Q13-125CP - Chemistry: Molecular Nature Of Matter And Change

Question

Is 50% by mass of methanol dissolved in ethanol different from 50% by mass of ethanol dissolved in methanol? Explain.

Step-by-Step Solution

Answer

Mole fraction of ethanol as a solute is 1.6 times smaller than mole fraction of methanol as solute.

Step 1: Methanol dissolved in ethanol

Calculating mole fractions of methanol and ethanol.

Mole fraction is the ratio of number of moles of one component of a solution or other mixture to the total number of moles representing all of the component.

 

Molecular mass of methanol =32g/mol

Molecular mass of ethanol = 46g/mol 

Ethanol density = 0.789 g/mL

Methanol density = 0.792 g/mL

50% methanol density= 0.9156g/ mL

50% ethanol density = 0.91384g/ mL

Consider the volume of solution is 100mL. Hence, the mass of methanol and mass of ethanol can be calculated as follow

$mass\hspace{0.33em}=\%CDV$

Where C is the concentration of methanol or ethanol, D is the density of methanol or ethanol and V is the volume of solution.

$mass\hspace{0.33em}of\hspace{0.33em}methanol=0.5\times 0.9156\times 100=45.78g$

$mass\hspace{0.33em}of\hspace{0.33em}ethanol=0.5\times 0.91384\times 100=45.69g$

Step 2: Mole fractions when methanol dissolved in ethanol

In this methanol dissolved in ethanol. So, we use 100mL of ethanol.

Hence, 100 mL mass of methanol $=0.9156\times 100=91.56g$

Mass of 50% methanol $=91.56-45.78=45.78g$

Mass of 100% ethanol $=0.798\times 100=78.9g$ 

Now calculate the moles of ethanol and moles of methanol by dividing their mass by molecular mass.

$$\begin{gathered} moles of methamol=\frac{45.78g}{32g/mol}=1.43mol \\ moles of ethanol=\frac{78.9g}{46g/mol}=1.72mol \end{gathered}$$

Mole fraction of solute methanol can be calculated by dividing its moles by total moles.

$$\begin{gathered} Total moles=1.43+1.72 \\ =3.15 \end{gathered}$$

$$\begin{gathered} moles fraction of methanol=\frac{1.43mol}{3.15mol} \\ =0.45 \end{gathered}$$

Hence, methanol present as solute in ethanol with mole fraction of 0.45

Step 3: Mole fraction when ethanol dissolved in methanol

In this case, ethanol dissolved in methanol. So, use 100mL of methanol.

Hence, in 100mL mass of ethanol $=0.91384\times 100=91.384g$ 

Mass of 50% ethanol $=91.384-45.69=45.69g$

Mass of 100% methanol $=0.792\times 100=79.2g$

Now calculate the moles of ethanol and moles of methanol by dividing their mass by molecular mass.

 $$\begin{gathered} moles of methamol=\frac{72.9g}{32g/mol}=2.48mol \\ moles of ethanol=\frac{45.69g}{46g/mol}=0.993mol \end{gathered}$$

Mole fraction of solute ethanol can be calculated by dividing its moles by total moles.

Total moles $=2.48+0.993=3.473moles$

$$\begin{gathered} Mole fraction of ethanol=\frac{0.993mol}{3.473mol} \\ =0.28 \end{gathered}$$

Thus, ethanol present as solute in methanol with mole fraction of 0.28. 

Step 4: Difference in both solution

From the above calculations it is clear that mole fraction of ethanol as a solute is 1.6 times smaller than mole fraction of methanol as solute.