Respuesta :
Molality is defined as the ratio of number of moles of solute to the mass of solvent in kilograms.
The formula of molality is:
[tex]Molality = \frac{number of moles of solute}{mass of solvent in kg}[/tex] - (1)
The formula of density is:
[tex]Density = \frac{mass}{volume}[/tex] - (2)
Consider, [tex]Volume = 1 L = 1000 mL[/tex]
Rearranging the formula (2):
[tex]mass of solution = density \times volume[/tex]
Substituting the values:
[tex]mass of solution = 1.143 g/mL \times 1000 mL = 1143 g[/tex]
Since, the aqueous solution is 50% by mass that is:
[tex]50 = \frac{mass of H_2SO_4}{mass of solution}\times 100[/tex]
Rearranging the equation:
[tex]mass of H_2SO_4 = \frac{50}{100}\times mass of solution[/tex]
[tex]mass of H_2SO_4 = \frac{50}{100}\times 1143 = 571.5 g[/tex]
Now, for determining the number of moles of [tex]H_2SO_4[/tex]:
[tex]n_{H_2SO_4 } = \frac{mass of H_2SO_4 }{Molar mass of H_2SO_4 }[/tex]
[tex]n_{H_2SO_4 } = \frac{571.5 g}{98.08 g/mol} = 5.83 moles[/tex]
[tex]mass of solvent = mass of solution - mass of solute[/tex]
[tex]mass of solvent = 1143 g - 571.5 g = 571.5 g = 0.5715 kg[/tex]
Substituting the values in formula (1):
[tex]molality = \frac{5.83 moles}{0.5715 kg} = 10.20 m[/tex]
Hence, the molality of the solution is [tex]10.20 m[/tex].
