Question

How many atoms are in 153 g of calcium?

Answer 1

Hint: The answer to this question is based on the fact that one mole of any substance contains Avogadro's number of molecules and multiplying this value to the number of moles given gives the answer. Convert the given amount of calcium carbonate into a number of moles.

Complete step by step answer:
From the lower classes of general chemistry, we have studied the definitions of several basic concepts such as meaning for moles, molecules, atoms and also the Avogadro number or the Avogadro constant.
Now, we shall recall those terms and concepts so that we can obtain the required answer.
- One mole of a substance is nothing but the measure of the amount of a substance according to the International System of Units.
- One molecule is the group of atoms bonded together which represents the small fundamental unit of a chemical compound.
- An atom is the smallest particle of a chemical that can exist and which combines with the same or other atoms to constitute a molecule.
- Avogadro number is the constant that is the proportionality factor which relates the number of constituent particles in a sample with the amount of the substance in that sample.
- The S.I. unit for this constant value is given as $mo{{l}^{-1}}$ and is defined by the symbol ‘N’ or ${{N}^{0}}$.
Thus, according to his law, the Avogadro constant is the value which is given for one mole of substance and that is,
1 mole = $6.022\times {{10}^{23}}$ molecules.
Now, 1 mole of $CaC{{O}_{3}}$ contains $6.022\times {{10}^{23}}$ number of molecules.
Let us now find the number of atoms in 153 g of calcium.
Now, we have to convert the given mass of calcium to the number of moles of calcium with the help of its molar mass and according to the data given in the periodic table, the molar mass of $Ca$ is 40 $gmo{{l}^{-1}}$ and thus,
 153g $Ca\times \dfrac{1}{10.8}=3.82$ moles $Ca$ .
Therefore, the total number of atoms present in this compound will be,
3.82 mole $Ca\times \dfrac{6.022\times {{10}^{23}}atoms}{1}=2.3\times {{10}^{24}}$ atoms of $Ca$.
Therefore, the correct answer is 153 g of calcium has $2.3\times {{10}^{24}}$ number of atoms.

Note: It is important to note that the Avogadro number also relates the molar volume of a substance to that of the average volume which is nominally occupied by one of its particles when both are expressed in the same units of volume.