Question

How many moles are present in $5.3{{ g}}$ of anhydrous sodium carbonate?
A.$0.03$
B.$0.04$
C. $0.05$
D.$0.01$

Answer 1

Sodium carbonate is an inorganic compound having the molecular formula ${{N}}{{{a}}_2}{{C}}{{{O}}_3}$ . It normally exists in the form of hydrates but heating of hydrated sodium carbonate leads to the removal of water molecules and formation of anhydrous sodium carbonate, also known as calcined soda.

Complete answer:
According to the International System of Units, mole is the unit of measurement of a substance. One mole of any substance contains $6.022 \times {10^{23}}$ atoms, molecules, ions or electrons of that substance.
Molar mass of any substance is the mass of one mole of that substance in grams. The number of moles in that substance is the amount that substance. The molar mass of a substance depends on the molecular formula of that substance along with the distribution of each of the isotopes of that element present in the substance. The unit of molar mass is ${{g mo}}{{{l}}^{ - 1}}$ .
In order to calculate the number of moles of a substance, we have to divide the mass of that substance in grams by the molar mass of that substance.
In this question, we are given the mass and name of the chemical compound. As the compound for which we have to calculate the number moles is anhydrous sodium carbonate ${{N}}{{{a}}_2}{{C}}{{{O}}_3}$ , we can calculate the molar mass by knowing the atomic masses of the constituent elements in it.
Atomic mass of ${{Na}}$ $=$ 23 ${{u}}$
Atomic mass of ${{C}}$ $=$ $12$ ${{u}}$
Atomic mass of ${{O}}$ $=$ $16$ ${{u}}$
$\therefore$ Molar mass of ${{N}}{{{a}}_2}{{C}}{{{O}}_3}$ $=$ $\left( {23 \times 2} \right) + 12 + \left( {16 \times 3} \right)$
$\Rightarrow$ $$ $46 + 12 + 48$
$\Rightarrow$ $$ $106$ ${{g mo}}{{{l}}^{ - 1}}$
To calculate the number of moles we use the formula, ${{n = }}\dfrac{m}{M}$ ,
where, ${{n}}$ is the number of moles
${{m}}$ is the mass of the compound
${{M}}$ is the molar mass of the compound

So, we can calculate the number of moles of ${{N}}{{{a}}_2}{{C}}{{{O}}_3}$ , by substituting the values of mass and molar mass in the formula.
$\Rightarrow$ ${{m}}$ $=$ $5.3{{ g}}$
$\Rightarrow$ ${{M}}$ $=$ $106$ ${{g mo}}{{{l}}^{ - 1}}$
$\Rightarrow$ ${{n = }}\dfrac{{5.3{{ g}}}}{{106{{ g mo}}{{{l}}^{ - 1}}}}$
$\Rightarrow$ ${{n = 0}}{{.05 moles}}$

Hence, option (C) is the correct answer.

Note:
Sodium carbonate is a white coloured water-soluble salt which has an alkaline nature when dissolved in water. It is a very useful drying agent used in chemistry laboratories to absorb any moisture content from organic compounds because of its ability to form a wide range of hydrates of its own.