Calculate the difference between molality and molarity of 40% NaOH (w/w). The density of the solution is 1.2 g/mL.
Understand the Problem
The question is asking to calculate the difference between molality and molarity for a 40% NaOH solution, given its density. This involves understanding the definitions of molality and molarity, as well as performing some calculations using the provided data.
Answer
The difference between molality and molarity is $4.67 \, \text{mol/kg}$.
Answer for screen readers
The difference between molality and molarity for a 40% NaOH solution is approximately $4.67 , \text{mol/kg}$.
Steps to Solve
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Calculate the mass of the solution To find the mass of the solution, we can assume 1 liter of solution. Using the density, we have: [ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \Rightarrow \text{Mass} = \text{Density} \times \text{Volume} ] [ \text{Mass} = 1.2 , \text{g/mL} \times 1000 , \text{mL} = 1200 , \text{g} ]
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Determine the mass of NaOH in the solution Since it is a 40% (w/w) solution, this means 40 grams of NaOH are present in every 100 grams of solution. Therefore, in 1200 g of solution: [ \text{Mass of NaOH} = 0.40 \times 1200 , \text{g} = 480 , \text{g} ]
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Calculate moles of NaOH To find the number of moles of NaOH, we use its molar mass. The molar mass of NaOH is approximately 40 g/mol. [ \text{Moles of NaOH} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{480 , \text{g}}{40 , \text{g/mol}} = 12 , \text{mol} ]
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Calculate the volume of solvent (water) in the solution The mass of the solvent (water) can be found by subtracting the mass of NaOH from the total mass of the solution: [ \text{Mass of water} = 1200 , \text{g} - 480 , \text{g} = 720 , \text{g} ] Next, convert the mass of water to liters, knowing the density of water is approximately 1 g/mL: [ \text{Volume of water} = \frac{720 , \text{g}}{1 , \text{g/mL}} = 720 , \text{mL} = 0.72 , \text{L} ]
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Calculate the molarity of the solution Molarity is defined as the number of moles of solute per liter of solution. Since we’ve found 12 moles of NaOH in 1 liter of solution: [ \text{Molarity} = \frac{\text{Moles of NaOH}}{\text{Volume of solution in L}} = \frac{12 , \text{mol}}{1 , \text{L}} = 12 , \text{M} ]
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Calculate the molality of the solution Molality is defined as the number of moles of solute per kilogram of solvent (water). We’ve calculated 12 moles of NaOH in 0.72 kg of water: [ \text{Molality} = \frac{\text{Moles of NaOH}}{\text{Mass of solvent in kg}} = \frac{12 , \text{mol}}{0.72 , \text{kg}} \approx 16.67 , \text{mol/kg} ]
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Calculate the difference between molality and molarity Finally, to find the difference: [ \text{Difference} = \text{Molality} - \text{Molarity} = 16.67 , \text{mol/kg} - 12 , \text{M} = 4.67 , \text{mol/kg} ]
The difference between molality and molarity for a 40% NaOH solution is approximately $4.67 , \text{mol/kg}$.
More Information
Molality and molarity are two different measures of concentration. Molarity measures how many moles of solute are in one liter of solution, while molality measures how many moles of solute are in one kilogram of solvent. This problem illustrates the importance of understanding both concepts when working with solutions.
Tips
- Confusing the definitions of molality and molarity.
- Forgetting to convert grams of water to kilograms when calculating molality.
- Not accounting for the density of the solution when calculating mass.
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