We're gonna draw a line there and that's gonna intersect right here in the pail, greenish yellow region. So that takes care of that to find our carrot. We simply take The amount by which we have the most of our 62.5%. And that's gonna be from our goal When we convert that to moles. We're going to do that. We're going to multiply that by our 24g that we have, And so we do that. We get 15 carat of gold. And with that we have answered the question, I hope this helped, and until next time.

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