Calculate the molality of a 9.2 M solution of perchloric acid given that the density of this solution is 1.54 g/mL.

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06-02-2020
Chemistry

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Calculate the molality of a 9.2 M solution of perchloric acid given that the density of this solution is 1.54 g/mL.

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Аноним Аноним · Answer 1 · 2020-02-06T06:57:52+01:00

Answer: The molality of perchloric acid in the solution is 14.95 m

Explanation:

We are given:

Molarity of perchloric acid solution = 9.2 M

This means that 9.2 moles of perchloric acid are contained in 1 L or 1000 mL of solution

To calculate the number of moles, we use the equation:

[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]

Moles of perchloric acid = 9.2 moles

Molar mass of perchloric acid = 100.5 g/mol

Putting values in above equation, we get:

[tex]9.2mol=\frac{\text{Mass of perchloric acid}}{100.5g/mol}\\\\\text{Mass of perchloric acid}=(9.2mol\times 100.5g/mol)=924.6g[/tex]

To calculate mass of a substance, we use the equation:

[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex]

Density of solution = 1.54 g/mL

Volume of solution = 1 L = 1000 mL

Putting values in above equation, we get:

[tex]1.54 g/mL=\frac{\text{Mass of solution}}{1000mL}\\\\\text{Mass of solution}=(1.54g/mL\times 1000mL)=1540g[/tex]

We are given:

Mass of solute (perchloric acid) = 924.6 grams

Mass of solution = 1540 grams

Mass of solvent = Mass of solution - mass of solute = [1540 - 924.6] g = 615.4 g

To calculate the molality of solution, we use the equation:

[tex]\text{Molality}=\frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ (in grams)}}[/tex]

Where,

[tex]m_{solute}[/tex] = Given mass of solute (perchloric acid) = 924.6 g

[tex]M_{solute}[/tex] = Molar mass of solute (perchloric acid) = 100.5 g/mol

[tex]W_{solvent}[/tex] = Mass of solvent = 615.4 g

Putting values in above equation, we get:

[tex]\text{Molality of perchloric acid}=\frac{924.6\times 1000}{100.5\times 615.4}\\\\\text{Molality of perchloric acid}=14.95m[/tex]

Hence, the molality of perchloric acid in the solution is 14.95 m

CintiaSalazar CintiaSalazar · Answer 2 · 2022-02-03T14:31:54+01:00

Considering the definition of molality, the molality of a 9.2 M solution of perchloric acid is 14.95 [tex]\frac{moles}{kg}[/tex].

Definition of molality

Molality is a measure of concentration that is defined as 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]

Molality is expressed in units [tex]\frac{moles}{kg}[/tex].

Number of moles of solute

Being the molarity is the number of moles of solute that are dissolved in a certain volume a molarity of 9.2 M means that 9.2 moles of perchloric acid are contained in 1 L or 1000 mL of solution.

Then, the number of moles of solute is 9.2 moles of perchloric acid.

Kilograms of solvent

In first place, density is the ratio of the weight (mass) of a substance to the volume it occupies. So, a density of 1.54 [tex]\frac{g}{mL}[/tex]means that you have 1.54 grams per 1 mL of solution or 1540 grams per 1 L (1000 mL) of solution. So, the mass of solution is 1540 grams in 1 L of solution

The mass of solution is the sum between the mass of solute and the mass of solvent.

Being the moles of perchloric acid 9.2 moles and the molar mass of perchloric acid 100.5 [tex]\frac{g}{mole}[/tex], the mass of the solute perchloric acid is calculated as:

mass of solute= number of moles of solute× molar mass

mass of solute= 9.2 moles× 100.5 [tex]\frac{g}{mole}[/tex]

mass of solute= 924.6 grams

Considering 1 L of solution, then, the mass of solvent is calculated as:

mass of solution= mass of solute +the mass of solvent

1540 grams = 924.6 grams +the mass of solvent

1540 grams - 924.6 grams= mass of solvent

615.4 grams= 0.6154 kg= mass of solvent

Finally, the mass of solvent is 0.6154 kg.

Molality of a 9.2 M solution of perchloric acid

So, being the number of moles of solute 9.2 moles and mass of solvent 0.6154 kg, the molality is calculated as:

[tex]Molality=\frac{9.2 moles}{0.6154 kg}[/tex]

Molality= 14.95 [tex]\frac{moles}{kg}[/tex]

Finally, the molality of a 9.2 M solution of perchloric acid is 14.95 [tex]\frac{moles}{kg}[/tex].

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