The karat scale used to describe gold alloys is based on mass percentages. (b) If an alloy is formed that is 50 mol% copper and 50 mol% gold, what is the karat number of the alloy? What is the color of this alloy?

Video transcript

Hello everyone today. We have the following problem. The composition of gold alloys is described using the carrot scale based on mass percentages determined a carrot number of an aloe alloy made of 24.4% gold and 75.6% copper predict the color of the aloe using the figure below. So the first thing that you want to do is we want to assume that we are using a total of one mole. And in doing so we can turn our moles are percentages in two regular moles or moles of gold. We're gonna take that 24.4 and turn that to a percentage by doing .244 moles. I'm gonna do the same thing with our copper at 75.6 is going to be 0.756 moles of copper. So second, we're gonna want to go ahead and find the mass of each of these properties. And so for the mass of our gold, we're simply going to take the Molds that we have 0. balls of gold. We're gonna multiply that by the molar mass, we're gonna put the molds of gold at the bottom. We're gonna put our moles of our Gold according to the table on the numerator, which will be about 196.7 grams. That's gonna give us 48.06 g of gold. And we'll do the same for copper. We're gonna take our 0.756 moles of copper. We're gonna multiply that by the molar mass per the periodic table. So that one mole of copper is gonna equal 63. g of copper. Giving us 48.4 g of copper. Next we have to find the mass percentages of each one. And so the mass percent of our gold is going to start off with our amount of grams of gold that we have Divided by the total mass that we have. So we have 48.6 from the gold and we have 48.04 from the copper. And in doing so, we get just about 50%. And so by default, our percent mass of copper must also be about 50%. We're going to find out where 50% intersects with our 50% of gold and copper on this chart. So we're gonna start from this corner here, we're gonna draw a line to the 50% for the for the gold. And we'll do the same for the copper Covers down here will take 50% and we'll go across like that and we see that they intersect at the yellowish portion. And so our color here, it's going to be yellowish to find the carrot. We simply have to take our 50% or . And multiply it by how many moles of gold that we have, which is 20 for giving us 12 carats. And so this is going to be the final answer to our problem. Overall, I hope this helped, and until next time.