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# 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"##