Question

The formula unit mass of $C{a_3}{\left( {P{O_4}} \right)_2}$ is:
A. $360$
B. $240$
C. $118$
D. $310$

Answer 1

Hint:
We know that we have formula unit mass for ionic compounds that can be determined by using the atomic masses of its constituent atoms.

Complete step by step solution
In quantitative chemistry we use different types of masses associated with a given quantity or entity of matter. Here, we will discuss some of them briefly:

- Atomic mass: As Dalton proposed atoms to be the smallest unit of matter which have characteristic properties for a given element; atomic mass is one of them. Mass of an atom of a given element is fixed and is known to us as atomic mass. It is not possible to weigh only $1$ atom and thus relative atomic mass is used. As present, the reference atom is $C - 12$ and the IUPAC recommended unit is “u” that is a unified mass.
- Molecular mass: We know that a molecule is made of elements which may be of the same element or different. For example ${H_2}$ gas and $N{H_3}$. The mass of one molecule of a compound that can be determined by adding up the atomic masses of all the atoms present in $1$ molecule is called molecular mass and has the same units as that of atomic mass, “u”.
- Formula unit mass: We have ionic compounds which exist not as molecules but formula units. Examples are $NaCl$ and $CaC{l_2}$. For these, we use formula unit mass in place of molecular mass but the method of calculation is the same.

Now let’s have a look at the given compound with formula $C{a_3}{\left( {P{O_4}} \right)_2}$. We can calculate its formula unit mass by using the atomic mass of calcium, phosphorus and oxygen as follows:
$
{M_{C{a_3}{{\left( {P{O_4}} \right)}_2}}} = \left\{ {3 \times M\left( {Ca} \right)} \right\} + \left\{ {2 \times M\left( P \right)} \right\} + \left\{ {8 \times M\left( O \right)} \right\}\\
 = \left( {3 \times 40\;u} \right) + \left( {2 \times 31\;u} \right) + \left( {8 \times 16\;u} \right)\\
 = {\rm{310}}\;u
$

Hence, the formula mass of $C{a_3}{\left( {P{O_4}} \right)_2}$ is determined to be ${\rm{310}}$ which makes the option D to be the correct one.

Note:
We have to calculate the number of atoms carefully as there are some present in the parenthesis as well.