Question

The balanced equation of the reaction when calcium phosphate is heated with a mixture of sand and carbon is given by:
A: $2C{a}_3{\left(P{O}_4\right)}_2+6Si{O}_2+10C\underset{}{\overset{}{\to }}6CaSi{O}_3+10CO+P_4$
B: $2C{a}_3{\left(P{O}_4\right)}_2+4Si{O}_2+15C\underset{}{\overset{}{\to }}6CaSi{O}_3+10CO+P_4$
C: $2C{a}_3{\left(P{O}_4\right)}_2+6Si{O}_2+6C\underset{}{\overset{}{\to }}6CaSi{O}_3+10CO+P_4$
D: $2C{a}_3{\left(P{O}_4\right)}_2+5Si{O}_2+10C\stackrel{}{\to }6CaSi{O}_3+10CO+P_4$

Answer 1

Hint: A balanced chemical equation is an equation that has the same number of reactants as well as products. Mass is always conserved; this means the chemical equation must be balanced. Because if the chemical equation will not be balanced it will have a different number of atoms on both sides which will cause imbalance of mass and law of conservation of mass will violate.

Complete step by step answer:
In this question we have to write a balanced chemical equation when calcium phosphate will be heated with a mixture of sand and carbon. Chemical formula of calcium phosphate is $C{a}_3{\left(P{O}_4\right)}_2$ and sand is $Si{O}_2$ . Carbon is represented by $C$. When calcium phosphate reacts with sand and carbon products formed are calcium silicate, carbon monoxide and phosphorus. Chemical formula of calcium silicate is $CaSi{O}_3$ , carbon monoxide is $CO$ and phosphorus is $P_4$ . First let’s write reactants and products in form of an equation:
$C{a}_3{\left(P{O}_4\right)}_2+Si{O}_2+C\stackrel{}{\to }CaSi{O}_3+CO+P_4$
In the above reaction we find out that the number of atoms of calcium, oxygen and phosphorus are not balanced. Number of atoms of calcium, phosphorus and oxygen in reactants are $3,2,10$ respectively and the number of atoms of calcium, phosphorus and oxygen in products are $1,4,4$ respectively. To balance number of atoms of calcium and phosphorus molecules of $C{a}_3{\left(P{O}_4\right)}_2$ should be $2$ and molecules of $CaSi{O}_3$ should be $6$. The reaction is:
$2C{a}_3{\left(P{O}_4\right)}_2+Si{O}_2+C\stackrel{}{\to }6CaSi{O}_3+CO+P_4$
Now atoms of calcium and phosphorus are balanced but atoms of silicon and oxygen are imbalanced. To balance the number of atoms of silicon there should be $6$ molecules of $Si{O}_2$. Now the reaction is:
$2C{a}_3{\left(P{O}_4\right)}_2+6Si{O}_2+C\stackrel{}{\to }6CaSi{O}_3+CO+P_4$
Now atoms of all elements are balanced but atoms of oxygen are not balanced. To balance atoms of oxygen there should be $10$ molecules of $CO$ and $C$. Now the reaction is:
$2C{a}_3{\left(P{O}_4\right)}_2+6Si{O}_2+10C\stackrel{}{\to }6CaSi{O}_3+10CO+P_4$
In this reaction atoms of all the elements are balanced this means this is the balanced chemical reaction.

So answer of this question is option A that is $2C{a}_3{\left(P{O}_4\right)}_2+6Si{O}_2+10C\underset{}{\overset{}{\to }}6CaSi{O}_3+10CO+P_4$.

Note:
Law of definite proportions is also called the law of constant composition. According to this law a chemical compound always contains its components in a fixed proportion. This means chemical components have a definite ratio by mass and this doesn’t depend on their method of production.