A solution is prepared by mixing30.mL pentane (C5H12, *d* = 0.63 g/cm3) with 65mL hexane (C6H14, *d* = 0.66 g/cm3). Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the pentane.

(a)

mass percent

%

(b)

mole fraction

(c)

molality

mol/kg

(d)

molarity

mol/L

To solve this problem, we'll proceed step by step for each part:

### Given Data:
- Volume of pentane (\( V_{\text{C5H12}} \)) = 30 mL
- Density of pentane (\( d_{\text{C5H12}} \)) = 0.63 g/cm³
- Volume of hexane (\( V_{\text{C6H14}} \)) = 65 mL
- Density of hexane (\( d_{\text{C6H14}} \)) = 0.66 g/cm³
- Molar mass of pentane (\( M_{\text{C5H12}} \)) = 72.15 g/mol
- Molar mass of hexane (\( M_{\text{C6H14}} \)) = 86.18 g/mol

### Step 1: Calculate the Masses
The mass of each component can be calculated using the formula:
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
For pentane:
\[
\text{Mass of pentane} = 0.63 \, \text{g/cm}^3 \times 30 \, \text{mL} = 18.9 \, \text{g}
\]
For hexane:
\[
\text{Mass of hexane} = 0.66 \, \text{g/cm}^3 \times 65 \, \text{mL} = 42.9 \, \text{g}
\]

### Step 2: Calculate the Total Mass
\[
\text{Total Mass} = 18.9 \, \text{g} + 42.9 \, \text{g} = 61.8 \, \text{g}
\]

### (a) Mass Percent of Pentane
\[
\text{Mass Percent of Pentane} = \left( \frac{\text{Mass of Pentane}}{\text{Total Mass}} \right) \times 100\%
\]
\[
\text{Mass Percent of Pentane} = \left( \frac{18.9 \, \text{g}}{61.8 \, \text{g}} \right) \times 100\% \approx 30.58\%
\]

### (b) Mole Fraction of Pentane
First, calculate the moles of each component:
\[
\text{Moles of Pentane} = \frac{18.9 \, \text{g}}{72.15 \, \text{g/mol}} \approx 0.262 \, \text{mol}
\]
\[
\text{Moles of Hexane} = \frac{42.9 \, \text{g}}{86.18 \, \text{g/mol}} \approx 0.498 \, \text{mol}
\]
Now, the total moles:
\[
\text{Total Moles} = 0.262 \, \text{mol} + 0.498 \, \text{mol} = 0.760 \, \text{mol}
\]
The mole fraction of pentane:
\[
\text{Mole Fraction of Pentane} = \frac{\text{Moles of Pentane}}{\text{Total Moles}} = \frac{0.262 \, \text{mol}}{0.760 \, \text{mol}} \approx 0.345
\]

### (c) Molality of Pentane
Molality is calculated as:
\[
\text{Molality} = \frac{\text{Moles of Solute (Pentane)}}{\text{Mass of Solvent (Hexane) in kg}}
\]
\[
\text{Molality} = \frac{0.262 \, \text{mol}}{0.0429 \, \text{kg}} \approx 6.11 \, \text{mol/kg}
\]

### (d) Molarity of Pentane
Molarity is calculated as:
\[
\text{Molarity} = \frac{\text{Moles of Solute (Pentane)}}{\text{Total Volume of Solution in L}}
\]
Total Volume = 30 mL + 65 mL = 95 mL = 0.095 L
\[
\text{Molarity} = \frac{0.262 \, \text{mol}}{0.095 \, \text{L}} \approx 2.76 \, \text{mol/L}
\]

### Final Answers:
- **(a) Mass Percent of Pentane**: \( \approx 30.58\% \)
- **(b) Mole Fraction of Pentane**: \( \approx 0.345 \)
- **(c) Molality of Pentane**: \( \approx 6.11 \, \text{mol/kg} \)
- **(d) Molarity of Pentane**: \( \approx 2.76 \, \text{mol/L} \)

Would you like more details on any part of this solution or have any other questions? Here are some related problems you might consider:

1. Calculate the mass percent of hexane in the solution.
2. Determine the density of the solution.
3. Calculate the volume percent of pentane in the solution.
4. Find the mole fraction of hexane.
5. How would the mass percent change if 50 mL of hexane was used instead?

**Tip:** Always ensure units are consistent when performing calculations, especially with volume and mass.

Learn how to calculate the mass percent, mole fraction, molality, and molarity of pentane in a solution made by mixing pentane and hexane. Detailed step-by-step solution with formulas and calculations provided.

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