Question

balance the equation
Ca2CO3+HNO3---> Ca2NO3+H2O+CO2

Answer 1

$\begin{aligned} CaCO_3 + HNO_3 \to Ca(NO_3)_2 + H_2O + CO_2 \end{aligned}$

To balance the chemical reaction using algebraic method,

$\begin{aligned} aCaCO_3 + bHNO_3 \to cCa(NO_3)_2 + dH_2O + eCO_2 \end{aligned}$

for Calcium --- a = c

for Carbon --- a = e

for Oxygen --- 3a + 3b = 6c + d + 2e

for Hydrogen --- b = 2d

for Nitrogen --- b = 2c

To solve, we have to set one of the coefficients to a fixed number.

Let us set d = 1

for Hydrogen;

b = 2d

b = 2(1)

$\therefore$ b = 2

for Nitrogen;

b = 2c

2 = 2c

$\therefore$ c = 1

for calcium;

a = c

$\therefore$ a = 1

for carbon;

e = a

$\therefore$ e = 1

Let's put all coefficients into Oxygen and find out if our coefficients are actually correct

$\therefore$ For Oxygen;

3a + 3b = 6c + d + 2e

3(1) + 3(2) = 6(1) + 1 + 2(1)

3 + 6 = 6 + 1 + 2

9 = 9

$\therefore$ a = 1, b = 2, c = 1, d = 1, e = 1

and the balanced chemical reaction is;

$\begin{aligned} CaCO_3 + 2HNO_3 \to Ca(NO_3)_2 + H_2O + CO_2 \end{aligned}$