How many grams of benzoic acid (molar mass = 122.12 g/mol) must be dissolved in 9.00 g of lauric acid to create a solution with a molality of 0.910 mol/kg lauric acid? (Hint: Pay attention to units)
The Correct Answer and Explanation is :
To solve this, we use the definition of molality ((m)):
[
m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}
]
Here:
- (m = 0.910 \, \text{mol/kg}) (given)
- Mass of solvent (lauric acid) = (9.00 \, \text{g} = 0.00900 \, \text{kg})
- Molar mass of benzoic acid = (122.12 \, \text{g/mol})
We rearrange the formula for molality to calculate the moles of solute (benzoic acid):
[
\text{Moles of solute} = m \times \text{kilograms of solvent}
]
Substitute the values:
[
\text{Moles of solute} = 0.910 \, \text{mol/kg} \times 0.00900 \, \text{kg} = 0.00819 \, \text{mol}
]
Now, calculate the mass of benzoic acid required:
[
\text{Mass of benzoic acid} = \text{moles of benzoic acid} \times \text{molar mass of benzoic acid}
]
[
\text{Mass of benzoic acid} = 0.00819 \, \text{mol} \times 122.12 \, \text{g/mol} = 1.000 \, \text{g}
]
Final Answer:
1.00 g of benzoic acid must be dissolved in 9.00 g of lauric acid to achieve a molality of 0.910 mol/kg.
Explanation:
Molality is a measure of the concentration of a solution based on the number of moles of solute per kilogram of solvent. Here, we need to calculate the mass of benzoic acid (solute) that will provide the specified molality when dissolved in a given mass of lauric acid (solvent).
- First, convert the mass of the solvent into kilograms because molality is defined using kilograms.
- Use the molality formula to find the required moles of solute.
- Convert the moles of solute to mass using the molar mass of benzoic acid.
This step-by-step process ensures the units are consistent and yields an accurate result.