Question

How to balance the following equations using algebraic method ( A value is 2 ) ( please include explanation )1- KNO3 + H2CO3 = K2CO3 + HNO32- Pb(OH)4 + Cu2O = PbO2 + CuOH3- Cr(NO2)2 + (NH4)2SO4 = CrSO4 + NH4NO24- KOH + Co3(PO4)2 = K3PO4 + Co(OH)25- Sn(NO2)4 + Pt3N4 = Sn3N4 + Pt(NO2)46-B2Br6 + HNO3 = B(NO3)3 + HBr7-ZnS + AlP = Zn3P2 + Al2S3

Answer 1

To balance the given equation using algebraic method, assign variables to the coefficients of each substance, for example, in this case:

$a\cdot KNO_3+b\cdot H_2CO_3\to c\cdot K_2CO_3+d\cdot HNO_3$

The coefficient of KNO3 is a, for H2CO3 is b, for K2CO3 is c and for HNO3 is d.

Now, make an element balance per each element present in the reaction. For example, for potassium, in the reactants it is present a times, in the products it is present 2c (coefficient times subscript), it means that:

$a=2c$

For oxygen, in the reactants it is present 3a+3b times, in the products it is present 3c+3d times:

$3a+3b=3c+3d$

For nitrogen:

$a=d$

For hydrogen:

$2b=d$

For carbon:

$b=c$

Now, the statement tells us to use 2 as the value of a. Using this value and the algebraic equations stated, we can find the b, c and d:

$\begin{gathered} a=2c \\ 2c=a \\ c=\frac{a}{2} \\ c=\frac{2}{2} \\ c=1 \end{gathered}$$\begin{gathered} b=c \\ b=1 \end{gathered}$$\begin{gathered} a=d \\ d=a \\ d=2 \end{gathered}$

Now, that we have the values for a, b, c and d, we can replace them in the chemical equation to obtain the balanced equation:

$2KNO_3+H_2CO_3\to K_2CO_3+2HNO_3$