Question

The formula of metal oxide of a metal A is ${ A }_{ 2 }{ O }_{ 3 }$. Determine the formula of its phosphate.
(a) ${ A }_{ 3 }{ PO }_{ 4 }$
(b) ${ A }_{ 2 }{ (PO }_{ 4 }{ ) }_{ 2 }$
(c) ${ A(PO) }_{ 2 }$
(d) ${ { APO }_{ 4 } }$

Answer 1

Hint : Look at the formula and try to determine the charges on the individual cations and anions that form the given compound. That way, you will be able to determine the valence shown by the cation and the anion.

Complete step by step solution :
Since the valence of both the phosphate ion and A ion is 3, thus the answer is (d). This poses the question, what exactly is valency or valence. The valency or valence of an element is defined as its combining power when it combines which other atoms or a group of atoms in a compound. This combining power is determined by the number of hydrogen atoms that it combines with. For example carbon has a valency of 4 since it combines with four hydrogen atoms to give methane, oxygen has a valency of 2 since it combines with two oxygen atoms to give water, Nitrogen has a valency of 3 since it combines with three hydrogen atoms to give ammonia, Chlorine has a valency of 1 since it combines with one hydrogen atom to give hydrogen chloride.
The elements that have one, two, three or four electrons in their outermost shell or valence shell, they have the valency of one, two, three and four respectively. For elements having more than 4 electrons in their valence shell, their valency can be easily found by using the formula:
Valency = 8-number of electrons in the valence shell.
Thus oxygen which has 6 electrons in its outermost shell has a valency of 2 (8-6=2). Chlorine which has seven electrons in its valence shell has a valency of 1 (8-7=1).
Now, if a metal A has a valency of 2, then its oxide formula will be ${AO}$ since both of them have a valency of 2 and therefore they will cancel out each other while writing the formula. Generally you should follow the following rules while writing the formula of a compound:
-Determine the valency of the two species involved. If they are anions or cations such as phosphate ion or sulphate ion, then their valence is equal to the magnitude of their charge.

-Cross multiply the valency of the two species in the simplest ratio.

$\begin{matrix} Species: \\\ Valence: \end{matrix}\begin{matrix} A \\\ 2 \end{matrix}+\begin{matrix} B \\\ 3 \end{matrix}\xrightarrow { Cross\quad multiply\quad 2\quad and\quad 3\quad in\quad the\quad simplest\quad ratio } { A }_{ 3 }{ B }_{ 2 }$

For the given species ${ A }_{ 2 }{ O }_{ 3 }$ using the above method in reverse order, we come to know that the valence of A is 3 or its cationic form is ${ A }^{ 3+ }$. Therefore its phosphate will be (d) ${ { APO }_{ 4 } }$ since both of them have the same valency of 3.
$\begin{matrix} Species: \\\ Valence: \end{matrix}\begin{matrix} { A }^{ 3+ } \\\ 3 \end{matrix}+\begin{matrix} P{ O }_{ 4 }^{ 3- } \\\ 3 \end{matrix}\xrightarrow { Cross\quad multiply\quad 3\quad and\quad 3\quad in\quad the\quad simplest\quad ratio } AP{ O }_{ 4 }$

Therefore the correct answer is (d) ${ { APO }_{ 4 } }$.

Note : The valence of a species is not fixed. For example many of the p-block elements show different valencies since they can expand their valence using d and f orbitals.