To determine the number of molecules of glucose in a 750.0 g sample, we'll need to follow a series of steps rooted in chemistry and stoichiometry. Here's a detailed breakdown of the solution:
1. Determine the Molar Mass of Glucose (C₆H₁₂O₆):
Glucose (C₆H₁₂O₆) consists of 6 carbon (C) atoms, 12 hydrogen (H) atoms, and 6 oxygen (O) atoms.
- The atomic mass of carbon (C) is approximately 12.01 g/mol.
- The atomic mass of hydrogen (H) is approximately 1.008 g/mol.
- The atomic mass of oxygen (O) is approximately 16.00 g/mol.
Calculate the molar mass of glucose:
[tex]\[
\text{Molar mass of C₆H₁₂O₆} = (6 \times 12.01) + (12 \times 1.008) + (6 \times 16.00)
= 72.06 + 12.096 + 96.00 = 180.156 \text{ g/mol}
\][/tex]
2. Calculate the Number of Moles of Glucose in the Sample:
Use the given mass of the glucose sample and the molar mass calculated above.
[tex]\[
\text{Moles of glucose} = \frac{\text{mass of glucose sample}}{\text{molar mass of glucose}} = \frac{750.0 \text{ g}}{180.156 \text{ g/mol}}
= 4.163058682475188 \text{ moles}
\][/tex]
3. Determine the Number of Molecules:
Avogadro's number tells us that 1 mole of any substance contains [tex]\(6.022 \times 10^{23}\)[/tex] molecules.
[tex]\[
\text{Number of molecules} = \text{moles of glucose} \times \text{Avogadro's number}
= 4.163058682475188 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole}
= 2.506993938586558 \times 10^{24} \text{ molecules}
\][/tex]
Therefore, in a 750.0 g sample of glucose, there are [tex]\( \mathbf{2.506993938586558 \times 10^{24}} \)[/tex] molecules of glucose.
