Question

The density of toluene (C7H8) is 0.867 g/mL, and the density of thiophene (C4H4S) is 1.065 g/mL. A solution is made by dissolving 8.10 g of thiophene in 250.0 mL of toluene.
(a) Calculate the mole fraction of thiophene in the solution.
(b) Calculate the molality of thiophene in the solution.
(c) Assuming that the volumes of the solute and solvent are additive, what is the molarity of thiophene in the solution?

Answer 1

Considering the solution of mole fraction, molality and molarity, you obtain that:

(a) the mole fraction of thiophene in the solution is 0.039.

(b) the molality of thiophene in the solution 0.4429 $\frac{moles}{kg}$.

(c)  the molarity of thiophene in the solution is 0.373$\frac{moles}{L}$.

You know that:

• Density toluene (C₇H₈)= 0.867 $\frac{g}{mL}$
• Density thiophene (C₄H₄S)= 1.065 $\frac{g}{mL}$
• Volume of toluene (C₇H₈)= 250 mL= 0.250 L (being 1000 mL= 1 L)
• Mass of thiophene (C₄H₄S)= 8.10 grams

• (a) Mole fraction

The molar 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.

Being the molar mass of each compound equals to:

• Toluene (C₇H₈)= 92 $\frac{g}{mol}$
• Thiophene (C₄H₄S)= 84 $\frac{g}{mol}$

the number of moles of each compound can be calculated as:

• Toluene (C₇H₈)= $250 mLx\frac{0.867 grams}{1 mL} x \frac{1 mole}{92 grams}$= 2.35 moles
• Thiophene (C₄H₄S)= $8.10 gramsx\frac{1 mole}{84 grams}$= 0.096 moles

The total moles is obtained from the addition of the moles of the solute (C₄H₄S) and the solvent (C₇H₈):

total moles = moles C₄H₄S + moles C₇H₈ = 0.096 moles + 2.35 moles = 2.45 moles

Then, the mole fraction of thiophene in the solution can be calculated as:

$mole fraction of thiophene=\frac{0.096 moles}{2.45 moles}$

Solving:

mole fraction of thiophene= 0.039

Finally, the mole fraction of thiophene in the solution is 0.039.

• (b) Molality

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:

$Molality=\frac{number of moles of solute}{kilograms of solvent}$

In this case, you know:

• number of moles of solute (C₄H₄S)= 0.096 moles
• Mass of solvent = $250 mLx\frac{0.867 grams}{1 mL}$ = 216.75 g = 0.21675 kg (being 1000 g=1 kg)  

Replacing:

$Molality C_{4} H_{4}S =\frac{0.096 moles}{0.21675 kg}$

molality C₄H₄S= 0.4429 $\frac{moles}{kg}$

Finally, the molality of thiophene in the solution 0.4429 $\frac{moles}{kg}$.

• (c) Molarity

Molarity is the number of moles of solute that are dissolved in a certain volume and is determined by the following expression:

$Molarity=\frac{number of moles of solute}{volume}$

Assuming that the volumes of solute and solvent are additive, you can add the volume of C₄H₄S and C₇H₈.

But first, you need yo know the volume of C₄H₄S, which can be calculated from the mass and density:

$Volume C_{4} H_{4}S =8.10 grams\frac{1 mL}{1.065 grams}$= 7.606 mL= 0.007606 L

Then, the total volume of the solution is calculated as:

total volume of the solution= volume C₇H₈ + volume C₄H₄S

total volume of the solution= 0.250 L + 0.007606 L = 0.257606 L

So, the molarity of thiophene in the solution can be calculated as:

$Molarity C_{4} H_{4} S=\frac{number of moles of C_{4} H_{4} S}{totalvolumeof the solution}$

Replacing:

$Molarity C_{4} H_{4} S=\frac{0.096 moles}{0.257606 L}$

Solving:

Molarity C₄H₄S= 0.373 $\frac{moles}{L}$

Finally, the molarity of thiophene in the solution is 0.373$\frac{moles}{L}$.

In summary, you get:

(a) the mole fraction of thiophene in the solution is 0.039.

(b) the molality of thiophene in the solution 0.4429 $\frac{moles}{kg}$.

(c)  the molarity of thiophene in the solution is 0.373$\frac{moles}{L}$.

Learn more about

• density:

1. brainly.com/question/952755?referrer=searchResults
2. brainly.com/question/1462554?referrer=searchResults

• mole fraction:

1. brainly.com/question/14434096?referrer=searchResults
2. brainly.com/question/10095502?referrer=searchResults

• molality

1. brainly.com/question/20366625?referrer=searchResults
2. brainly.com/question/4580605?referrer=searchResults

• molarity with this example:

1. brainly.com/question/15406534?referrer=searchResults