Question

balance the chemical equation below using the smallest possible whole number stoichiometric coefficients.
ca₃(po₄)₂(s) + sio₂(s) + c(s) → casio₃(s) + p₄(s) + co(g)

Explanation:

Step1: Balance phosphorus atoms

There are \(2\) phosphorus atoms in \(Ca_3(PO_4)_2\) and \(4\) in \(P_4\). Multiply \(Ca_3(PO_4)_2\) by \(2\) to get \(4\) phosphorus atoms.
\(2Ca_3(PO_4)_2(s)+SiO_2(s)+C(s)\to CaSiO_3(s)+P_4(s)+CO(g)\)

Step2: Balance calcium atoms

After multiplying \(Ca_3(PO_4)_2\) by \(2\), there are \(6\) calcium atoms. Multiply \(CaSiO_3\) by \(6\) to balance calcium.
\(2Ca_3(PO_4)_2(s)+SiO_2(s)+C(s)\to 6CaSiO_3(s)+P_4(s)+CO(g)\)

Step3: Balance silicon atoms

After multiplying \(CaSiO_3\) by \(6\), there are \(6\) silicon atoms. Multiply \(SiO_2\) by \(6\) to balance silicon.
\(2Ca_3(PO_4)_2(s)+6SiO_2(s)+C(s)\to 6CaSiO_3(s)+P_4(s)+CO(g)\)

Step4: Balance oxygen atoms

Left - hand side: \(2\times4\times2 + 6\times2=16 + 12 = 28\) oxygen atoms. Right - hand side: \(6\times3+CO\) oxygen. Let the coefficient of \(CO\) be \(x\). Then \(18 + x=28\), so \(x = 10\).

Step5: Balance carbon atoms

Since the coefficient of \(CO\) is \(10\), multiply \(C\) by \(10\) to balance carbon.

Answer:

\(2Ca_3(PO_4)_2(s)+6SiO_2(s)+10C(s)\to 6CaSiO_3(s)+P_4(s)+10CO(g)\)