<< Chapter < Page Chapter >> Page >

This is easiest to see with an example. Some of the most common chemical reactions are those in which compounds of hydrogen and carbon, called hydrocarbons, are burned in oxygen gas to form carbon dioxide and water. The simplest hydrocarbon is methane, and using the methods of this study, we can find that methane has the molecular formula, CH 4 . The chemical equation which represents the burning of methane is:

1 CH 4 molecule + 2 O 2 molecules → 1 CO 2 molecule + 2 H 2 O molecules

It is important to note that the number of atoms of each type is conserved during the chemical reaction. The reactants and products both contain 1 carbon atom, 4 hydrogen atoms, and 2 oxygen atoms. This is called a “balanced” chemical equation, and it expresses the postulate of the Atomic Molecular Theory that the numbers of atoms of each element does not change during a chemical reaction.

In chemical algebra, we can ask and answer questions such as, “If we burn 1.0 kg of methane, what is the mass of carbon dioxide which is produced?” Such a question would clearly be of importance in understanding the production of greenhouse gases like CO 2 . The chemical equation above expresses a relationship between the number of molecules of methane which are burned and the number of molecules of CO 2 produced. From the equation, each molecule of CH 4 produces one molecule of CO 2 . Therefore, if we knew how many molecules of CH 4 we have in a sample, we know how many molecules of CO 2 we will produce.

The chemical equation works for any number of molecules. If we burn N molecules of CH 4 , we produce N molecules of CO 2 . This will work no matter what N is. Therefore, we can say that 1 mole of CH 4 molecules will produce 1 mole of CO 2 molecules. The chemical equation works just as well for moles as it does for molecules, since 1 mole is just a fixed number of molecules. And we know how to calculate the number of moles from a measurement of the mass of the sample.

Recall that we are interested in what happens when we burn 1.00 kg = 1000 g of methane. We just need to know the mass of a mole of methane. Since one molecule of methane has relative mass 16.0, then one mole of methane has mass 16.0 g/mol. Then the number of moles in 1000 g of methane can be calculated by dividing by the mass of 1.0 mole of methane:

n CH 4 = 1000 g 16 . 0g / mol = 62 . 5 moles size 12{n rSub { size 8{ ital "CH" rSub { size 6{4} } } } = { {"1000"g} over {"16" "." 0g/ ital "mol"} } ="62" "." 5 ital "moles"} {}

This means we have counted the number of particles of CH 4 in our sample. And we know that the number of particles of CO 2 produced must be the same as this, because the chemical equation shows us the 1:1 ratio of CH 4 to CO 2 . So, 62.5 moles of CO 2 are produced by this reaction and this 1.0 kg sample.

We are usually more interested in the mass of the product, and we can calculate this, too. The mass of one mole of CO 2 is found from the mass of one mole of C and two moles of O, and is therefore 44.0 g. This is the mass for one mole. The mass for 62.5 moles will be

m CO 2 = n CO 2 M CO 2 62 . 5 moles 44 . 0g / mol = 2750 g = 2 . 75 kg size 12{m rSub { size 8{ ital "CO" rSub { size 6{2} } } } =n rSub { ital "CO" rSub { size 6{2} } } size 12{M rSub { ital "CO" rSub { size 6{2} } } left ( size 12{"62" "." 5 ital "moles"} right ) left ( size 12{"44" "." 0g/ ital "mol"} right )} size 12{ {}="2750"g=2 "." "75" ital "kg"}} {}

Therefore, for every 1 kg of methane burned, we produce 2.75 kg of CO 2 .

The important conclusion from this example of chemical algebra is that it is possible to calculate masses of products from masses of reactants. We do so by using a balanced chemical equation and by understanding that the equation gives us the ratio of moles of reacting materials just as it gives us the ratio of molecules of reacting materials. This is because numbers of moles and numbers of molecules are simply different ways of counting the number of particles.

Chemical algebra is usually referred to as “stoichiometry,” a somewhat intimidating term that makes the calculations seem harder and more abstract than they are. We really only need to remember two things. First, from the Atomic Molecular Theory, a chemical reaction can be represented by a balanced chemical equation which conserves the numbers of atoms of each element. Second, the balanced equation provides the ratio of the number of product molecules to the number of reactant molecules, either in numbers of molecules or numbers of moles. Thus, we can solve problems efficiently by calculating the number of moles.

A final interesting note about Avogadro’s number is helpful in understanding what 1 mole is. A question often asked is, where did the number 6.022×10 23 come from? If we wanted to pick a very large number for the number of particles in a mole, why didn’t we pick something easier to remember, like 6×10 23 , or even 1×10 23 ? The value of Avogadro’s number comes from the fact that we chose 1 mole to be the number of carbon atoms in 12.01g of carbon. Since 1 carbon atom has mass 12.01 amu, then the mass of N A carbon atoms is N A ×12.01 amu. But 1 mole of carbon atoms has mass 12.01 g, so 12.01 g must equal N A ×12.01 amu:

12.01 g = N A ×12.01 amu

This means that

1 g = N A amu

This shows that Avogadro’s number is just the conversion factor for mass between grams and amu. We didn’t randomly pick Avogadro’s number. Rather, we picked the unit of mass amu, and it turns out that there are Avogadro’s number of amu in one gram.

Review and discussion questions

  1. State the Law of Combining Volumes and provide an example of your own construction which demonstrates this law.
  2. Explain how the Law of Combining Volumes, combined with the Atomic Molecular Theory, leads directly to Avogadro's hypothesis that equal volumes of gas at equal temperatures and pressure contain equal numbers of particles.
  3. Use Avogadro's hypothesis to demonstrate that oxygen gas molecules cannot be monatomic.
  4. The density of water vapor at room temperature and atmospheric pressure is 0.737 g/L. Compound A is 80.0% carbon by mass, and 20.0% hydrogen. Compound B is 83.3% carbon by mass and 16.7% hydrogen. The density of gaseous Compound A is 1.227 g/L, and the density of Compound B is 2.948 g/L. Show how these data can be used to determine the molar masses of Compounds A and B, assuming that water has molecular mass 18.
  5. From the results in Problem 4, determine the mass of carbon in a molecule of Compound A and in a molecule of Compound B. Explain how these results indicate that a carbon atom has atomic mass 12.
  6. Explain the utility of calculating the number of moles in a sample of a substance.
  7. Explain how we can conclude that 28g of nitrogen gas (N 2 ) contains exactly as many molecules as 32g of oxygen gas (O 2 ), even though we cannot possibly count this number.

By John S. Hutchinson, Rice University, 2011

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Concept development studies in chemistry 2013. OpenStax CNX. Oct 07, 2013 Download for free at http://legacy.cnx.org/content/col11579/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Concept development studies in chemistry 2013' conversation and receive update notifications?