Considering the definition of percentage by mass and molality, the molality of Na₃PO₄ in the solution is 0.948 [tex]\frac{moles}{kg}[/tex].
The percentage by mass expresses the concentration and indicates the amount of mass of solute present in 100 grams of solution.
In other words, the percentage by mass of a component of the solution is defined as the ratio of the mass of the solute to the mass of the solution, expressed as a percentage.
The percentage by mass is calculated as the mass of the solute divided by the mass of the solution, the result of which is multiplied by 100 to give a percentage. This is:
[tex]percentage by mass=\frac{mass of solute}{mass of solution}x100[/tex]
Molality is the ratio of the number of moles of any dissolved solute to kilograms of solvent.
The Molality of a solution is determined by the expression:
[tex]molality=\frac{number of moles of solute}{kilograms of solvent}[/tex]
Considering 100 grams as a sample of the solution, then the value of the percentage of concentration given indicates that 13.5 g correspond to Na₃PO₄.
Remember that percent concentration by mass is calculated using the mass of solute and the mass of the solution, which includes both the solute and the solvent. Then:
mass solution= mass solute + mass solvent
100 g= 13.5 g + mass solvent
100 g - 13.5 g= mass solvent
86.5 g= mass solvent
Then, you know:
Then, replacing in the definition of molality:
[tex]molality=\frac{0.082 moles}{0.0865 kg}[/tex]
Solving:
molality= 0.948 [tex]\frac{moles}{kg}[/tex]
Finally, the molality of Na₃PO₄ in the solution is 0.948 [tex]\frac{moles}{kg}[/tex].
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