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QUESTION

# A titanium cube contains 2.6*10^23 atoms. The density of titanium is 4.50 g/cm^3. What is the edge length of the cube?

The answer is 1.66 "cm"

So, start with the fact that you have 2.6 * 10^23 atoms of TI, which will allow you to determine how many you actually have

2.6 * 10^23 "atoms" * ("1 mole Ti")/("6.022" * 10^23 "atoms") = 0.43 "moles"

From here, use "Ti"'s molar mass to find out how many grams you have.

"0.43 moles" * ("47.9 grams")/("1 mole Ti") = "20.6 grams"

Use the given to determine the volume you have

rho = m/V => V = m/(rho) = ("20.6 g")/("4.50 g/cm"^3) = "4.58 cm"^3

Since you're dealing with a cube, which has a volume of V_("cube") = "edge"^3, your edge length will be

"edge" = V^(1/3) = "1.66 cm"