3. Amount of substance. Mole. Avogadro’s Number. Molar mass

Three very important concepts - the mole, Avogadro’s number and molar mass - provide the basis for relating masses in grams to numbers of atoms. The first, the mole, is the SI unit for amount of substance. The mole is the amount of a substance that contains the same number of particles as the number of atoms in exactly 12 g of ¹²C. The abbreviation for the mole is mol. The mole is a counting unit, like one dozen. In writing, a chemist might refer to 1 mol of Carbon, or 2 mol of Iron, or 2,567 mol of calcium. Amount of substance (in mol) is indicated as Greek letter υ.

The number of particles in a mole has been experimentally determinates in a number of ways. The best modern value is 6,022137·10²³ particles. This number is of such importance to chemistry that it is named in honor of the Italian scientist Amedeo Avogadro (1776-1856), whose ideas were crucial in the early understanding of chemistry. Avogadro’s number N_A- 6,022137·10²³ - is the number of particles in exactly one mole of each pure substance. In most cases, Avogadro’s number is rounded to 6,02·10²³ (or mol^-1).

Molar mass (M_m) is the mass in grams of one mole of pure substance (g/mol). Molar masses of elements contain equal numbers of atoms. One mole of a substance is one molar mass of this substance. An alternative definition of the mole is the amount of a substance that contains an Avogadro’s number of particles of chemical units.

The molar mass is used as the conversion factor in chemical calculations. For a specific substance, a known number of grams can be converted into moles or a known number of moles can be converted into grams. Figure 1 shows the conversions of molar mass, moles, and Avogadro’s number.

In general, mass of any chemical substance (in grams) is connected with amount of this substance by the next ratio:

ν , (1)

where ν - amount of any pure substance (mol or kmol);

m - mass of any pure substance (g or kg);

M_m - molar mass (g/mol or kg/kmol).

Number of moles of an element

Mass of an element (grams)

X Molar mass of element (Mm)

=

Number of atoms of an element

x 6,02·10²³ =

Figure 1. Relationships between mass, the number of moles, and the number of atoms of an element in the sample

Example of solution

1.To determine a relative molecular mass of Sodium Sulfate Na₂SO₄.

Relative molecular mass М_r is determined as sum of relative atomic masses А_r of elements in this compound:

M_r(Na₂SO₄)=2Ar(Na)+A_r(S)+4A_r(O)=223+32+416=142 c.u.

2. To determine molar mass of Calcium Nitrite Са(NO₃)₂.

Molar mass of substance, expressed in grams, is numerically equal to relative molecular mass expressed in a.m.u. So, calculating relative molecular mass of Са(NO₃)₂, we obtain:

M_r(Ca(NO₃)₂)=A_r(Ca)+2A_r(N)+6A_r(O)=40+214+616=164 c.u.

And molar mass of Calcium Nitrite is equal to 164 g/mol.

3. How many atoms and moles are contained in 60 g of Carbon ¹²С? Determine mass of one Carbon atom in grams.

If mass of substance m and its molar mass M_m are known, we could determine the amount of substance (number of moles) in this mass:

M_m is equal to 1 mol;

m –“- x mol; and ν = x = .

Since m=60 g, М_m (С)=12 g/mol, then ν =

Multiplying number of moles (5 moles) by Avogadro’s number N_A we determine the number of atoms in given mass of substance:

N =νN_A=56,0210²³=3,0110²⁴ atoms.

Next step - to be divisible molar mass of Carbon М_m (С)=12 g/mol by Avogadro’s number N_A for calculation of mass of Carbon one atom in grams:

4. How many moles of Hydrobromide HBr are contained in 0,162 grams of this compound?

Determine a relative molecular mass of HBr:

M_r(HBr)=A_r(H)+A_r(Br)=1+80=81.

S o, molar mass of HBr is equal to 81 g/mol. Calculate the number of moles in 0,162 g of HBr:

5. For neutralization of acid it was used 6 moles of Calcium Hydroxide Ca(OH)₂. How many grams of Ca(OH)₂ are equal to such number of moles?

Calculate a molar mass of Ca(OH)₂:

M_r(Ca(OH)₂)=40+216+21=74 g/mol.

Mass of 6 moles: m=υM_r =6 g74 g/mol =444 g.

6. To calculate a mass part of Sodium in Sodium Sulfate Na₂SO₄.

Calculate a molar mass of Sodium Sulfate М_r (Na₂SO₄) = 142 g/mol. 1 mole of Sodium Sulfate contains 2 moles of Sodium atoms. Its mass is equal to: m =2 A_r (Na) = 223 = 46 g.

Mass part  (Na) is the ratio of Sodium mass to total mass of substance:

7. To determine a mass part of waterless salt in crystalline hydrate.

M olar mass of crystalline hydrate of blue vitriol M_r(CuSO₄5H₂O)= M_r(CuSO₄)+5M_r(H₂O)=160+90=250 g/mol? One mole of hydrate (250 g) contains 160 g of waterless salt. We calculate Mass part  (CuSO₄) as ratio of Copper Sulfate mass to mass of hydrate: