Avogadro's number is the number of items in one mole. The number is experimentally determined based on measuring the number of atoms in precisely 12 grams of the carbon-12 isotope, giving a value of approximately 6.022 x 1023. You can use Avogadro's number in conjunction with atomic mass to convert a number of atoms or molecules into the number of grams. For molecules, you add together the atomic masses of all the atoms in the compound to get the number of grams per mole. Then you use Avogadro's number to set up a relationship between the number of molecules and mass. Here's an example problem that shows the steps:
Question: Calculate the mass in grams of 2.5 x 109 H2O molecules. Solution: Step 1 - Determine the mass of 1 mole of H2O The chemical formula for water is H2O. To obtain the mass of 1 mole of water, look up the atomic masses for hydrogen and oxygen from the Periodic Table. Depending on the table you use, you may need to adjust the number of significant figures for each atomic mass. There are two hydrogen atoms and one oxygen for every H2O molecule, so the mass of H2O is:
mass of H2O = 2 (mass of H) + mass of O Step 2 - Determine the mass of 2.5 x 109 H2O molecules One mole of H2O is 6.022 x 1023 molecules of H2O (Avogadro's number). This relation is then used to 'convert' a number of H2O molecules to grams by the ratio: mass of X molecules of H2O / X molecules = mass of a mole of H2O molecules / 6.022 x 1023 molecules Solve for the mass of X molecules of H2O mass of X molecules of H2O = ( mass of a mole H2O · X molecules of H2O ) / 6.022 x 1023 H2O molecules
mass of 2.5 x 109 molecules of H2O = ( 18.02 g · 2.5 x 109) / 6.022 x 1023 H2O molecules Answer The mass of 2.5 x 109 molecules of H2O is 7.5 x 10-14 g. The key to success for this type of problem is paying attention to the subscripts in a chemical formula. For example, in this problem, there were two atoms of hydrogen and one atom of oxygen. If you're getting the incorrect answer for this type of problem, the usual cause is having the number of atoms wrong. For example, in the formula H2O, there are two atoms of hydrogen (the subscript) and one atom of oxygen (no subscript is the same as "1"). In H2SO4, there are two atoms of hydrogen, one atom of sulfur, and four atoms of oxygen. Another common problem is not watching your significant figures, which can throw off your answer in the last decimal place. Base the number of significant digits on the number given in the problem for the number of molecules.
Updated March 08, 2020 By Riti Gupta Reviewed by: Lana Bandoim, B.S.
The human brain has a difficult time thinking about both really big numbers and really small numbers. In the chemistry lab, you will often find yourself confronted with both.
Say you have a simple salt solution you will be working with in lab. It's easy enough for you to see the solution. It's clear and aqueous. But, how do you know how many individual molecules of salt there are in this solution?
You can't just look at the solution and figure it out. Counting molecules in a solution isn't as simple as counting jelly beans in a jar. You can't even pop a sample of the solution under a light microscope to try and see the molecules. They're simply too small!
Then how can you account for how many salt molecules there are? The key is Avogadro's number.
Inside your salt solution not only can you not see the molecules, but there are tons of them. In fact, there are so many that it can be very difficult to really understand the number of them. You're dealing with enormous numbers of a very tiny particle. But, chemistry requires the knowledge of how many particles for many reasons, among which include predicting reactions and making solutions.
You need to know the number of molecules and how this relates to mass since, more often than not, when you make a solution, you are weighing out the component in question. For example, you do not count the individual number of molecules you need in a salt solution. Instead you weigh out the amount of solute that corresponds to the number of molecules you want.
The mole allows a bridge between the unfathomable world of huge numbers of tiny molecules and being able to actually weigh substances out and work with them. A mole of a substance contains 6.022 x 1023 particles of that substance. This is Avogadro's number.
A mole is thus a collective number. It's similar to another collective number you may be familiar with: a dozen. A dozen can refer to anything: a dozen donuts is always twelve donuts, and a dozen flamingos is always twelve flamingos.
In the same way, a mole of donuts would be 6.022 x 1023 donuts, and a mole of flamingos would be 6.022 x 1023 flamingos. A mol of NaCl would also be a 6.022 x 1023 molecules of NaCl.
The relationship between moles and mass is known as molar mass or the number of grams in one mole of a substance. The molar mass for any element can be found under the symbol on the periodic table.
For example, the molar mass of carbon is 12.01 g/mol. This means that in one mole of carbon there are 12.01 grams of carbon.
Say you have 2 moles of NaCl. How many molecules of NaCl is that? Here's where you can use Avogadro's number:
Thus, 2 moles of NaCl contain 1.2 x 1024 molecules of NaCl.
What about if instead of 2 moles, you were given 2 grams of NaCl. How many molecules of NaCl does that contain?
To figure this out, you will need the molar mass of NaCl which is 58.44 g/mol. First, convert the grams to moles using the molar mass and then use Avogadro's number to find the number of molecules:
This calculation tells you that there are 2.1 x 1022 molecules of NaCl in 2 grams of NaCl. |
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