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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