# Dimensional Analysis?

If a bucket has a volume of 8.00 qt. and is full of gold whose density is 19.3 g/cm³, how many moles of gold are in the bucket?

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• Anonymous
5 months ago

Well.. it's pretty easy if you know how to do dimensional analysis.

First convert the 8.00qt to cm^3 (since both are units of volume)

1 quart is 946.353 cm^3

Then multiply that by 19.3 g/cm^3 to get just grams (since the cm^3 from both cancel)

Then use 196.96657g/mol from the periodic table as the mass of gold to convert it to moles of gold

[grams from above calculations] x (1 mol / 196.96657g)

I don't have a calculator on hand, so just plug the numbers

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• A better question is could you carry the bucket of gold?

(8.00 qt) x (946.353 cm³ / 1 qt) x (19.3 g Au / 1 cm³) x (1 kg / 1000g) = 146 kg .... or .... 321 pounds.

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• (8.00 qt) x (946.353 cm³/qt) x (19.3 g Au/cm³) / (196.97 g Au/mol) = 741.82 mol = 742 mol Au

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• 8 US quart = 7568 cm³

7568 cm³ x 19.3 g/cm³ = 146062 g

Au is 197 g/mol

146062 g / 197 g/mol = 741 mol

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