Question

: What is the molar mass of sodium carbonate decahydrate : $ N{a_2}C{O_3} \cdot 10{H_2}O $ .

Answer 1

Hint: In this question we have to calculate the molar mass of sodium carbonate decahydrate. So for calculating the molar mass we will multiply the number of atoms with their respective atomic mass and then we add all of them to get the required value. First of all we will understand the definition of molar mass and then we will solve this question.

Complete answer:
As we know that molar mass is the total mass of all the atoms contained by a compound in grams that makes a mole of that particular compound. We know the molecular formula of sodium carbonate which is $ N{a_2}C{O_3} $ .
For calculating the molar mass we should know the atomic mass of atoms that are forming the compound.
Here in this question we have sodium carbonate decahydrate i.e.
 $ N{a_2}C{O_3} \cdot 10{H_2}O $
We can see that sodium contains two atoms of Sodium, one atom of Carbon, three atoms of oxygen.
So the molar mass of these atoms are:
Molar mass of Sodium is
 $ Na = 23gmo{l^{ - 1}} $
Molar mass of Carbon is
 $ C = 12gmo{l^{ - 1}} $
And the molar mass of Oxygen is
 $ O = 16gmo{l^{ - 1}} $ .
We know that the atomic mass of water is
  $ {H_2}O = 18.02 $
We will calculate the formula unit mass or molar mass separately, for easier calculation.
So the molar mass of $ N{a_2}C{O_3} $ is
 $ 2 \times $ atomic mass of $ Na $ $ + $ $ 1 \times $ atomic mass of $ C $ $ + $ $ 3 \times $ atomic mass of $ O $
By substituting the values, we have:
 $ = 2 \times 23 + 1 \times 12 + 3 \times 16 $
It gives us
 $ = 106u $
Now we will calculate the molar mass of $ 10{H_2}O $ is
 $ 10 \times $ atomic mass of $ {H_2}O $
By substituting the values, we have:
 $ = 10 \times 18.02 $
It gives us
  $ = 180.02u $
We will now add both of them together:
 $ 106 + 180.02 = 286.02u $
Hence the required answer is $ 286u $ .

Note:
We should always remember the molecular formula and molar mass of elements in advance so that it can make our solutions easier. The molecular formula of sodium carbonate heptahydrate is
 $ N{a_2}C{O_3} \cdot 7{H_2}O $ .
 Similarly the molecular formula of sodium carbonate monohydrate is represented by
 $ N{a_2}C{O_3} \cdot {H_2}O $ . It is also known as crustal carbonate.