To find the molarity and molality of a 10% (by mass) glucose solution, we can follow these steps:
### Step 1: Understand the Given Information
- Molar mass of glucose = 180 g/mol
- The solution is 10% glucose by mass, meaning there are 10 grams of glucose in 100 grams of solution.
- The density of the solution = 1.2 g/mL.
### Step 2: Calculate the Mass of Solvent
Since the solution is 10% glucose by mass, the mass of the solvent (water) can be calculated as follows:
- Total mass of solution = 100 g
- Mass of glucose = 10 g
- Mass of water (solvent) = Total mass - Mass of glucose = 100 g - 10 g = 90 g.
### Step 3: Calculate the Number of Moles of Solute (Glucose)
Using the molar mass of glucose, we can find the number of moles of glucose:
\[
\text{Number of moles of glucose} = \frac{\text{mass of glucose}}{\text{molar mass of glucose}} = \frac{10 \, \text{g}}{180 \, \text{g/mol}} = \frac{1}{18} \, \text{mol} \approx 0.556 \, \text{mol}.
\]
### Step 4: Calculate Molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
\[
\text{Molality} = \frac{\text{Number of moles of solute}}{\text{mass of solvent in kg}} = \frac{0.556 \, \text{mol}}{0.090 \, \text{kg}} \approx 6.18 \, \text{mol/kg}.
\]
### Step 5: Calculate the Volume of the Solution
To find the volume of the solution, we can use the density:
\[
\text{Density} = \frac{\text{mass}}{\text{volume}} \implies \text{Volume} = \frac{\text{mass}}{\text{density}}.
\]
Substituting the values:
\[
\text{Volume of solution} = \frac{100 \, \text{g}}{1.2 \, \text{g/mL}} = \frac{100}{1.2} \approx 83.33 \, \text{mL} = 0.08333 \, \text{L}.
\]
### Step 6: Calculate Molarity
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[
\text{Molarity} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in L}} = \frac{0.556 \, \text{mol}}{0.08333 \, \text{L}} \approx 6.67 \, \text{mol/L}.
\]
### Final Answers
- Molarity = 6.67 M
- Molality = 6.18 m
