To calculate molar mass from molality, you need additional information about the solution, specifically the mass of the solute in grams and the mass of the solvent in kilograms. Here's the step-by-step process:
Steps to Calculate Molar Mass from Molality
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Determine the molality (m) of the solution: Molality is defined as the number of moles of solute per kilogram of solvent. It will be given in units of mol/kg.
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Determine the mass of the solute (in grams): This value must be provided or derivable from other information given in the problem.
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Determine the mass of the solvent (in kilograms): This value must also be provided or derivable from other information given in the problem.
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Calculate the moles of solute: Use the following formula:
- moles of solute = molality (m) × mass of solvent (kg)
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Calculate the molar mass: Use the following formula:
- Molar mass (g/mol) = mass of solute (g) / moles of solute
Example
Let's say you have a solution with a molality of 0.5 mol/kg. You know that 10 grams of solute are dissolved in 2 kg of solvent. What is the molar mass of the solute?
- Molality (m): 0.5 mol/kg
- Mass of solute: 10 grams
- Mass of solvent: 2 kg
- Moles of solute: 0.5 mol/kg * 2 kg = 1 mole
- Molar mass: 10 g / 1 mole = 10 g/mol
Therefore, the molar mass of the solute is 10 g/mol.
Summary
In short, you calculate the number of moles of solute from the molality and the mass of the solvent, and then divide the mass of the solute (in grams) by the number of moles to find the molar mass.
