In the previous section, we saw the details about Gram atomic mass (GAM). In this section we will see it's application. We will illustrate it using some examples:
Example 1: A sample of oxygen has a mass of 40 grams. How many oxygen atoms are present in it?
Solution:
1. Given mass of oxygen = 40 grams
2. 1 GAM of oxygen = 16 grams
3. How many GAMs are present in 40 grams?
Ans: 40⁄16 = 2.5
4. One GAM of any element will contain NA atoms of that element.
So number of oxygen atoms = 2.5 × NA = 2.5 × 6.022×1023
Example 2: A sample of helium has a mass of 40 grams. How many helium atoms are present in it?
Solution:
1. Given mass of helium = 40 grams
2. 1 GAM of helium = 4 grams
3. How many GAMs are present in 40 grams?
Ans: 40⁄4 = 10
4. One GAM of any element will contain NA atoms of that element.
So number of helium atoms = 10 × NA = 10 × 6.022×1023
Example 3: A sample of hydrogen has a mass of 40 grams. How many hydrogen atoms are present in it?
Solution:
1. Given mass of hydrogen = 40 grams
2. 1 GAM of hydrogen = 1 grams
3. How many GAMs are present in 40 grams?
Ans: 40⁄1 = 40
4. One GAM of any element will contain NA atoms of that element.
So number of hydrogen atoms = 40 × NA = 40 × 6.022×1023
Example 4: A sample of carbon has a mass of 120 grams. How many carbon atoms are present in it?
Solution:
1. Given mass of carbon = 120 grams
2. 1 GAM of carbon = 12 grams
3. How many GAMs are present in 120 grams?
Ans: 120⁄12 = 10
4. One GAM of any element will contain NA atoms of that element.
So number of carbon atoms = 10 × NA = 10 × 6.022×1023
In the next section, we will see two more examples
Example 1: A sample of oxygen has a mass of 40 grams. How many oxygen atoms are present in it?
Solution:
1. Given mass of oxygen = 40 grams
2. 1 GAM of oxygen = 16 grams
3. How many GAMs are present in 40 grams?
Ans: 40⁄16 = 2.5
4. One GAM of any element will contain NA atoms of that element.
So number of oxygen atoms = 2.5 × NA = 2.5 × 6.022×1023
Example 2: A sample of helium has a mass of 40 grams. How many helium atoms are present in it?
Solution:
1. Given mass of helium = 40 grams
2. 1 GAM of helium = 4 grams
3. How many GAMs are present in 40 grams?
Ans: 40⁄4 = 10
4. One GAM of any element will contain NA atoms of that element.
So number of helium atoms = 10 × NA = 10 × 6.022×1023
Example 3: A sample of hydrogen has a mass of 40 grams. How many hydrogen atoms are present in it?
Solution:
1. Given mass of hydrogen = 40 grams
2. 1 GAM of hydrogen = 1 grams
3. How many GAMs are present in 40 grams?
Ans: 40⁄1 = 40
4. One GAM of any element will contain NA atoms of that element.
So number of hydrogen atoms = 40 × NA = 40 × 6.022×1023
Example 4: A sample of carbon has a mass of 120 grams. How many carbon atoms are present in it?
Solution:
1. Given mass of carbon = 120 grams
2. 1 GAM of carbon = 12 grams
3. How many GAMs are present in 120 grams?
Ans: 120⁄12 = 10
4. One GAM of any element will contain NA atoms of that element.
So number of carbon atoms = 10 × NA = 10 × 6.022×1023
The above examples illustrate the method to find the number of atoms in any given sample
Gram Molecular mass
■ Let us start this discussion with an element with a simple atom. So we will take hydrogen.
1. Consider 1 GAM of hydrogen
2. We know that one GAM of any element will contain NA atoms of that element.
3. Now split it into groups. Each group should contain exactly two atoms
• Then 'number of groups' will be equal to NA ⁄2
4. Now consider any one group. It has two hydrogen atoms.
5. But two hydrogen atoms make up one hydrogen molecule. (Recall that hydrogen is diatomic. That is why it's molecule is written as H2)
6. So in one GAM of hydrogen atoms, there will be NA ⁄2 molecules of hydrogen
7. The converse is obvious:
■ If we want NA hydrogen molecules, we must take 2 GAM of hydrogen
• 1 GAM of hydrogen is 1 gram.
• So to get NA hydrogen molecules, we must take 2 grams of hydrogen atoms
• 1 GAM of hydrogen is 1 gram.
• So to get NA hydrogen molecules, we must take 2 grams of hydrogen atoms
■ Another example with oxygen:
1. Consider 1 GAM of oxygen
2. We know that one GAM of any element will contain NA atoms of that element.
3. Now split it into groups. Each group should contain exactly two atoms
• Then 'number of groups' will be equal to NA ⁄2
4. Now consider any one group. It has two oxygen atoms.
5. But two oxygen atoms make up one oxygen molecule. (Recall that oxygen is diatomic. That is why it's molecule is written as O2)
6. So in one GAM of oxygen atoms, there will be NA ⁄2 molecules of oxygen
7. The converse is obvious:
■ If we want NA oxygen molecules, we must take 2 GAM of oxygen
• 1 GAM of oxygen is 16 grams.
• So to get NA oxygen molecules, we must take 32 grams of oxygen atoms
8. Let in step (3), the groups contain exactly 3 atoms
• 1 GAM of oxygen is 16 grams.
• So to get NA ozone molecules, we must take 16 × 3 = 48 grams of oxygen atoms
• So to get NA oxygen molecules, we must take 32 grams of oxygen atoms
8. Let in step (3), the groups contain exactly 3 atoms
• Then 'number of groups' will be equal to NA ⁄3
9. Now consider any one group. It has three oxygen atoms.
10. But three oxygen atoms make up one ozone molecule. (Recall that oxygen is triatomic. That is why it's molecule is written as O3)
11. So in one GAM of oxygen atoms, there will be NA ⁄3 molecules of ozone
12. The converse is obvious:
■ If we want NA ozone molecules, we must take 3 GAM of oxygen • 1 GAM of oxygen is 16 grams.
• So to get NA ozone molecules, we must take 16 × 3 = 48 grams of oxygen atoms
■ Another example with sulphur:
1. Consider 1 GAM of sulphur
2. We know that one GAM of any element will contain NA atoms of that element.
3. Now split it into groups. Each group should contain exactly eight atoms
• Then 'number of groups' will be equal to NA ⁄8
4. Now consider any one group. It has eight sulphur atoms.
5. But eight sulphur atoms make up one sulphur molecule. (Recall that one sulphur molecule has eight sulphur atoms. That is why it's molecule is written as S8)
6. So in one GAM of sulphur atoms, there will be NA ⁄8 molecules of sulphur
7. The converse is obvious:
■ If we want NA sulphur molecules, we must take 8 GAM of sulphur
• 1 GAM of sulphur is 32 gram.
• So to get NA sulphur molecules, we must take 32 × 8 = 256 grams of sulphur atoms
• So to get NA sulphur molecules, we must take 32 × 8 = 256 grams of sulphur atoms
■ Another example with helium:
1. Consider 1 GAM of helium
2. We know that one GAM of any element will contain NA atoms of that element.
3. Now split it into groups. Each group should contain exactly one atom
• Then number of groups will be equal to NA
4. Now consider any one group. It has one helium atom.
5. But one helium atom is actually one helium molecule. (Recall that helium is mono atomic)
6. So in one GAM of helium atoms, there will be NA molecules of helium
7. The converse is obvious:
■ If we want NA helium molecules, we need take only 1 GAM of helium
• 1 GAM of helium is 4 grams.
• So to get NA helium molecules, we must take 4 grams of helium atoms
Consider a molecule of water. How many grams of water should we take so that, there will be NA molecules of water?
For this problem, we will use another approach:
1. If there is to be NA molecules of H2O, there must be:
• (NA × 2 = 2NA) hydrogen atoms and
• NA oxygen atoms
2. What is the mass of 2NA hydrogen atoms?
• Mass of NA atoms of any element is it's GAM
• So mass of NAhydrogen atoms is GAM of hydrogen which is equal to 1 gram
• So mass of 2NA hydrogen atoms = 2 × 1 = 2 grams
3. What is the mass of NA oxygen atoms?
• Mass of NA atoms of any element is it's GAM
• So mass of NA oxygen atoms is GAM of oxygen which is equal to 16 grams
4. It seems that 2 grams of hydrogen and 16 grams of oxygen will give us NA water molecules. Let us check:
5. Let us consider (2+16) = 18 grams of water. Let this '18 grams' consist of 2 grams of hydrogen and 16 grams of oxygen
6. We can group it in the following way:
• The 2NA hydrogen atoms (obtained from 2 grams of hydrogen) should be split into NA groups, so that, each group has 2 hydrogen atoms
• The NA oxygen atoms (obtained from 16 grams of oxygen) should be split into NA groups, so that, each group has 1 oxygen atoms
7. Thus the 2 grams of hydrogen is now split into NA groups. Let this be Set 1
• The 16 grams of oxygen is also now split into NA groups. Let this be Set 2
The two sets are shown in fig.10.3 below:
8. Both the sets have the same number (NA) of groups
• So each group from Set1 will get a partner from Set 2
9. When a group from Set 1 (consisting of two hydrogen atoms) enter into partnership with a group from Set 2 (consisting of one oxygen atom), we get a molecule (H2O) of water
10. Since there are NA groups in each set, we will get NA water molecules
11. Thus we can conclude: 18 grams of water will give NA water molecules
• So to get NA helium molecules, we must take 4 grams of helium atoms
In the above discussion, we were considering molecules of elements. Let us now consider molecules of compounds.
Consider a molecule of water. How many grams of water should we take so that, there will be NA molecules of water?
For this problem, we will use another approach:
1. If there is to be NA molecules of H2O, there must be:
• (NA × 2 = 2NA) hydrogen atoms and
• NA oxygen atoms
2. What is the mass of 2NA hydrogen atoms?
• Mass of NA atoms of any element is it's GAM
• So mass of NAhydrogen atoms is GAM of hydrogen which is equal to 1 gram
• So mass of 2NA hydrogen atoms = 2 × 1 = 2 grams
3. What is the mass of NA oxygen atoms?
• Mass of NA atoms of any element is it's GAM
• So mass of NA oxygen atoms is GAM of oxygen which is equal to 16 grams
4. It seems that 2 grams of hydrogen and 16 grams of oxygen will give us NA water molecules. Let us check:
5. Let us consider (2+16) = 18 grams of water. Let this '18 grams' consist of 2 grams of hydrogen and 16 grams of oxygen
6. We can group it in the following way:
• The 2NA hydrogen atoms (obtained from 2 grams of hydrogen) should be split into NA groups, so that, each group has 2 hydrogen atoms
• The NA oxygen atoms (obtained from 16 grams of oxygen) should be split into NA groups, so that, each group has 1 oxygen atoms
7. Thus the 2 grams of hydrogen is now split into NA groups. Let this be Set 1
• The 16 grams of oxygen is also now split into NA groups. Let this be Set 2
The two sets are shown in fig.10.3 below:
 |
| Fig.10.3 |
• So each group from Set1 will get a partner from Set 2
9. When a group from Set 1 (consisting of two hydrogen atoms) enter into partnership with a group from Set 2 (consisting of one oxygen atom), we get a molecule (H2O) of water
10. Since there are NA groups in each set, we will get NA water molecules
11. Thus we can conclude: 18 grams of water will give NA water molecules
In the next section, we will see two more examples
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