 The balanced equation of the reaction when calcium phosphate is heated with a mixture of sand and carbon is given by:A: $2C{a_3}{\left( {P{O_4}} \right)_2} + 6Si{O_2} + 10C\xrightarrow[{}]{}6CaSi{O_3} + 10CO + {P_4}$ B: $2C{a_3}{\left( {P{O_4}} \right)_2} + 4Si{O_2} + 15C\xrightarrow[{}]{}6CaSi{O_3} + 10CO + {P_4}$C: $2C{a_3}{\left( {P{O_4}} \right)_2} + 6Si{O_2} + 6C\xrightarrow[{}]{}6CaSi{O_3} + 10CO + {P_4}$D: $2C{a_3}{\left( {P{O_4}} \right)_2} + 5Si{O_2} + 10C\xrightarrow{{}}6CaSi{O_3} + 10CO + {P_4}$ Verified
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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.

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:
$C{a_3}{\left( {P{O_4}} \right)_2} + Si{O_2} + C\xrightarrow{{}}CaSi{O_3} + CO + {P_4}$
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:
$2C{a_3}{\left( {P{O_4}} \right)_2} + Si{O_2} + C\xrightarrow{{}}6CaSi{O_3} + CO + {P_4}$
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:
$2C{a_3}{\left( {P{O_4}} \right)_2} + 6Si{O_2} + C\xrightarrow{{}}6CaSi{O_3} + CO + {P_4}$
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:
$2C{a_3}{\left( {P{O_4}} \right)_2} + 6Si{O_2} + 10C\xrightarrow{{}}6CaSi{O_3} + 10CO + {P_4}$
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 $2C{a_3}{\left( {P{O_4}} \right)_2} + 6Si{O_2} + 10C\xrightarrow[{}]{}6CaSi{O_3} + 10CO + {P_4}$.

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.