Answer :
Let's tackle the question step by step for each part.
### Part 1: Number of Atoms in the Iron Sample
To determine the number of atoms in a sample given the number of moles, you need to use Avogadro's number, which is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms (or molecules) per mole.
Given:
- Number of moles: [tex]\( 0.490 \)[/tex] mol
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mol
We can calculate the number of atoms of iron as follows:
[tex]\[ \text{Number of atoms} = 0.490 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \][/tex]
This multiplication will yield:
[tex]\[ \text{Number of atoms} = 2.95078 \times 10^{23} \][/tex]
Therefore, the number of atoms in the sample if the substance is iron is:
[tex]\[ \boxed{2.95078 \times 10^{23} \, \text{atoms}} \][/tex]
### Part 2: Number of Atoms in the Titanium Sample
The approach is the same for titanium since the number of moles and Avogadro's number remain unchanged.
Given:
- Number of moles: [tex]\( 0.490 \)[/tex] mol
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mol
We can calculate the number of atoms of titanium as follows:
[tex]\[ \text{Number of atoms} = 0.490 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \][/tex]
This multiplication will yield:
[tex]\[ \text{Number of atoms} = 2.95078 \times 10^{23} \][/tex]
Therefore, the number of atoms in the sample if the substance is titanium is:
[tex]\[ \boxed{2.95078 \times 10^{23} \, \text{atoms}} \][/tex]
### Part 3: Number of Molecules in the Benzene Sample
For benzene ([tex]\( C_6H_6 \)[/tex]), we calculate the number of molecules using the same method as above.
Given:
- Number of moles: [tex]\( 0.490 \)[/tex] mol
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] molecules/mol
We can calculate the number of molecules of benzene as follows:
[tex]\[ \text{Number of molecules} = 0.490 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \][/tex]
This multiplication will yield:
[tex]\[ \text{Number of molecules} = 2.95078 \times 10^{23} \][/tex]
Therefore, the number of molecules in the sample if the substance is benzene is:
[tex]\[ \boxed{2.95078 \times 10^{23} \, \text{molecules}} \][/tex]
### Summary
- Iron: [tex]\( 2.95078 \times 10^{23} \)[/tex] atoms
- Titanium: [tex]\( 2.95078 \times 10^{23} \)[/tex] atoms
- Benzene ([tex]\( C_6H_6 \)[/tex]): [tex]\( 2.95078 \times 10^{23} \)[/tex] molecules
### Part 1: Number of Atoms in the Iron Sample
To determine the number of atoms in a sample given the number of moles, you need to use Avogadro's number, which is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms (or molecules) per mole.
Given:
- Number of moles: [tex]\( 0.490 \)[/tex] mol
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mol
We can calculate the number of atoms of iron as follows:
[tex]\[ \text{Number of atoms} = 0.490 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \][/tex]
This multiplication will yield:
[tex]\[ \text{Number of atoms} = 2.95078 \times 10^{23} \][/tex]
Therefore, the number of atoms in the sample if the substance is iron is:
[tex]\[ \boxed{2.95078 \times 10^{23} \, \text{atoms}} \][/tex]
### Part 2: Number of Atoms in the Titanium Sample
The approach is the same for titanium since the number of moles and Avogadro's number remain unchanged.
Given:
- Number of moles: [tex]\( 0.490 \)[/tex] mol
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mol
We can calculate the number of atoms of titanium as follows:
[tex]\[ \text{Number of atoms} = 0.490 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \][/tex]
This multiplication will yield:
[tex]\[ \text{Number of atoms} = 2.95078 \times 10^{23} \][/tex]
Therefore, the number of atoms in the sample if the substance is titanium is:
[tex]\[ \boxed{2.95078 \times 10^{23} \, \text{atoms}} \][/tex]
### Part 3: Number of Molecules in the Benzene Sample
For benzene ([tex]\( C_6H_6 \)[/tex]), we calculate the number of molecules using the same method as above.
Given:
- Number of moles: [tex]\( 0.490 \)[/tex] mol
- Avogadro's number: [tex]\( 6.022 \times 10^{23} \)[/tex] molecules/mol
We can calculate the number of molecules of benzene as follows:
[tex]\[ \text{Number of molecules} = 0.490 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \][/tex]
This multiplication will yield:
[tex]\[ \text{Number of molecules} = 2.95078 \times 10^{23} \][/tex]
Therefore, the number of molecules in the sample if the substance is benzene is:
[tex]\[ \boxed{2.95078 \times 10^{23} \, \text{molecules}} \][/tex]
### Summary
- Iron: [tex]\( 2.95078 \times 10^{23} \)[/tex] atoms
- Titanium: [tex]\( 2.95078 \times 10^{23} \)[/tex] atoms
- Benzene ([tex]\( C_6H_6 \)[/tex]): [tex]\( 2.95078 \times 10^{23} \)[/tex] molecules
