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## Q. 2.3

Consider arsenic (As), a favorite poison used in crime stories. This element is discussed at the end of Chapter 1. Taking Avogadro’s number to be 6.022 × $10^{23}$, calculate

ⓐ the mass of an arsenic atom.

ⓑ the number of atoms in a ten-gram sample of arsenic.

ⓒ the number of protons in 0.1500 lb of arsenic.

 ANALAYSIS Avogadro’s number (6.022 × $10^{23}$) Information given: atomic mass Information implied: mass of an arsenic atom Asked for:

STRATEGY

Change atoms to grams (atoms → g) by using the conversion factor

$\frac{6.022 × 10^{23} atoms}{atomic mass}$

 ANALAYSIS mass of sample (10.00 g) from (a) mass of one As atom (1.244 × $10^{-22}$) g/atom) Information given: number of atoms in a 10-gram sample Asked for:

STRATEGY

Change grams to atoms (g → atom) by using the conversion factor

$\frac{1 atom}{1.244 × 10^{-22} g}$

 ANALAYSIS mass of sample (0.1500 lbs) from (a) mass of one As atom (1.244 × $10^{-22}$ g/atom) Information given: atomic number pounds to grams conversion factor Information implied: number of protons in 0.1500 lb As Asked for:

STRATEGY

Change pounds to grams, grams to atoms, and atoms to protons by using the conversion factors

$\frac{453.6 g}{1 lb}$                   $\frac{no. of protons (Z) }{1 atom}$            $\frac{1 atom}{1.244 × 10^{-22}g}$

## Verified Solution

 1 atom As × $\frac{74.92 g As}{6.022 × 10^{23} atoms As}$ = 1.244 ×  $10^{-22}$ g mass of an As atom

 10.00 g As × $\frac{1 atom}{1.244 × 10^{-22} g As}$ = 8.038 × $10^{22}$ atoms As atoms of As

 0.1500 lb × $\frac{453.6 g}{1 lb}$ × $\frac{1 atom}{1.244 × 10^{22}}$g × $\frac{33 protons}{1 atom As}$ = 1.805 × $10^{25}$ protons number of protons

END POINT

Because atoms are so tiny, we expect their mass to be very small: 1.244 × $10^{-22}$ g sounds reasonable. Conversely, it takes
a lot of atoms, in this case, 8.038 × $10^{22}$ atoms, to weigh ten grams.