Chemistry question: dimensional analysis?

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kristennnnn

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how do i solve this problem?:
The density of pure silver is 10.5 g/cm^3 at 20 degrees celsius. if 5.25 g of pure silver pellets is added to a graduated cylinder containing 11.2 mL of water, to what volume level will the water in the cylinder rise?
show all work please and thank you :]
 
Well, you need to find out just what volume 5.25 g of pure silver has. Once you find that, you already know that whatever that volume is, it'll displace the water by the exact amount, so you can add the volume of the silver to the volume of the water to find the final volume.

10.5 g/cm^3 allows you to find the volume of any amount of pure silver at 20 C.

Dimensional analysis is the check you do to make sure you ended up with the right type of units. In this case, you want to end up with volume.

10.5 g per 1cm^3 is the same thing as 1 cm^3 per 10.5 g, so you can flip 10.5 g/ cm^3 to become 1 cm^3/10.5g. Then just multiply by your weight of silver:

5.25g x 1 cm^3/ 10.5g = .5 cm^3 see how grams canceled out grams and left cm^3?

For water, 1 cm^3 = 1 mL.

Then just add .5 to 11.2 mL of water to get 11.7 mL of water as a final volume.
 
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