Question

mass of lauric acid = 8.001g

mass of benzoic acid = 1.001g

freezing temperature of pure lauric acid = 43.3 c

freezing point of the benzoic acid- lauric acid mix = 38.3 c

1- calculate the molality(m), in mol/kg, using the formula delta(t) = Kf * m. the Kf value for lauric acid is 3.9 C*Kg/mol

2- Calculate moles of benzoic acid solute, using the molality and the mass in (kg) of lauric acid solvent.

3- calculate the experimental molecular weight of benzoic acid, in g/mol.

4-Determine the accepted molecular weight of benzoic acid from its formula, C6H5COOH.

5- Calculate the percent discrepancy between the experimental and accepted values.

Answer 1

Answer 2

Given Data:

• Mass of lauric acid (solvent): 8.001 g = 0.008001 kg

• Mass of benzoic acid (solute): 1.001 g

• Freezing point of pure lauric acid ($T_f$): 43.3°C

• Freezing point of mixture ($T_{mix}$): 38.3°C

• Cryoscopic constant ($K_f$) for lauric acid: 3.9 °C·kg/mol

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Step 1: Calculate Molality ($m$)

Freezing point depression ($\mathrm{\Delta }{T}_f$):

$$\mathrm{\Delta }{T}_f=T_f-T_{mix}=43.3-38.3=5.0\text{°C}$$

Using $\mathrm{\Delta }{T}_f=K_f\cdot m$:

$$m=\frac{\mathrm{\Delta }{T}_f}{K_f}=\frac{5.0}{3.9}=1.282\text{mol/kg}$$

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Step 2: Calculate Moles of Benzoic Acid

Molality ($m$) = moles of solute / kg of solvent:

$$\text{Moles of benzoic acid}=m\times \text{mass of lauric acid (kg)}=1.282\times 0.008001=0.01026\text{mol}$$

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Step 3: Calculate Experimental Molecular Weight (MW)

$$\text{MW}=\frac{\text{mass of benzoic acid (g)}}{\text{moles}}=\frac{1.001}{0.01026}=97.56\text{g/mol}$$

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Step 4: Accepted Molecular Weight of Benzoic Acid

Formula ($C_6{H}_{5}COOH$):

$$\text{MW}=(7\times 12.01)+(6\times 1.01)+(2\times 16.00)=122.12\text{g/mol}$$

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Step 5: Percent Discrepancy

$$\text{Discrepancy}=\mid \frac{\text{Experimental MW}-\text{Accepted MW}}{\text{Accepted MW}}\mid \times 100=\mid \frac{97.56-122.12}{122.12}\mid \times 100=20.1\mathrm{\%}$$

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Answers:

1. Molality ($m$): 1.28 mol/kg (3 sig figs)

2. Moles of benzoic acid: 0.0103 mol (3 sig figs)

3. Experimental MW: 97.6 g/mol (3 sig figs)

4. Accepted MW: 122.12 g/mol

5. Percent discrepancy: 20.1%