Chemistry

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.

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asked by Kid
  1. 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.

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  2. 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.

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    posted by VLbyday

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