A street merchant is trying to sell you a 14 karat (24 karat is 100% pure) bracelet for $450. The gold is alloyed with copper. Before buying the item, you weigh it to be 110 grams and you also measure its water displacement as 7.59 mL. What is the % composition of the gold bracelet? The density of gold is 19.3 g/mL and the density of copper is 8.92 g/mL.
If 24 karat = 100% pure, then I calculated 14 karat to be 58.3% pure gold. (14 karat/24 karat = 0.583)
Total density of a 100% pure gold and copper bracelet:
19.3g/mL + 8.92g/mL = 28.22g/mL
Mass of gold in 100% pure gold bracelet:
(7.59mL)(28.22g/mL) = 214.1898g = 214g
Mass of gold in 14 karat bracelet:
(214g)(58.3%) = 124.9440499 = 125g
So there should be 125g of gold in a 14 karat bracelet.
...I don't know what to do next or of my work so far is even correct or relevant.
I think something is amiss. First, you can't add the densities. Thank about it, A density of >28 g/mL is more than U or those very heavy metals so that can't be right. You know the density of the alloy must be somewhere between 19.3 and 8.92 and 28 doesn't fit that bill. Next, your figure of 125 g can't be right; the problem says the mass is 110 g. I agree that the percent Au in a 14 k bracelet is correct at 58.3%.
I would do this.
Let X = mass Au
and Y = mass Cu.
equation 1 mass Au + mass Cu = 110 so
X + Y = 110
equation 2 is vol Au + vol Cu = 7.59 mL and volume = mass/density so
(X/19.3) + (Y/8.92) = 7.59
Solve those two equations simultaneously to find mass Au and mass Cu, then calculate percent composition.
The solution I posted above assumes that the volumes in alloys are additive and that may not be true (but I think that's the assumption made by the author of the problem). Sometimes alloys shrink, sometimes they expand, and sometimes they are additive.
Your calculations so far seem correct and relevant. To find the percentage composition of gold in the bracelet, you need to compare the mass of gold to the total mass of the bracelet.
The total mass of the bracelet is given as 110 grams, and you have calculated that the mass of gold in the bracelet is 125 grams.
To find the percentage composition of gold, you can use the formula:
% composition = (mass of gold / total mass) * 100
Plugging in the values:
% composition = (125g / 110g) * 100
% composition = 113.64%
Therefore, the % composition of gold in the bracelet is approximately 113.64%.
Your work so far is correct and relevant. You have determined that there should be 125 grams of gold in the bracelet.
To find the percentage composition of gold in the bracelet, you need to consider the total mass of the bracelet and calculate what proportion of that mass is made up of gold.
Total mass of the bracelet is 110 grams.
To find the percentage composition of gold in the bracelet, use the formula:
Percentage composition of gold = (mass of gold / total mass of bracelet) x 100
Plugging in the values:
Percentage composition of gold = (125g / 110g) x 100 = 113.63%
The percentage composition of gold in the bracelet is approximately 113.63%.
However, it seems like there might be an error in your calculation for the mass of gold in the 14 karat bracelet. Instead of multiplying by 58.3%, you should be multiplying by 0.583 (which is the decimal equivalent of 58.3%). So the correct calculation should be:
Mass of gold in 14 karat bracelet = (214g)(0.583) = 124.962 g ≈ 125g
Using the correct calculation, the percentage composition of gold in the 14 karat bracelet is:
Percentage composition of gold = (125g / 110g) x 100 = 113.64%
So the correct percentage composition of gold in the bracelet is approximately 113.64%.