Why is this redox reaction not balanced? Please balance it. #"H"_2"SO"_4(aq) + "K"_2"Cr"_2"O"_7(aq) + "SO"_2(g) -> "Cr"_2"SO"_4(aq) + "H"_2"O"(l) + "K"_2"SO"(aq)#

There is a typo in your response, or there was an error wherever you looked. It should read:

Your Google search yielded an unbalanced number of oxygen atoms; trust but double check!

Your curiosity is admirable. :)

WARNING: LONG REPLY!

To keep things simple, let's start by looking at the reaction between sulfur dioxide and dichromate; we can add the potassium and sulfate counterions (but not the sulfate product) later.

Now, a few important terms to remember:

This demonstrates why the subsequent actions make sense:

This would come in handy in situations where you need to reuse the same half-reaction more than once. At my university, for instance, we do a series of permanganate reactions with each of the halides.

WRITE THE HALF-REACTION OF REDUCTION

Since we now know that dichromate was reduced (i.e., its oxidation state became less positive or its oxygen atom count dropped), the initial half-reaction might be as follows:

Stabilize the atoms that aren't hydrogen or oxygen.

The oxygen atoms now.

Since every atom is in balance, we can now examine the charge.

The oxidation half-reaction is the next thing we cover.

COMPOSING THE HALF-REACTION OF OXIDATION

Same procedure, but this time we start with writing this:

Follow the same procedures as above to get:

ENTIRE REACTION

Now eliminate the substances that match on each side.

Generally, you can leave this alone, but since you requested the counterions to be there, let's add them back.

RESTORING THE CONVENTIONS

The oxygen atoms in your reaction are not balanced. Here's how to continue from the balanced information we just received above.

Thus, it ought to be:

That's right, the reaction is now balanced and includes all of the counterions!

And cancel out the common reagents to give........

Which I think is balanced with respect to mass and charge, as indeed it must be if it is to reflect chemical reality.

See here for other examples.

Redox reaction in balance: [ \text{H}_2\text{SO}_4(aq) + \text{K}_2\text{Cr}_2\text{O}_7(aq) + \text{SO}_2(g) \rightarrow \text{Cr}_2\text{SO}_4(aq) + \text{H}_2\text{O}(l) + \text{K}_2\text{SO}(aq) ]