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Chapter 2

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}

Step-by-Step

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.