How do I balance this chemical equation with a fraction?

[rakeru]

Homework Statement

Hi! I am currently learning how to balance equations in chemistry but something that I don't understand is using fractions to balance an equation. I have a problem that I can't work out because I'm so confused!

The problem says:

Complete and balance the acid-base reaction:

HCl(aq) + Ba(OH)₂(aq) →

Homework Equations

The Attempt at a Solution

I know that it forms water and a salt. It would be

HCl(aq) + Ba(OH)₂(aq)→ H₂O + BaCl

Right?? Then, to balance it.. barium and chlorine are already balanced. The problem is that to balance the hydrogen I have 2 and 3. I'm not sure if it's easy to understand what I'm saying..

How would I do this? I know that I have to use a fraction as a coefficient and then multiply all the coefficients by the denominator of that fraction. But how do I find the numbers that go on that fraction??

Pleease help! Thank you.

 

[rakeru]

Oh my! I realized that I missed the 2 on the barium chloride subscript! I got my answer, but I still would like to know how to find the numbers in a fraction.. :<

My answer is:

2HCl+Ba(OH)₂→2H₂O+BaCl₂

Is this correct?

 

[Riemann Metric]

That looks properly balanced to me. If you want to find fractional coefficients, you usually look at something like the combustion of Ethane

C₂H₆+O₂ Yields H₂O+CO₂

To balance we get:
C₂H₆+(7/2)O₂ Yields 3H₂O+2CO₂
Right? But what we need to do is get rid of the fraction, since it isn't possible to have half a molecule without splitting it, and that would require another process. So, we multiply everything by two:

2C₂H₆+7O₂ Yields 6H₂O+4CO₂

So to find the fraction first, you need to look at the number of what we need. See how we have seven oxygen total in the product side? Well, the subscript for oxygen in the reactants is two, so we multiply by 7/2 to get 7 total.

 

[rakeru]

Ahh I see! But let's say that you have to do that with a compound and not a free element.. would you put the fraction before the compound? Does that mean you would have to balance other elements again?

Also, why did you put the fraction on the reactant side? Could it also be on the other side? Do you always use the number of the subscript in the products as the numerator?

If you have a compound, what subscript do you use for the denominator?? Sorry for all these questions!

 

[Riemann Metric]

Yes, you could put the fraction anywhere that it's needed: remember, when you balance equations, all you need to do is make sure that the individual components of the molecules (the elements) all add up.
The fraction can go on either side to make sure that the equation is balanced, but usually it ends up going on the last compound that you balance (you end up doing oxygen last because it is a free element and can easily be changed to suit the balance of all the other components).
You don't have to necessarily use a certain subscript for the denominator, but 2 was used here because 7/2*2=7, and I needed 7 oxygen to balance the equation. However, we cannot have fractional coefficients in a final equation, so we multiply everything by two.
You can think of balancing equations in terms of simple algebra. All you need to do is balance the components by adding coefficients until each side has the same amount of everything.

 

[rakeru]

Okay, thanks again. :)

 

[Riemann Metric]

No problem-glad to help.