Balancing and Applying Chemical Equations

Date: 01/20/2005 at 16:18:52
From: Lan
Subject: Mole Ration and balancing equation

I don't know how to balance the chemical equation of
  
  __C2H5OH + __O2 ---> __CO2 + __H2O

I also need to determine the mass of CO2 produced from the combustion 
of 100g of the ethanol (C2H5OH).

Date: 01/21/2005 at 12:18:08
From: Doctor Achilles
Subject: Re: Mole Ration and balancing equation

Hi Lan,

Thanks for writing to Dr. Math.

Here's how I learned how to balance equations:

Step 1: Find the biggest and most complicated molecule in the
equation.  In your case, that's the ethanol (C2H5OH).  Make 1 of
those.  This gives you:

  1 C2H5OH + _ O2 -> _ CO2 + _ H2O

Step 2: Look for an element on the right side of the equation that
only appears in one molecule.  For example, carbon (C) is only in CO2
and is not in H2O.  Next, count up how many atoms you have of that
element.  You have 1 C2H5OH molecule on the left, so that means you
have two carbons.  If you start with 2 carbons, you better end up with
2 carbons.  The only way to end up with 2 carbons is to have 2 CO2's
on the right side.  So we have:

  1 C2H5OH + _ O2 -> 2 CO2 + _ H2O

Step 3: The only molecule on the right that is left is H2O.  We start
with 6 hydrogen atoms on the left.  How many H2O molecules would we
need on the right to end up with 6 hydrogen atoms?

Step 4: Count up the total number of oxygen atoms on the right.  You
already have one oxygen atom on the left in your one C2H5OH molecule.
How many more O2 molecules do you need to balance the equation?

Ok, so now you have the equation.  The next part is to figure out what
mass of CO2 you get when you combust 100 g of ethanol.  (Combustion
just means combining with oxygen, so you're going to be using the
equation that you just solved.)

Step 1: Convert the mass of ethanol (100 grams) to moles.  To do that,
you need to know the molecular weight of C2H5OH.

The molecular weight is the sum of the atomic weights of all the 
atoms.  You have 2 carbons (each one weighs 12 grams/mole) plus you
have 6 hydrogens (each one weighs 1 gram/mole) plus you have one
oxygen (which weighs 16 grams/mole) so your ethanol has a mass of
(2*12)+(6*1)+(1*16) = 46 grams/mole.

So we have 100 grams and we need to divide by 46 grams/mole which
gives us 100/46 = 2.17 moles of ethanol.

Step 2: Figure out how many moles of CO2 will be produced by
combusting 2.17 moles of ethanol.

We know that 1 mole of ethanol will produce 2 moles of CO2.  So 2
moles of ethanol will produce 4 moles of CO2.  So that means that 2.17
moles of ethanol will produce 2.17*2 = 4.34 moles of CO2.

Step 3: Figure out how many grams are in 4.34 moles of CO2.  To do
that we need (you guessed it!) the molecular weight of CO2.

CO2 has 1 carbon (12 grams/mole) and 2 oxygens (16 grams/mole each). 
So find the molecular weight (in grams/mole) of a CO2 molecule and
multiply by 4.34 moles to get the mass of CO2 (in grams) that is produced.

Hope this helps.  If you have other questions or you'd like to talk
about this some more, please write back.

- Doctor Achilles, The Math Forum
  http://mathforum.org/dr.math/