following is a crude but effective method for estimating the order for magnitude of Avogadro's number by using stearic acid ( C18 H36 O2 ). When stearic acid is added to water, its molecules collect at the surface and form a monolayer. The cross-sectional area of each stearic acid molecule has been measured to be 0.21 nm^2. In one experiment it is found that 1.4 × 10^-4g of stearic acid is needed to form a monolayer over water in a dish of diameter 20cm. Based on these measurements, derive value of Avogadro's number.(molar mass of stearic acid is 284g per mol).
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Answer:
The area of the dish of 20cm diameter (10cm=0.1m radius) has area =πr
2
=π×0.01m
2
0.21×10
−18
m
2
is the area of 1 molecule
∴π×0.01m
2
is the area of
0.21×10
−18
π×0.01
molecules
1.4×10
−4
g stearic acid=
284
1.4×10
−4
mol
=
284
1.4×10
−4
N
o
molecules
=
284
1.4×10
−4
N
o
=
0.21×10
−18
π×0.01
N
o
=3.30×10
23
1 amu is
N
o
1
=
3.03×10
23
1
=3.33×10
−24
g.
Explanation:
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