Question

Find the total number of pennies in a tenth of a mole of pennies.
A.$6.02 \times {10^{23}}$ pennies
B.10 pennies
C.$6.02 \times {10^{22}}$ pennies
D.$0.1$ pennies
E.1 penny

Answer 1

Hint: According to the mole concept, a mole represents Avogadro’s number of particles irrespective of their nature. Thus, one mole of any species is equal to Avogadro’s number of that species. Thus, the quantity of matter containing Avogadro’s number of particles represents one mole of that species.

Complete step by step answer:
A mole is the larger unit which is used for comparing the amounts of different substances. This term ‘mole’ must be followed by the words atoms, molecules, ions, protons, electrons etc., in order to represent the nature of the particles which are under consideration.
There are some important generalizations of the mole concept. According to one generalization, one mole can be defined as the number of particles (atoms or molecules or electrons or ions) which are equal to the number of atoms present in $0.012$ kg of C – 12 isotope.
Hence, mole is defined as 1 gm molecule $ = 6.02 \times {10^{23}}$ molecules. The number $6.02 \times {10^{23}}$ is known as the Avogadro number and is denoted by the letter N.
According to another generalization, one mole of atoms, ions, electrons, protons and molecules is equal to $6.02 \times {10^{23}}$ atoms, ions, electrons, protons and molecules respectively.
Hence, one mole of pennies will contain $6.02 \times {10^{23}}$ number of pennies.
Therefore, a tenth of a mole of pennies will contain $\dfrac{1}{{10}} \times 6.02 \times {10^{23}} = 6.02 \times {10^{22}}$ number of pennies.

So, the correct option is C.

Note:
The mole is also related to the weight of the substance. Weight of one mole of atoms of any element in grams is equal to its gram atomic weight or one gram atom. Similarly, the weight of one mole of molecules of a substance is equal to its gram molecular weight or one gram molecule.
Since 1 gm molecule $ = 6.02 \times {10^{23}}$ molecules, thus,
1 gm molecule
$
   = {\text{Atomicity}} \times 6.02 \times {10^{23}}{\text{atoms}} \\
  {\text{ = Atomicity}} \times 1{\text{gmatom}} \\
 $
 For ionic compounds, 1 gm molecule $ = 6.02 \times {10^{23}}$ formula units.