Question

How do you calculate the molar mass of each of the following compounds?
\[Cu{\left( {OH} \right)_2}\] , \[MgO\] , \[Mg{\left( {N{O_3}} \right)_2}\] , \[NaCl\] , \[{\left( {N{H_4}} \right)_2}S{O_4}\] , \[{H_2}S{O_4}\] , \[C{a_3}{\left( {P{O_4}} \right)_2}\] , \[N{H_4}N{O_3}\]

Answer 1

Hint: The molar mass of a compound is referred as the molecular weight of the compound. We use the term molar when we consider one mole of a compound.

Complete step by step answer:
The molar mass of a compound is defined as the mass of the compound which is equal to the amount of the compound present in one mole of it. It is numerically equal to the summation of the atomic weights of each of the elements present in the compound.
To calculate the molecular weights of the given compounds we need the standard atomic weights of each element. The molar mass is expressed in units of \[g/mol\] . The molar mass of a compound \[{A_x}{B_y}\] is
$ = x \times atomic{\text{ }}mass{\text{ }}of{\text{ }}A + y \times atomic{\text{ }}mass{\text{ }}of{\text{ }}B$
From the periodic table, the atomic mass of every element is used for the calculation.
The molar mass of the given compounds are calculated as:
\[Cu{\left( {OH} \right)_2}\]is composed of one copper atom, two oxygen atoms, and two hydrogen atoms.
Atomic mass of \[Cu = 63.546u\]
Atomic mass of \[O = 15.9994u\]
Atomic mass of \[H = 1.00797u\]
\[Cu{\left( {OH} \right)_2}\]: Atomic mass of \[Cu\] + \[2{\text{ }} \times \] atomic mass of \[O\] + \[2{\text{ }} \times \] atomic mass of \[H\]
\[ = 63.546 + 2 \times 15.9994 + 2 \times 1.00797\]
$ = 63.645 + 31.9988 + 2.01594 = 97.56g/mol.$
\[MgO\] is composed of one magnesium atom and one oxygen atom.
Atomic mass of \[Mg = 24.305u\]
Atomic mass of \[O = 15.9994u\]
\[MgO\]: Atomic mass of \[Mg\] + atomic mass of \[O\]
$ = 24.305 + 15.9994 = 40.30g/mol$ .
\[Mg{\left( {N{O_3}} \right)_2}\]is composed of one magnesium atom, two nitrogen atoms, and six oxygen atoms.
Atomic mass of \[Mg = 24.305u\]
Atomic mass of \[N = 14.0067u\]
Atomic mass of \[O = 15.9994u\]
\[Mg{\left( {N{O_3}} \right)_2}\]: Atomic mass of \[Mg\] + \[2{\text{ }} \times \] atomic mass of \[N\] + \[6{\text{ }} \times \] atomic mass of \[O\]
$ = 24.305 + 2 \times 14.0067 + 6 \times 15.9994$
$ = 24.305 + 28.0134 + 95.9964 = 148.31g/mol$ .
\[NaCl\] is composed of one sodium atom and one chlorine atom.
Atomic mass of \[Na = 22.9898\]
Atomic mass of \[Cl = 35.453u\]
\[NaCl\]: Atomic mass of \[Na\] + atomic mass of \[Cl\]
$ = 22.9898 + 35.453 = 58.44g/mol$ .
\[{\left( {N{H_4}} \right)_2}S{O_4}\]is composed of two nitrogen atoms, eight hydrogen atoms, one sulfur atom, and four oxygen atoms.
Atomic mass of \[N = 14.0067u\]
Atomic mass of \[H = 1.00797u\]
Atomic mass of \[S = 32.06u\]
Atomic mass of \[O = 15.9994u\]
\[{\left( {N{H_4}} \right)_2}S{O_4}\]: \[2{\text{ }} \times \] Atomic mass of \[N\] + \[8{\text{ }} \times \] atomic mass of \[H\] + atomic mass of \[S\] + \[4{\text{ }} \times \] atomic mass of \[O\]
$ = 2 \times 14.0067 + 8 \times 1.00797 + 32.06 + 4 \times 15.9994$
$ = 28.0134 + 8.06376 + 32.06 + 63.9976 = 132.13g/mol$ .
\[{H_2}S{O_4}\]is composed of two hydrogen atoms, one sulfur atom, and four oxygen atoms.
Atomic mass of \[H = 1.00797u\]
Atomic mass of \[S = 32.06u\]
Atomic mass of \[O = 15.9994u\]
\[{H_2}S{O_4}\]: \[2{\text{ }} \times \] Atomic mass of \[H\] + atomic mass of \[S\] + \[4{\text{ }} \times \] atomic mass of \[O\]
$ = 2 \times 1.00797 + 32.06 + 4 \times 15.9994$
$ = 2.01594 + 32.06 + 63.9976 = 98.07g/mol$ .
\[C{a_3}{\left( {P{O_4}} \right)_2}\]is composed of three calcium atoms, two phosphorus atoms, and eight oxygen atoms.
Atomic mass of \[Ca = 40.08u\]
Atomic mass of \[P = 30.9738\]
Atomic mass of \[O = 15.9994u\]
\[C{a_3}{\left( {P{O_4}} \right)_2}\]: \[3{\text{ }} \times \] Atomic mass of \[Ca\] + \[2{\text{ }} \times \]atomic mass of \[P\] + \[8{\text{ }} \times \] atomic mass of \[O\]
\[ = 3 \times 40.08 + 2 \times 30.9738 + 8 \times 15.9994\]
$ = 120.24 + 61.9476 + 127.9952 = 310.18g/mol$ .
\[N{H_4}N{O_3}\]is composed of two nitrogen atoms, four hydrogen atoms, and three oxygen atoms.
Atomic mass of \[N = 14.0067u\]
Atomic mass of \[H = 1.00797u\]
Atomic mass of \[O = 15.9994u\]
\[N{H_4}N{O_3}\]: \[2{\text{ }} \times \] Atomic mass of \[N\] + \[4{\text{ }} \times \] atomic mass of \[H\] + \[3{\text{ }} \times \] atomic mass of \[O\]
$ = 2 \times 14.0067 + 4 \times 1.00797 + 3 \times 15.9994$
$ = 28.0134 + 4.03188 + 47.9982 = 80.04g/mol$ .

Note: The molar masses of isotopes vary due to change in the number of neutrons present inside the nucleus. A mole of a substance is defined as the ratio of amount of the substance taken and the molar mass or molecular weight of the substance.