Pure gold is usually too soft for jewelry, so it is often alloyed...

Question

Pure gold is usually too soft for jewelry, so it is often alloyed
with other metals. How many gold atoms are in an 0.255-
ounce, 18 K gold bracelet? (18 K gold is 75% gold by mass.)

Accepted Answer

welcome back everyone in this example, we're told that gold is a Lloyd with medals for use in jewelry. And to calculate the number of gold atoms in a 0.300 ounce. 12 cold or 12 carats. Sorry, gold bracelet were given the percent of gold by mass. Where we have the conversion factor where 12 carats is equal to 50% of our gold. And so what this means is that we can interpret our massive gold as 50 g since it's gold by mass. So this is 50 g of gold. So what we should begin with is our first unit given in the prompt. And that is the 500.300 ounces given in the prompt. So we are going to start with that volume. We have 0.300 ounces Of our 12 Karat Gold Bracelet. And we want to go ahead and cancel this unit ounces out because our final unit should be atoms. So this is our final unit. And so because we are beginning with ounces, we want to recall the conversion factor to go from ounces to grams. And so we should recall from our textbooks or online that one ounce which we will place in the denominator. So we can cancel it out is equivalent to 28. g. And so this allows us to cancel out ounces. And now we're left with units of grams. But luckily from the prompt that gave us our percent of gold by mass. And we're told that 12 carats is equivalent to 50 g of our gold. And so this means we can multiply by this conversion factor. Where we should recall that because we have a percent of gold by mass. This is out of 100%. And so we can interpret this as out of 100 g of gold, which according to the prompts are 12 carats of gold is just 50 g of gold. And so now we're able to cancel out our units of grams. And now we can focus on going from grams to our final unit atoms. And so we have to cancel out this gram unit. So we're going to recall from the periodic table our molar mass of gold. And when we look to our periodic table, we see it's a value of 196.97 g of gold. And so we're going to place that in the denominator. So we have 1 96.97 g of gold. And this is obviously equivalent to one mole of gold because this is a molar mass value. So there should be grams per mole. So one mole of gold is in our numerator. And now we're able to cancel our units of grams of gold. Now we're at moles of gold. And so we want to focus on going into atoms and we should recall that for that unit atoms. We're going to use avocados number which will give us our quantity in atoms. And so we should recall that according to avocados number we have for one mole of gold. we want that in the denominator. So it can cancel out that is equivalent to 6.22 times 10 to the 23rd power gold atoms avocados number. And so now we can cancel out moles of gold and we're left with our final units being gold atoms. And so when we plug this quotient into our calculators, we're going to get a final value of 1. times 10 to the 22nd power gold atoms. And because we have our final unit in atoms, this does give us our actual number of gold atoms. And so this would be our final answer to complete this example. So what's highlighted in yellow is our final answer. This corresponds to choice D and our multiple choice. So I hope that everything that I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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