[nectarines]

I know this seems extremely simple, but I've been taking practice tests for my gen chem final, and the balancing equations problems have been the most challenging for me. Here are examples:

?P + ?HNO3 + ?H2O -> ?H3PO4 + ?NO

?Cu + ?HNO3 -> ?Cu(NO3)2 + ?NO + ?NO2 + ?H2O, where NO and NO2 are formed in a 2:3 ratio

Can someone explain the process of solving these? I can do most balancing problems, but these are just ridiculous.

[curiouscat]

Have you been taught how to solve simultaneous linear equations?

Then, write atom balances. Say, in 2nd example for Cu, H, N, O.
4 linear eq. in 6 unknowns. Solve.

Matrix based solving might speed up the process.

It isn't the way Chem. classes typically teach but I find it neater. If you're lucky maybe your Scientific Calculator will have a linear eq. solving function too.
 

[curiouscat]

a Cu + b HNO3    c Cu(NO3)2 + d NO + e NO2 + f H2O

(Cu)  a = c
(H)   b  =  2f
(N)  b = 2c +d + e
(O) 3b = 6c +d + 2e + f

3d=2e

Solve.

[AWK]

?Cu + ?HNO3 -> ?Cu(NO3)2 + ?NO + ?NO2 + ?H2O, where NO and NO2 are formed in a 2:3 ratio

It will be more simple to split this eqution into two equations with NO and NO₂ formed separately.




correction of printing error (quote instead of subscript)

[Borek]

As AWK wrote, these are two separate processes and each has to be balanced separately.

[AWK]

In this case the other possibility is joining 2NO + 3NO₂ into artificial molecule N₅O₈
?Cu + ?HNO₃ -> ?Cu(NO₃)₂ + ?N₅O₈ + ?H₂O

[Ben Cohen]

It's all about making connections between the elements and using variables efficiently

[Big-Daddy]

a Cu + b HNO3    c Cu(NO3)2 + d NO + e NO2 + f H2O

(Cu)  a = c
(H)   b  =  2f
(N)  b = 2c +d + e
(O) 3b = 6c +d + 2e + f

3d=2e

Solve.

6 variables in 4 equations? This cannot be solved numerically by the standard method of solving simultaneous linear equations.

[curiouscat]

a Cu + b HNO3    c Cu(NO3)2 + d NO + e NO2 + f H2O

(Cu)  a = c
(H)   b  =  2f
(N)  b = 2c +d + e
(O) 3b = 6c +d + 2e + f

3d=2e

Solve.

6 variables in 4 equations? This cannot be solved numerically by the standard method of solving simultaneous linear equations.

5 equations. Also have "3d=2e"?

[Borek]

6 variables in 4 equations? This cannot be solved numerically by the standard method of solving simultaneous linear equations.

Quite often we do miss one equation when balancing reactions, but we also have additional condition that the solution should consist of the smallest integers - and that's enough to find the unique solution.

[curiouscat]

6 variables in 4 equations? This cannot be solved numerically by the standard method of solving simultaneous linear equations.

This cannot be solved numerically uniquely by the standard method of solving simultaneous linear equations.

An under-determined system of simultanous linear eqns. is not the same as an inconsistent system.

[Big-Daddy]

6 variables in 4 equations? This cannot be solved numerically by the standard method of solving simultaneous linear equations.

This cannot be solved numerically uniquely by the standard method of solving simultaneous linear equations.

An under-determined system of simultanous linear eqns. is not the same as an inconsistent system.

What is the process to force a solution out of something like this?

(When I say force a solution I mean find numerical values by actual number calculation rather than guesswork.)

[Borek]

What is the process to force a solution out of something like this?

(When I say force a solution I mean find numerical values by actual number calculation rather than guesswork.)

I told you - there is an additional condition that can be used. Depending on how you approach the problem you either need some guesswork, or you can do it algorithmically. In a way it is not much different from finding the empirical formula - you have numbers that have to be converted to integers without changing ratios. It is not that difficult, as you can do Gauss elimination using rational numbers, so in the end it is just a matter of finding GCD of all coefficients.

See also http://www.chembuddy.com/?left=balancing-stoichiometry&right=algebraic-method

[curiouscat]

What is the process to force a solution out of something like this?

(When I say force a solution I mean find numerical values by actual number calculation rather than guesswork.)

http://www.solitaryroad.com/c132.html

[Big-Daddy]

What is the process to force a solution out of something like this?

(When I say force a solution I mean find numerical values by actual number calculation rather than guesswork.)

I told you - there is an additional condition that can be used. Depending on how you approach the problem you either need some guesswork, or you can do it algorithmically. In a way it is not much different from finding the empirical formula - you have numbers that have to be converted to integers without changing ratios. It is not that difficult, as you can do Gauss elimination using rational numbers, so in the end it is just a matter of finding GCD of all coefficients.

See also http://www.chembuddy.com/?left=balancing-stoichiometry&right=algebraic-method

You specified only the condition before, not the process for calculating this. I had seen that algebraic method and it is the one I was referring to. But I suppose with reference to curiouscat's example that whole number guesswork becomes trivial at this stage however complicated the original problem.

I suppose that due to my lack of knowledge of what a Gaussian elimination is that this is probably what I was asking for when I asked what process was needed to force the solution.