Question

What is the percentage composition of $N{{a}_{2}}{{S}_{2}}{{O}_{3}}.5{{H}_{2}}O$ ?

Answer 1

Percentage composition of a compound is defined as the ratio of each atom to the total amount of compound, multiplied by $100$ . The percentage composition can be calculated in terms of grams of the element.

Formula used: $P.C=\dfrac{A.M}{M.M}\times 100$
where, $P.C$ is the percentage composition, $A.M$ is the atomic of element and $M.M$ is the molar mass of the compound.

Complete step by step answer:
First we will write down the atomic mass of all the elements present in the given compound.
Then we will calculate the molar mass of the compound.
The final step would be to divide the atomic mass of the element by the total mass of compound and multiply by $100$
Here, the molecular given is $N{{a}_{2}}{{S}_{2}}{{O}_{3}}.5{{H}_{2}}O$
The atomic mass of sodium $(Na)$ is $23$
The atomic mass of sulphur $(S)$ is $32$
The atomic mass of oxygen $(O)$ is $16$
The atomic mass of hydrogen $(H)$ is $1$
The molar mass of this compound can be calculated as:
$23\times 2+32\times 2+16\times 3+5\times 2+16\times 5=248$
Now, we have to calculate the percentage composition for each element.
The percentage composition of sodium is:
$\%{Na}=\dfrac{A.M}{M.M}\times 100$
The atomic mass of two atoms of sodium is $46$
The molar mass of $N{{a}_{2}}{{S}_{2}}{{O}_{3}}.5{{H}_{2}}O$ is $248$
Now, substituting the values in the formula, we get,
$\%{Na}=\dfrac{46}{248}\times 100=18.54$
Percentage composition of sodium is $18.54$
The percentage composition of sulphur is:
$\%{S}=\dfrac{A.M}{M.M}\times 100$
The atomic mass of two atoms of sulphur is $64$
Now, substituting the values in the formula, we get,
$\%{Na}=\dfrac{64}{248}\times 100=25.8$
The percentage composition of oxygen is:
$\%{O}=\dfrac{A.M}{M.M}\times 100$
The atomic mass of eight atoms of oxygen is $128$
The molar mass of $N{{a}_{2}}{{S}_{2}}{{O}_{3}}.5{{H}_{2}}O$ is $248$
Now, substituting the values in the formula, we get,
$\%{O}=\dfrac{128}{248}\times 100=51.61$
The percentage composition of hydrogen is:
$\%{H}=\dfrac{A.M}{M.M}\times 100$
The atomic mass of 10 atoms of hydrogen is $10$
The molar mass of $N{{a}_{2}}{{S}_{2}}{{O}_{3}}.5{{H}_{2}}O$ is $248$
Now, substituting the values in the formula, we get,
$\%{O}=\dfrac{10}{248}\times 100=4.03$

Note: Percentage composition of any element in a compound gives us the percentage of that element present in the compound .
Molar mass is different from atomic mass as atomic mass is the mass of an atom, but the molar mass is the mass of the whole molecule combining all atoms.
Molar mass is calculated by adding up the atomic masses of all elements, bonded to form a molecule, each multiplied by the number of atoms of that element in the molecule.