The answer would be :
[0]HCN + CuSO4 = CuSO4 + [0]Cu(CN)2
Thus is because the left-hand side contain Hydrogen, whereas the right-hand side does not. To balance an equation, an element cannot be added. And therefore, Hydrogen must be removed completely, along with Carbon and Nitrogen, as they each formed a chemical bond with hydrogen, and the composition would change if so.
Explanation chemically :
HCN + CuSO4 = CuSO4 + Cu(CN)2
Left-hand side :
1 H
1 C
1 N
1 Cu
1 S
4 O
Right-hand side :
0 H
1 Cu
1 S
4 O
1 Cu
2 C
2 N
Comparison between the two sides :
First:
1 H = 0 H (therefore to balance it, times the left hand side by 0 : (0)(1) H = 0 H = 0 H)
Because we're multiplying the left-hand side hydrogen atom by 0, and it is bonded with Carbon and Nitrogen, Carbon and Nitrogen is multiplied by 0 as well.
(0) H x (0) C x (0) N = (0) HCN = 0
Hydrogen is balanced.
Second :
Left-hand side Carbon and Nitrogen is 0 (0HCN).
Therefore, right-hand side Carbon and Nitrogen must also be 0.
Cu(CN)2
0 should be multiplied to the CN bracket to bring them to 0. However, there is a Cu atom in from of the CN molecule. So the 0 would be placed in front of the Cu atom, like this :
(0) Cu(CN)2.
The 0 in front of the Cu atom ensures that all the atoms will be multiplied by 0
(0 Cu(CN)2 = (0) Cu x (0) (CN)2 = 0
Carbon and Nitrogen are balanced.
Third :
CuSO4 is already balanced as both sides have an equal amount of each atom.
Therefore, the answer is [0] HCN + [1] CuSO4 = [1] CuSO4 + [0] Cu(CN)2