Question

How many atoms are in 75 grams of calcium?

Answer 1

Hint: The answer here is based on the calculation of total number of molecules present which takes into account of the Avogadro number of molecules and the value of Avogadro constant is$6.023\times {{10}^{23}}$

Complete step by step solution:
In the classes of general chemistry, we have come across the very basic concept which deals with the calculation of number of molecules present in the compound and also about the Avogadro constant.
Let us now calculate the total number of atoms present in 75 grams of calcium.
- According to Avogadro's hypothesis, one mole of any substance contains$6.023\times {{10}^{23}}$in it.
- The atomic number of calcium is 20 and mass number is 40.08g/mol. Calcium exists as monatomic metal and now let us convert this into a number of moles of calcium.
- The calculation is as follows, $75g\times \dfrac{1}{40.08g/mol}=1.87mol$
Now, let us multiply this value with the Avogadro number of molecules and that will give us, $1.87mol\times 6.022\times {{10}^{23}}=1.13\times {{10}^{24}}$ atoms $Ca$
Hence, we can conclude that there are a total of $1.13\times {{10}^{24}}$atoms in 75 grams of calcium atoms.

Additional information:
- Unit of this Avogadro number is defined as the number of particles present per mole of a substance and therefore the unit is written as$mo{{l}^{-1}}$and thus this Avogadro number can be written as$6.022\times {{10}^{23}}mo{{l}^{-1}}$
- It is the unit that may constitute electrons, atoms, ions or molecules which is dependent upon the nature of the substance and also the character of the reaction.

Note:
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.