Sure! Let's solve for the molarity of the glucose solution step-by-step.
### Step 1: Determine the molecular weight of glucose
The molecular formula for glucose is [tex]\(\text{C}_6\text{H}_{12}\text{O}_6\)[/tex]. To find the molecular weight, we sum the atomic weights of all the atoms in the molecule:
- Carbon (C): [tex]\(6 \times 12.01 \, \text{g/mol} = 72.06 \, \text{g/mol}\)[/tex]
- Hydrogen (H): [tex]\(12 \times 1.01 \, \text{g/mol} = 12.12 \, \text{g/mol}\)[/tex]
- Oxygen (O): [tex]\(6 \times 16.00 \, \text{g/mol} = 96.00 \, \text{g/mol}\)[/tex]
So, the total molecular weight of glucose is:
[tex]\[ 72.06 + 12.12 + 96.00 = 180.16 \, \text{g/mol} \][/tex]
### Step 2: Calculate the number of moles of glucose
Next, we convert the given mass of glucose (75.0 g) to moles using the molecular weight:
[tex]\[ \text{moles of glucose} = \frac{\text{mass of glucose}}{\text{molecular weight of glucose}} \][/tex]
[tex]\[ \text{moles of glucose} = \frac{75.0 \, \text{g}}{180.16 \, \text{g/mol}} \approx 0.4163 \, \text{mol} \][/tex]
### Step 3: Calculate the molarity of the solution
Molarity ([tex]\(M\)[/tex]) is defined as the number of moles of solute per liter of solution. We have 0.4163 moles of glucose and 8.96 liters of solution:
[tex]\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution}} \][/tex]
[tex]\[ \text{Molarity} = \frac{0.4163 \, \text{mol}}{8.96 \, \text{L}} \approx 0.0465 \, \text{M} \][/tex]
Therefore, the molarity of the solution is approximately 0.0465 M.
