Today in class we talked about the mass of an atom. When we look at the periodic table the relative, weighted average atomic mass is the mass of a single atom in atomic mass units (u). For example, for carbon the relative, weighted average atomic mass is 12.011 u. That is the mass of a single atom in units of 'u'. In units of grams the mass of a single carbon atom is 1.994 x 10-23 g.

We did a couple problems using this information...

 

Problem 1:

How many atoms in 24.022 u of carbon?

Since 1 carbon atom weighs 12.011 u we can do the following calculation,

 

Problem 2:

How many atoms in 5.583 x 10-22 g of carbon?

Since 1 carbon atom weighs 1.994 x 10-23 g we can do the following calculation,

Try some on your own.

1. Calculate how many atoms are in each of the following;

a) 526.56 u of phosphorus atoms

b) 6.918 x 10-23 g of lithium atoms (note the mass of one lithium atom is 1.153 x 10-23 g)

2. What is the mass (in atomic mass units) of a silicon atom?

 

Next we talked about determining the number of carbon atoms in 12.011 g of carbon. Now this was an interesting question. We recognized the 12.011 but the units are different they are grams not u's! So to solve this problem we must use the same approach as Problem 2 above.

Problem 3:

Calculate the number of carbon atoms in 12.0011 g of carbon.

So 12.011 g of carbon contain 6.023 x 1023 C atoms.

Problem 4: How many carbon atoms in 28.0 g of carbon?

If there are 6.023 x 1023 C atoms in 12.011 g of carbon, then

Try some on your own.

1. How many atoms are in each of the following; (you do not have to do a calculation for this question, just tell me how many atoms)

a) 55.85 g of iron atoms

b) 28.085 g of silicon atoms

c) 56.17 g of silicon atoms

 

In fact the relative, weighted average atomic mass for any element in units of grams (rather than atomic mass units) contains 6.023 x 1023 atoms of the element.

I introduced a name for these quantities...a mol. A mol is 6.023 x 1023 anythings. If I have 6.023 x 1023 atoms of carbon I have a mol of carbon. Also 6.023 x 1023 atoms of carbon weigh 12.011 g so a mol of carbon not only contains 6.023 x 1023 atoms, but a mol of carbon also weighs 12.011 g!

Problem 5:

Calculate how many moles in 12.011 g of carbon.

Since 1 mol of carbon is equal to its relative, weight average atomic mass expressed in grams. than in this case there is 1 mol in 12.011 g of carbon.

Problem 6:

Calculate how many moles in 35.8 g of carbon.

Here we solve the problem similar to others we have been doing. Since 1 mol of carbon weighs 12.011 g I just need to divide.

Problem 7:

Calculate how many moles in 2.12 x 1023 atoms of Zn. 1 mol of Zn has 6.023 x 1023 atoms therefore we need to set this problem up in the following way,

The InClass Problem Set that you will do in laboratory during the week of October 11 are just like the calculations above.

 

What follows is some of the same things I've just done, but said in a slightly different way.

At this point I have shown you several different types of chemical reactions which you can balance. Consider the balanced equation

Mg(s) + Cl2(g) -> MgCl2(s)

We can balance the equation and we recognize it is an example of a formation reaction. How do we read this equation? This equation reads 1 atom of magnesium combines with one molecule of chlorine to form the ionic compound magnesium chloride. If we wanted to do this reaction to prepare some magnesium chloride it would be difficult to find a single atom of magnesium and a single molecule of chlorine, even for the most experienced chemist. In the chemistry laboratory we must measure amounts of substances by mass. What is the relationship between the amount of substance and the number of atoms or molecules? How are we able to perform quantitative chemical reactions? There is an answer!

Lets return to the periodic table. In the periodic table the mass number for an element is given below the symbol.

The atomic mass for magnesium is 24.3 u. This is the relative average atomic mass for magnesium. The atomic weight for chlorine is 35.45 u. The symbol for chlorine is Cl. The formula for elemental chlorine is Cl2. The formula mass for elemental chlorine, Cl2, is 70.90 u, just two times the atomic mass. We can obtain formula weights by simply summing the atomic weight for each of the atoms in the formula. Therefore the formula mass of MgCl2 is 95.35 u.

These masses are important as they allow the indirect determination of the number of atoms, molecules or formula units in a substance. When doing chemical reactions, which are described by chemical equations, we need to know numbers of atoms or molecules. The indirect relationship between numbers and mass is given by the fundamental unit mol. The definition of the fundamental unit mol is the number of 12C atoms in 12 g of 12C. This number has been experimentally determined as 6.023 x 1023 atoms. This number is called Avogadro's number. A mol of any substance by definition as the amount of the substance which contains the same number of units as 12 g are in 12 g of 12C or 6.023 x 1023 units of the substance.

A mol of 12C atoms contains 6.023 x 1023 atoms of 12C

A mol of Cl2 molecules contains 6.023 x 1023 molecules of Cl2

A mol of NaCl contains 6.023 x 1023 formula units of NaCl

A mol of 12C atoms weighs the same in grams as the atomic mass of 12C, 12 g. The weight of any substance which contains 6.023 x 1023 units is given by its atomic or formula mass expressed in grams and is called the molar mass of the substance.

A mol of 12C atoms has a mass 12 g: the molar mass of 12C is 12 g

A mol of Cl2 molecules has a mass 70.90 g: the molar mass of Cl2 is 70.90 g

A mol of NaCl has a mass 58.5 g: the molar mass of NaCl is 58.5 g

If we revisit the reaction between magnesium and chlorine,

Mg(s) + Cl2(g) -> MgCl2(s)

This equation reads 1 atom of magnesium combines with one molecule of chlorine to form the ionic compound magnesium chloride. Or this equation reads 10 atoms of magnesium combines with 10 molecules of chlorine to form the 10 formula units of magnesium chloride. We can but in any number we wish as long as we adhere to relationship between the coefficients of each substance in the balanced equation. We count even use the Avogadro's number...this equation reads 6.023 x 1023 atoms of magnesium combines with 6.023 x 1023 molecules of chlorine to form the 6.023 x 1023 formula units of magnesium chloride.

But since we can not count out atoms, molecules or formula units we need another way to measure. Since we know how much an indivdual atom of magnesium weighs (4.04 x 10-23 g), how much an individual molecule of chlorine weighs (1.18 x 10-22 g), we could use a balance. By measuring out the mass of some magnesium and the mass of some chlorine we could determine how many atoms of magnesium were in the sample and how many molecules of chlorine.

24.3 g is the mass of one mol of magnesium and 70.9 g is the mass of one mol of chlorine molecules, and a mol of anything contains the number 6.023 x 1023. So 24.3 g of magnesium contains 6.023 x 1023 atoms of magnesium and 70.9 g of chlorine contains 6.023 x 1023 molecules of chlorine. Therefore we can also read the equation,

Mg(s) + Cl2(g) -> MgCl2(s)

as 1 mol of magnesium reacts with 1 mol of chlorine to produce 1 mol of magnesium chloride.

Lets look at some different ways to use mol, molar mass, and Avogadro's number...

Example 1:

Determine the number of moles of N2O5 in 45.6 g of N2O5 gas. Determine the number of nitrogen atoms.