Question

How many moles are present in $198.34\,g$ of $F{e_3}{\left( {P{O_4}} \right)_2}\,?$
(i) $0.455\,mol$
(ii) $0.555\,mol$
(iii) $0.655\,mol$
(iv) $0.755\,mol$

Answer 1

First multiply the atomic weight of the individual atoms with the number of individual atoms present in the molecule. Add them up to obtain the molecular weight of the given molecule. Then use the equation, number of moles present in a molecule $= \,\dfrac{{Given\,Weight}}{{Molecular\,Weight}}$ to calculate the number of moles present in the molecule.

Complete step by step solution:
In the given molecule $F{e_3}{\left( {P{O_4}} \right)_2}$, the individual atoms are $Fe,\,P$ and $O$.
Atomic weight of $Fe\,\, = \,\,55.845\,g\,mo{l^{ - 1}}$
Number of $Fe$ atoms present in the molecule $F{e_3}{\left( {P{O_4}} \right)_2}\,\, = \,\,3$
Atomic weight of $P\,\, = \,\,30.974\,g\,mo{l^{ - 1}}$
Number of $P$ atoms present in the molecule $F{e_3}{\left( {P{O_4}} \right)_2}\,\, = \,\,2$
Atomic weight of $O\,\, = \,\,15.999\,g\,mo{l^{ - 1}}$
Number of $O$ atoms present in the molecule $F{e_3}{\left( {P{O_4}} \right)_2}\,\, = \,\,8$
Therefore, the molecular weight of $F{e_3}{\left( {P{O_4}} \right)_2}$
$= \,($Atomic weight of $Fe\, \times$Number of $Fe$ atoms present in the molecule$)\, + \,($ Atomic weight of $P\, \times$Number of $P$ atoms present in the molecule$)\, + \,($ Atomic weight of $O\, \times$Number of $O$ atoms present in the molecule$)$
= \,\left\\{ {\left( {55.845 \times 3} \right) + \left( {30.974 \times 2} \right) + \left( {15.999 \times 8} \right)} \right\\}\,g\,mo{l^{ - 1}}
$= \,\left( {167.535 + 61.948 + 127.992} \right)\,g\,mo{l^{ - 1}}$
$= \,357.475\,g\,mo{l^{ - 1}}$
Now, we know Number moles present in a molecule$= \,\dfrac{{Given\,Weight}}{{Molecular\,Weight}}.........\left( 1 \right)$.
In this case the given weight $= \,198.34\,g$
Therefore using equation $\left( 1 \right)$ we get
Number moles present in $F{e_3}{\left( {P{O_4}} \right)_2}$ $= \,\dfrac{{198.34\,g}}{{357.475\,g\,mo{l^{ - 1}}}}\,\, = \,\,0.555\,mol$.
Hence the correct answer is (ii) $0.555\,mol$.

Additional Information: Mole is the unit of measurement for the amount of substance in SI units. A mole of a substance or a mole of particles is defined as containing exactly $6.022 \times {10^{23}}$ particles, which may be atoms, molecules, ions, or electrons. The current definition was adopted in November $2018$ as one of the seven SI base units, and is defined as the amount of substance of a system which contains as many elementary entities as there are atoms in $12\,g$of $^{12}C$.

Note: The most important step in this question is the calculation of the molecular weight of the given molecule. Calculate the molecular weight with proper units and in a stepwise manner. If the molecular weight comes out wrong then there will be error in the calculation of number of moles of the molecule.