Moles, mass, gas volumes and equations, s.t.p, r.t.p (O-level chemistry)

The mole

A mole of a substance is the mass in grams of the substance which is numerically equal to its relative atomic mass or its relative molecular mass.

E.g. One mole of carbon weighs 12g, 1 mole of oxygen molecule weights 32g.  1 mole of the compound ammonium sulphate weights 132g.

 A mole of any substance contains the same number of particles.  These particles can be molecules, atoms, ions, or electrons.

 

A mole of any substance contains 6.02 x 10²³ particles.  These number of particles in any mole of a substance (6.02 x 10²³) is called AVOGADRO’S NUMBER

 

There are 6.02 x 10²³ carbon atoms in 1 mol (12g) of carbon.  There are 6.02 x 10²³ oxygen molecules in 1 mol (32g) of oxygen.  There are 6.02 x 10²³ formula units of ammonium sulphate in 1 mol (132g) of ammonium sulphate.

 

Example 1

Taking Avogadro’s constant equal to 6 x 10²³

How many Cu atoms are there in a copper plate, weighing 48g [Cu = 64]

Solution: 

 

 Example 2   

How many grams of Ag [Ag = 108] contain 1. 2 x 10²³ atoms

 

Solution:

Let the number of moles in 1.2×10²³ atoms be X

1 mole of Ag contains 6 x10²³ atoms

X moles of Ag contains 1.2 x 10²³ atoms

Example 3

How many C atoms are there in a carbon rod weighing 8 g (C = 12)

Solution

12g of carbon contains 6 x10²³ atoms

Example 4

How many grams of copper (Cu = 64) contain 4.5 x 10²³ atoms?

Solution

6 x10²³ atoms of copper weigh 64g

Equations

If we consider the following equation:

            C  +  O₂  →  CO₂

The equation now may mean

1 atom of carbon reacts with 1 molecule of oxygen to yield 1 molecule of carbon dioxide.

12g of carbon reacts with 32g of oxygen to yield 44g of carbon dioxide

Or

1 mole of carbon atom reacts with 1 mole. of oxygen molecules to yield one mol of carbon dioxide molecules.

 

Similarly

2C + O₂    2CO

 

The equation means that

1. 2 carbon atoms react with 1 oxygen molecule to yield 2 carbon monoxide
2. 24g of carbon reacts with 32g of oxygen to yield 56g of carbon monoxide.

or

1. 2 mol of carbon atoms react with 1 mol of an oxygen molecule to yield 2 mol of carbon monoxide molecules.

 

Example 5

What is the mass of

• 1 mole of CaSO4

R.F.M        CaSO₄  =   40  +  32  +  4  X  16 = 136g

=>   1 mole weighs 136g

    0.1mole weigh 136 x 0.1 = 13.6g

 

• 3 moles of H₂O

 R.F.M  H₂O   =          18

Þ  2 x 1 + 16  =  18

 

1 mole of H₂O  =  18

3 moles of H₂O  =  18  x  3    =    54g

 

Example 7:    

According to the equation

            2C  +  O₂ → 2CO

How many moles of carbon will react with 0.2mol of oxygen?

Solution

From the equation

• mol of C reacted with 1 mol of O₂

=> 1 mole of O₂ requires  2 moles of C

 0.2 moles of O₂  requires   2 x 02  = 0.4 moles of C

 

Example 8:

According to the equation

            C₃H₈  +  50₂ →  3CO₂  +  4H₂O

 

• How many moles of CO₂ will be produced in the reaction of 3.2g of O₂?

Solution

Mass of 5 mole of oxygen molecules = 5 (2 x 16) = 160g

 160g of oxygen produce 3 mole of carbon dioxide

• How many grams of propane will react with 0.5moles of O₂?

Solution

Formula mass of propane, C₃H₈ = 12 x 3 + 1 x 8 = 44g

5 moles of oxygen react with 1 mole of propane

Calculation involving solutions

 

Definitions

 

1. The concentration of a solution is the number in gram or number of moles of the solute dissolved or contained in a known volume of solution.

 

Usually, the concentration of a solution is expressed in either number of grams or moles of solute per litre of solution.

 

2. The morality of a solution is the number of moles of the solute contained in 1 liter, 1dm^3, or 1000cm³ of the solution.

 

 

3. A two molar solution of sodium hydroxide (2M NaOH) is a solution containing two moles of the NaOH in 1000 cm³ of the solution

 

4. Some formulas

 

            Morality          =          Concentration in gm/L   (units for morality mol dm^-3)

                                                            R.F.M

 

            Or morality      =          No. of moles x 1000

                                                            Volume

 

            Mole                =          grams/mass

                                                  R.F.M

 

 

Example 1

 

20cm³ of 0.1M NaOH completely reacted with 50cm³ of dilute HCl. Calculate the Morality of the acid and concentration of the acid in g/l

 

Solution

 

Reacting equation

 

NaOH(aq)  + HCl (aq) → NaCl(aq)  +  H₂O(l)

 

Given: 20 cc              50cc

            0.1M              ?

 

Moles of NaOH that reacted:

 

 Moles of HCl. that reacted

From the equation mole ratio of NaOH:  HCl

                                                    1  :   1

Therefore 1 mole of NaOH reacted with 1 mole of HCl

 

Therefore, moles of HCl = 0.002 moles

 

Morality of HCl

(b)        formula mass HCl = 1+ 35.5 =  36.5

 

            1 mole  of HCl weighs 36.5g

            0.04moles weigh 36.5 x 0.4 = 1.46g /L   

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