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Question

Gold, which has a density of $$19.32\ g/cm^3$$, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber.
If a sample of gold, with a mass of $$27.60\ g$$, is pressed into a leaf of $$1.000\ \mu m$$ thickness, what is the area of the leaf?


Solution

The density of gold is
$$\rho =\dfrac {m}{V}=\dfrac {19.32\ g}{1\ cm^3}=19.32\ g/cm^3$$
We take the volume of the leaf to be its area $$A$$ multiplied by its thickness $$z$$. With density $$\rho =19.32\ g/cm^3$$ and mass $$m=27.63\ g$$, the volume of the leaf is found to be 
$$V=\dfrac {m}{\rho}=1.430\ cm^3$$.
We convert the volume to $$SI$$ units:
$$V=(1.430\ cm^3)\left(\dfrac {1\ m}{100\ cm}\right)^3=1.430\times 10^{-6}m^3$$
Since $$V=Az$$ with $$z=1\times 10^{-6}m$$ (metric prefixes can be found in Table $$1-2$$), we obtained

$$A=\dfrac {1.430\times 10^{-6}m^3}{1\times 10^{-6} m}=1.430\ m^2$$

Chemistry

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