Caffeine (C₈H₁₀N₄O₂) is a stimulant found in coffee and tea. A solution of caffeine in the solvent chloroform (CHCl₃) has a concentration of 0.0490 m.a. Calculate the percentage of caffeine by mass in the solution.b. Calculate the mole fraction of caffeine in the solution.

Question

13-01-2020
Chemistry

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Caffeine (C₈H₁₀N₄O₂) is a stimulant found in coffee and tea. A solution of caffeine in the solvent chloroform (CHCl₃) has a concentration of 0.0490 m.a. Calculate the percentage of caffeine by mass in the solution.b. Calculate the mole fraction of caffeine in the solution.

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jufsanabriasa jufsanabriasa · Answer 1 · 2020-01-14T20:53:08+01:00

Answer:

a. 0.952%

b. Mole fraction 0.00587.

Explanation:

In chemistry, concentration is defined as an amount of solute per amount of solution.

In the problem, caffeine is acting as solute and chloroform is the solvent.

0.0490m is 0.0490 mol of solute / kg of solution.

a. To obtain percentage by mass it is necessary to convert moles of caffeine in kg of solute, thus:

0.0490 mol Caffeine × (194.22g / mol) × (1kg / 1000g) = 0.00952 kg caffeine

194.22 g/mol is molar mass of Caffeine C₈H₁₀N₄O₂ (12,01g/mol×8 + 1.01g/mol×10 + 14.01g/mol×4 + 16.00g/mol×2 = 194.22g/mol)

Percentage by mass is:

0.00952 kg Caffeine / kg of solution ×100 = 0.952%

b. To obtain mole fraction it is necessary to find moles of chloroform, thus:

1 kg solution = Xkg chloroform + 0.00952 kg caffeine

0.99048 kg of chloroform × (1000g / 1kg) × (1mol / 119.37g) = 8.30 moles of chloroform

Molar mass of CHCl₃ 12,01g/mol×1 + 1.01×1 + 35.45g/mol×3 = 119.37g/mol

Thus, mole fraction of caffeine is:

0.0490 mol Caffeine / 8.30 moles chloroform + 0.0490 moles of caffeine = 0.00587

I hope it helps!

CintiaSalazar CintiaSalazar · Answer 2 · 2022-01-20T11:57:13+01:00

Considering the definition of molality, percentage by mass and mole fraction:

The percentage by mass of the solution is 0.952%.
The mole fraction of caffeine in the solution is 0.00587.

Molality

Molality is the ratio of the number of moles of any dissolved solute to kilograms of solvent. Molality is expressed in units [tex]\frac{moles}{kg}[/tex].

Then, 0.0490 m represents [tex]\frac{0.0490mol of solute}{kg of solution}[/tex], where caffeine is acting as solute and chloroform is the solvent.

Percentage by mass

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 mass 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]

In this case:

mass of solute= 0.0490 moles× 194.22 [tex]\frac{g}{mole}[/tex] × [tex]\frac{1 kg}{1000 g}[/tex]= 0.00952 kg caffeine where 194.22 [tex]\frac{g}{mole}[/tex] is molar mass of Caffeine
mass of solution= 1 kg

Then, the percentage by mass is calculated as:

[tex]Percentage by mass= \frac{0.00952 kg}{1 kg} x100[/tex]

Solving:

Percentage by mass= 0.952%

The percentage by mass of the solution is 0.952%.

Mole fraction

The mole fraction is a way of measuring the concentration that expresses the proportion in which a substance is found with respect to the total moles of the solution.

Remembering that caffeine is acting as solute and chloroform is the solvent, in first place you need to obtain the amount of moles of chloroform, knowing that:

1 kg solution = X kg chloroform + 0.00952 kg caffeine

So:

1 kg solution - 0.00952 kg caffeine= X kg chloroform

0.99048 kg of chloroform= X kg chloroform

Then, the amount of moles of chloroform is calculated as:

0.99048 kg of chloroform× [tex]\frac{1 mole}{119.37 g}[/tex] × [tex]\frac{1000 g}{1 kg}[/tex]= 8.30 moles of chloroform, where 119.37 is the molar mass of chloroform

Finally, remembering thar the amount of moles of caffeine is 0.0490 moles, the amount of moles of solution is:

amount of moles of solution= amount of moles of chloroform + amount of moles of caffeine

amount of moles of solution= 8.30 moles + 0.0490 moles

amount of moles of solution= 8.349 moles

So, the mole fraction is calculated as:

[tex]Mole fraction of caffeine=\frac{amount of moles of caffeine}{amount of moles of solution}[/tex]

[tex]Mole fraction of caffeine=\frac{0.0490moles}{8.349moles}[/tex]

Mole fraction of caffeine= 0.00587

Finally, the mole fraction of caffeine in the solution is 0.00587.

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