Warm-up

Ch 1

Number 2, ex. 2: How far apart are water molecules? Assume the density and molecular weight of water, and Avogadro’s number to zero decimal places (1 g/cc, 18g/mol, 6 x 10^23).

Start with units

• D(ensity) = 1 g/cm^3
• N (molecules/mol) = 6.02 x 10^23 N/mol
• M (mol weight) of H20 = 18 g/mol

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Answer

(A trick is realizing that we are just asking for the linear dimension of a single molecule which is just cube root of volume - envision a 3 x 3 x 3 cube occupied by 27 molecules)

N / M = number per gram M / V = g per cubic cm N / V = number per cubic cm V / N = cubic cm / molecule

(V / N)^1/3 = linear dimension (one side) of a molecule

\[ \frac{N/\mathrm{mol}}{M/\mathrm{mol}}\cdot\frac{M}{V} = \frac{N}{V}\] \[\frac{V}{N} = \frac{L^3}{N} \implies \frac{L}{N^{1/3}}\]

n.over.v <- ((6.0 * 10^23)/18) * (1) 

(n.over.v)^(-1/3) #cm

## [1] 3.107233e-08

(n.over.v)^(-1/3) / 100 # m

## [1] 3.107233e-10

About 3 Angstroms