Answer :
To find the number of molecules of glucose present in 1.8 grams of glucose, we need to follow a sequence of steps involving the molar mass of glucose and Avogadro's number.
### Step-by-Step Solution
Step 1: Determine the molar mass of glucose (C6H12O6).
The molar mass of glucose can be calculated by summing the atomic masses of all the atoms in a glucose molecule:
- Carbon (C): 6 atoms, atomic mass = 12.01 g/mol
- Hydrogen (H): 12 atoms, atomic mass = 1.008 g/mol
- Oxygen (O): 6 atoms, atomic mass = 16.00 g/mol
[tex]\[ \text{Molar mass of glucose} = (6 \times 12.01) + (12 \times 1.008) + (6 \times 16.00) \text{ g/mol} = 180.16 \text{ g/mol} \][/tex]
Step 2: Calculate the number of moles of glucose.
The number of moles ([tex]\( n \)[/tex]) is given by the formula:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} \][/tex]
Given:
- Mass of glucose = 1.8 g
- Molar mass of glucose = 180.16 g/mol
[tex]\[ n = \frac{1.8 \text{ g}}{180.16 \text{ g/mol}} \approx 0.00999112 \text{ mol} \][/tex]
Step 3: Use Avogadro's number to find the number of molecules.
Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex] molecules/mol. To find the number of molecules, multiply the number of moles by Avogadro's number:
[tex]\[ \text{Number of molecules} = \text{number of moles} \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of molecules} = 0.00999112 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 6.01665 \times 10^{21} \text{ molecules} \][/tex]
### Conclusion
Thus, the number of molecules of glucose present in 1.8 grams of glucose is approximately [tex]\( 6.01665 \times 10^{21} \)[/tex] molecules.
### Step-by-Step Solution
Step 1: Determine the molar mass of glucose (C6H12O6).
The molar mass of glucose can be calculated by summing the atomic masses of all the atoms in a glucose molecule:
- Carbon (C): 6 atoms, atomic mass = 12.01 g/mol
- Hydrogen (H): 12 atoms, atomic mass = 1.008 g/mol
- Oxygen (O): 6 atoms, atomic mass = 16.00 g/mol
[tex]\[ \text{Molar mass of glucose} = (6 \times 12.01) + (12 \times 1.008) + (6 \times 16.00) \text{ g/mol} = 180.16 \text{ g/mol} \][/tex]
Step 2: Calculate the number of moles of glucose.
The number of moles ([tex]\( n \)[/tex]) is given by the formula:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} \][/tex]
Given:
- Mass of glucose = 1.8 g
- Molar mass of glucose = 180.16 g/mol
[tex]\[ n = \frac{1.8 \text{ g}}{180.16 \text{ g/mol}} \approx 0.00999112 \text{ mol} \][/tex]
Step 3: Use Avogadro's number to find the number of molecules.
Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex] molecules/mol. To find the number of molecules, multiply the number of moles by Avogadro's number:
[tex]\[ \text{Number of molecules} = \text{number of moles} \times \text{Avogadro's number} \][/tex]
[tex]\[ \text{Number of molecules} = 0.00999112 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 6.01665 \times 10^{21} \text{ molecules} \][/tex]
### Conclusion
Thus, the number of molecules of glucose present in 1.8 grams of glucose is approximately [tex]\( 6.01665 \times 10^{21} \)[/tex] molecules.
