Chemistry

Atoms and Molecules

Problems Based On Moles Of Atoms

We have just studied that:
1 mole of atoms of an element = Gram atomic mass of the element =

6.022X10

²³ atoms
This gives us three relations:
(i) The first relation is :
1 mole of atoms = Gram atomic mass
This relation is used to convert the moles of atoms into mass in grams,and also to convert mass in grams into moles of atoms.
(ii) The second relation is :
1 mole of atoms = $6.022X10$ ²³ atoms
By using this relation we can convert the moles of atoms into number of atoms,and the number of atoms into moles of atoms.
(iii) The third relation is:
Gram atomic mass = $6.022X10$ ²³atoms
This relation is used to find out the number of atoms in a given mass of the element and also to calculate the mass of a given number of atoms.
We should remember these three relations because they will be used to solve numerical problems based on the moles of atoms.Here are some examples.
Sample Problem 1.How many moles are 5 grams of calcium ?(Atomic mass of calcium = 40 u).
Solution.We know that :
1 mole of atoms = Gram atomic mass
So,1 mole of calcium atoms = Gram atomic mass of calcium
= 40 g
Now,40 g of calcium = 1 mole of calcium
So,5 g of calcium =

\frac{1}{40}

x 5 mole
=

\frac{1}{8}

mole.
= 0.125 mole
Thus,there are 0.125 mole in 5 grams of calcium.
Note.The above problem can also be solved directly by using the formula :
Number of moles
of atoms =

\frac{Mass of element in grams}{Gram atomic mass of element}

\frac{5}{40}

\frac{1}{8}

= 0.125 mole
Thus, 5 grams of calcium constitute 0.125 mole of calcium.
A yet another way of writing the above formula is by using the term 'molar mass' in place of gram atomic mass .That is
Number of moles
of atoms=

\frac{Mass of element}{Molar mass of element}

In the above case,mass of element is 5 grams and molar mass of element is 40 g/mol.
Sample Problem 2.What is the mass of 4 moles of aluminium atoms ?
(Atomic mass of A1 = 27 u)
Solution.The atomic mass of aluminium is given to be 27 u.This means that 1 mole of aluminium atoms has a mass of 27 grams.
Now, 1 mole of aluminium atoms = 27 g
So,4 moles of aluminium atoms = 27x4 g
= 108 g
Thus,the mass of 4 moles of aluminium atoms is 108 grams.
Sample Problem 3.Calculate the number of atoms in 0.2 mole of sodium (Na).
Solution.We know that 1 mole of atoms contains

6.022X10

²³ atoms.
Now,
1 mole of sodium atoms =

6.022X10

²³ atoms
So,0.2 mole of sodium atoms =

6.022X10

²³ x0.2 atoms
=

12.044X10

²² atoms
Thus, 0.2 mole of sodium element has

12.044X10

²² atoms in it.
Sample Problem 4.How many moles are 9.033 x 1024 atoms of helium (He) ?
Solution.We know that:

6.022X10

²³atoms of helium = 1 mole
So,

9.033X10

²⁴ atoms of helium =

\frac{1}{6.022X1023}

9.033X10

²⁴
= 15 moles (or 15 mol)
Thus,

9.033X10

²⁴ atoms of helium are 15 moles of atoms.
Sample Problem 5.Calculate the number of iron atoms in a piece of iron weighing 2.8 g (Atomic mass of iron = 56 u).
Solution.1 mole of iron = Gram atomic mass of iron
= 56 grams
We know that 1 mole of iron element contains

6.022X10

²³ atoms of iron.
Now, 56 g of iron contains =

6.022X10

²³ atoms
So,2.8 g of iron contains =

\frac{6.022X1023}{56}

x2.8
=

\frac{6.022X1022}{2}

3.011x10

²² atoms
Thus,a piece of iron metal having a mass of 2.8 grams contains

3.011x10

²² atoms atoms of iron.
Sample Problem 6. If one mole of carbon atoms weighs 12 grams, what is mass in grams of 1 atom of carbon ?
Solution. 1 mole of carbon atoms means

6.022x10

²³ carbon atoms.In this case 1 mole of carbon atoms weighs 12 grams. This means that the mass of

6.022x10

²³ atoms of carbon is 12 grams.
Now,

6.022x10

²³atoms of carbon have mass = 12 g
So,1 atom of carbon has mass =

\frac{12}{6.022X1023}

1.99x10

^-23g
Thus,the absolute mass of 1 atom of carbon is

1.99x10

^-23 gram.
Sample Problem 7.Which has more number of atoms,100 grams of sodium or 100 grams of iron ?(Atomic masses : Na = 23 u ; Fe = 56 u)
Solution In order to solve this problem,we should convert 100 grams of sodium into moles of sodium,and also 100 grams of iron into m'oles of iron. The element having more moles will have more atoms.Please note that since the atomic mass of sodium is 23 u,the molar mass of sodium will be 23 g/mol.Similarly, since the atomic mass of iron is 56 u,the molar mass of .ron wall be 56 g/mol. We will now calculate the moles of sodium atoms (Na) and iron atoms (Fe),one by one.
(i)Moles of sodium = math>Mass of sodiumMolar mass of sodium
=

\frac{100}{23}

= 4.34
(ii) Moles of iron =math>Mass of ironMolar mass of iron
=

\frac{100}{56}

= 1.78
We find that 100 grams of sodium contain 4.34 moles of atoms whereas 100 grams of iron contain 178 moles of atoms.Since 100 grams of sodium has more moles,it contains more atoms than 100 grams of iron.
Sample Problem 8. If 1 g of carbon contains x atoms, what will be the number of atoms m 1 g of magnesium ?(C=12 U,Mg=24 U)
Solution The ratio of atoms in carbon and magnesium will be the same as the ratio of their moles.So,first of all we should find out :
(i) moles of carbon in 1 gram of carbon,and
(ii) moles of magnesium in 1 gram of magnesium
This can be done as follows.
(a) 1 mole of carbon = Gram atomic mass of carbon
= 12 grams
Now,12 g of carbon = 1 mole
So,1 g of carbon =

\frac{1}{12}

mole
Thus, we have

\frac{1}{12}

mole of carbon element and it contains x atoms of carbon.Now, since an equal number of moles of all the elements contain an equal number of atoms, so

\frac{1}{12}

moles of magnesium will also contain x atoms of magnesium. We will now calculate the moles of magnesium in 1 gram of magnesium.
(b) 1 mole of magnesium = Gram atomic mass of magnesium
= 24 grams
Now, 24 g of magnesium = 1 mole
So,1 g of magnesium =

\frac{1}{24}

mole
We know that :

\frac{1}{12}

mole of magnesium contains = x atoms
So,

\frac{1}{24}

mole of magnesium contains=

\frac{x X 12}{24}

\frac{x}{2}

atoms
Thus, if 1 gram of carbon contains x atoms,then 1 gram of magnesium will have

\frac{x}{2}

atoms in it.
Sample Problem 9. How many grams of neon will have the same number of atoms as 4 grams of calcium ? (Atomic masses :Ne = 20 u, Ca = 40 u)
Solution.To solve such problems we should remember that "equal number of moles of all the elements contain equal number of atoms".
(i) Let us first convert 4 grams of calcium into moles. We have been given that the atomic mass of calcium is 40 u, so 1 mole of calcium is 40 grams.
Now, 40 g of calcium = 1 mole
So,4g of calcium =

\frac{1}{40}

x4 mole
=

\frac{1}{10}

mole Now,

\frac{1}{10}

mole of calcium will have the same number of atoms as

\frac{1}{10}

mole of neon. So, we should now convert

\frac{1}{10}

mole of neon into mass in grams.
(ii) The atomic mass of neon is 20 u,so 1 mole of neon will be equal to 20 grams.
Now,1 mole of neon = 20 g
So,

\frac{1}{10}

mole of neon =20 x

\frac{1}{10}

g
= 2g
Thus,2 grams of neon will contain the same number of atoms as 4 grams of calcium.
Sample Problem 10. The mass of a single atom of an element X is

2.65x10

^-23.What is its atomic mass ? What could this element be ?
Solution.The atomic mass of an element is numerically equal to the mass of 1 mole of its atoms.Since 1 mole of atoms is

6.022x10

²³ atoms,so it means that the atomic mass of an element is numerically equal to the mass of its

6.022x10

²³ atoms.
Now,1 atom of element X has mass =

2.65x10

^-23 g
So,

6.022x10

²³ atoms of element X have mass =

2.65x10

^-23x

6.022x10

²³
= 15.96 g
=16 g
Thus,the atomic mass of the element X is 16 u.The element of atomic mass 16 u is oxygen,having the symbol O.

Notes

Atoms and Molecules - Notes

1. Drawbacks of Dalton’s Atomic Theory