Question

The molecular mass of ${{(N{{H}_{4}})}_{2}}C{{O}_{3}}$ is:
Given atomic mass of H =1, O =16, C = 12, N = 14.
(A) 96 gm/mole
(B) 98 gm/mole
(C) 94 gm/mole
(D) 80 gm/mole

Answer 1

Hint Atoms have their own specific atomic masses which are unique and empirical. Similarly, molecules have their molecular masses obtained from atomic masses of atoms comprising the same.

Complete step by step solution:
Firstly, let us know about the atomic and molecular masses in detail for better understanding.
Atomic mass- The atomic mass is simply the mass of an atom present in the modern periodic table. Its SI unit is kilograms.
Molecular mass- The molecular mass is the mass of a given molecule consisting of numerous atoms. Molecular mass or molar mass is used in stoichiometry calculations or vice versa is also true.
In actual practice, it is calculated by summing up the atomic weights of atoms making up the molecular formula of a substance.
Illustration-For calculation of molecular mass of any substance we should primarily know the atomic masses of atoms present in the substance.
If the atomic masses are unknown for the given problem then we should refer to the periodic table for specific atomic masses.
Given-
Atomic mass of hydrogen atom = 1 gm/mole
Atomic mass of oxygen atom = 16 gm/mole
Atomic mass of carbon atom = 12 gm/mole
Atomic mass of nitrogen atom = 14 gm/mole
Since your given compound is ${{(N{{H}_{4}})}_{2}}C{{O}_{3}}$ , you need to multiply the atomic weights by their respective subscripts.
Thus, atomic weight;
For hydrogen = (4$\times $2) $\times $ 1 gm/mole = 8 gm/mole
For oxygen = 3 $\times $ 16 gm/mole = 48 gm/mole
For carbon = 1 $\times $ 12 gm/mole = 12 gm/mole
For nitrogen = 2 $\times $ 14 gm/mole = 28 gm/mole
Now,
We would have to add all the weights to get the mass of the substance,
Molar / molecular mass of ${{(N{{H}_{4}})}_{2}}C{{O}_{3}}$ = (atomic weight of hydrogen) + (atomic weight of oxygen) + (atomic weight of carbon) + (atomic weight of nitrogen)
Hence,
Molecular mass = (8+48+12+28) gm/mole = 96 gm/mole

Therefore, option (A) 96 gm/mole is correct.

Note: Though the simplified definitions consist of SI units as kilogram still while calculating for masses we use mass of atom or molecule per mole i.e. gm/mole for easy and globally acceptable calculations.
Be specific while calculating the molecular masses as molecules and its subscripts are dignified by brackets.