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.