Question

How many grams of phosphoric acid would be needed to neutralize 100g of magnesium hydroxide? (The molecular weight of ${H_3}P{O_4} = 98g/mol$ and $Mg{\left( {OH} \right)_2} = 58.3g/mol$ ).
A.$66.7g$
B.$252g$
C.$112g$
D.$168g$

Answer 1

The best approach to solve this type of numerical is to write a chemical reaction for the given chemical compounds. For this numerical we are expected to write a neutralization reaction of phosphoric acid and then compare the moles using mole concept.
Formula Used: $n = \dfrac{w}{M}$ where,
n represents number of moles,
w represents given mass of chemical compound,
M represents molecular weight of the given compound.

Complete step by step answer:
As we know that it is better to write a chemical reaction for the neutralization process. So, here we will write a chemical reaction for phosphoric acid ${H_3}P{O_4}$ and magnesium hydroxide $Mg{\left( {OH} \right)_2}$ . The reaction is as follows:
$3Mg{\left( {OH} \right)_2} + 2{H_3}P{O_4} \to M{g_3}{\left( {P{O_4}} \right)_2} + 6{H_2}O$
This reaction concludes that $3$ moles of $Mg{\left( {OH} \right)_2}$ are required for neutralization.
Now we will write the given quantities to solve further. We have given that the molecular weight of ${H_3}P{O_4} = 98g/mol$ and $Mg{\left( {OH} \right)_2} = 58.3g/mol$.
Now using the formula, $n = \dfrac{w}{M}$
For $Mg{\left( {OH} \right)_2}$,
We have, $n = 3$ and $M = 58.3g/mol$, substitute the values in formula and calculate the given mass $\left( w \right)$.
$\Rightarrow w = n \times M$
$\Rightarrow w = 3 \times 58.3 = 174.9g$
For ${H_3}P{O_4}$ ,
We have, $n = 2$ and $M = 98g/mol$, substitute the values in formula and calculate the given mass $\left( w \right)$.
$\Rightarrow w = n \times M$
$\Rightarrow w = 2 \times 98 = 196g$
Now we can conclude that,
$3$ Moles of $Mg{\left( {OH} \right)_2}$ weighs $174.9g$,
$2$Moles of ${H_3}P{O_4}$ weighs $196g$,
Or simply $174.9g$ of $Mg{\left( {OH} \right)_2}$ requires $196g$ of ${H_3}P{O_4}$,
$\Rightarrow$ $1g$ of $Mg{\left( {OH} \right)_2}$ will require $\left( {\dfrac{{196}}{{174.9}}} \right)g$ of ${H_3}P{O_4}$.
Now according to the question we need an amount of phosphoric acid that would be needed to neutralize $100g$ of magnesium hydroxide. So we can easily get that as follows:
$100 \times 1g$ Of $Mg{\left( {OH} \right)_2}$ will require $\left( {\dfrac{{196}}{{174.9}} \times 100} \right)g$ of${H_3}P{O_4}$,
We just multiplied by $100$ to get the desired result,
$100g$ $Mg{\left( {OH} \right)_2}$ , will require $112.06g \approx 112.0g$ of ${H_3}P{O_4}$.
$112.0g$ of ${H_3}P{O_4}$ will be needed to neutralize $100g$ of magnesium hydroxide.

Therefore, the correct option is (C).

Note: Phosphoric acid ${H_3}P{O_4}$ is also known as orthophosphoric acid. The appearance of chemical compounds is a colorless solid. Phosphoric acid is a weak acid and can burn lips, tongue and can lead to nausea.