Balancing chemical equation

does anyone know how to solve? i tried couple of times and had hard time with it. is there any trick we can use to do it quickly?
thank you in advance

The equation for the preparation of nitrogen monoxide is:
a Cu + b HNO3 a Cu (NO3)2 + c H2O + 2NO
What is the value of b?

A 2
B 4
C 6
D 8
E 12
F 16

Hi.

Assuming you mistyped; instead of the second a it must be an arrow

The answer should be 4, in such questions you don’t have to work all the elements just the required ones.

If the assumption was wrong please clarify your Q.

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I believe the answer is 4
If thats correct:
One easy way that i would solve the question would be like this
firstly start from the most rare element and big molecule, Which is Cu in Cu(No3)2,by attributing the number 1 to Cu(NO3)2 And calculating the number of Cu will see that we are going to need 1 CU in the left side, Then the 2nd most rare would be N in Cu(NO3)2 Which shows there are 2N In the right side plus 2N from 2NO, Altogether 4N In the right side, the same numer of N should be in the left side,taken together the number that should be attributed to HN03 is 4.

If there was any faster way,I’d be delighted to be informed

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b = 2 + 2a (based off $2$NO and $a$Cu)

b = c (based off hydrogen)

We can sub in the smallest number that gives us a whole number answer for a, b, c. This is a = 1 (notice that if make b or c = 1 then a will be 1/4. We want whole numbers when balancing equations so we would have to multiply everything by 4, giving us the same answer).

b = 2 + 2(1) (based off $2$NO and $a$Cu)
b=4
b = c = 4 (based off hydrogen)

Therefore the answer is B

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