Question

How many atoms of calcium are in $1.00$ gram? How many atoms of iron are in $1.00$ gram? How many atoms of carbon are in $1.00$ gram?

Answer 1

Hint: One mole of every substance contains $6.022 \times {10^{23}}$ atoms/molecules/ions. Mole is a unit which is used to express the amount of substance according to the International System of Units.

Complete step by step answer:
We need to find out the number of atoms present in $1.00$ gram of calcium, iron and carbon separately.
We know that one mole of calcium contains $6.022 \times {10^{23}}$ atoms. The weight of one mole of every element is equal to its atomic mass. Atomic mass of calcium is $40.1$ g. Hence,
Weight of one mole of calcium $ = 40.1$ g
In other words, we can write,
Weight of $6.022 \times {10^{23}}$ atoms of calcium $ = 40.1$ g
Or, Number of atoms in $40.1$ g of calcium $ = 6.022 \times {10^{23}}$
Hence, number of atoms in $1.00$ g of calcium $ = \dfrac{{6.022 \times {{10}^{23}}}}{{40.1}} = 1.5 \times {10^{22}}$
Thus $1.00$ g of calcium contains $1.5 \times {10^{22}}$ atoms of calcium.
Similarly we can do it for iron and carbon.
Atomic mass of iron is $55.8$ g.
Hence, weight of one mole of iron $ = 55.8$ g
In other words, we can write,
Number of atoms in $55.8$ g of iron $ = 6.022 \times {10^{23}}$
Hence, number of atoms in $1.00$ g of iron $ = \dfrac{{6.022 \times {{10}^{23}}}}{{55.8}} = 1.08 \times {10^{22}}$
Thus $1.00$ g of iron contains $1.08 \times {10^{22}}$ atoms of iron.
Also,
Atomic mass of carbon is $12$ g.
Hence, weight of one mole of carbon $ = 12$ g
In other words, we can write,
Number of atoms in $12$ g of carbon $ = 6.022 \times {10^{23}}$
Hence, number of atoms in $1.00$ g of carbon $ = \dfrac{{6.022 \times {{10}^{23}}}}{{12}} = 5.02 \times {10^{22}}$
Thus $1.00$ g of carbon contains $5.02 \times {10^{22}}$ atoms of carbon.

Note:
The volume occupied by one mole of every substance at STP is $22.4$ litres.
Mass of one atom of an element is defined as its atomic mass. Atomic mass expressed in grams gives mass of one mole of the element. For molecules, instead of atomic mass we use molecular mass.