The equation summarises the reaction of copper and dilute nitric acid.
qCu + rHNO3 → sCu(NO3)2 + 6H2O + tNO2
What values of q, r, s and t are needed to balance the equation?

Answer:

3) q = 3, r = 12, s = 3, t = 6

There are a total of 12 Hydrogen atoms on the RHS and that is unchangeable.

Hydrogen is only present in HNO₃ on the LHS. 

Therefore, to balance the Hydrogen atoms on both sides, r = 12.

Copper is present on its own on LHS and in Cu(NO₃)₂ on RHS.

So q = s

Let us form algebraic equations.

For Copper,
q = s

For Oxygen,
3r = 6s + 6 + 2t
36 = 6s + 6 + 2t
30 = 6s + 2t —— (1)

For Hydrogen,
r = 12

For Nitrogen,
r = 2s + t
Since r = 12
12 = 2s + t —— (2)

Using simultaneous equations,
6s + 2t = 30
(2s + t = 12) x 2

6s + 2t = 30
4s + 2t = 24

2s = 6
s = 3

Since (q = s) and (s = 3),
q = 3

Using equation (2),
12 = 2s + t
t = 12 – 2s
t = 12 – 2(3)
t = 12 – 6
t = 6

q = 3, r = 12, s = 3, t = 6