Question

An aqueous solution is 15.0 % methanol (CH4O) by mass and has a density of 0.998 g/mL. Calculate thed. Mole %e. Mass %

Answer 1

(d) Mole % = 9.02%

(e) Mass % = 15.0%

Step-by-step explanation

Given that:

% methanol by mass of the aqueous solution = 15.0%

Density of methanol = 0.998 g/mol

What to find:

To calculate (d) Mole % (e) Mass %

Step-step solution:

(d) Mole %

You need to pick a sample volume of this solution and use the given density to find its mass.

Let's take a 1.00 L sample of this solution. The solution has a density of

0.998 g/mL, meaning that you get 0.998 g for every 1 mL of solution.

The mass of the 1.00 L sample will thus be:

`\begin{gathered} Mass=Density* Volume=0.998g\text{/}mL*(1.00*1000mL) \\ \\ Mass=998\text{ }g \end{gathered}`

Now, it is known that this solution is 15.0% w/w methanol. In simple terms, this tells you that you get 15.0 g of ethanol for every 100 g of solution.

So the sample will contain:

`998g\text{ }solution*\frac{15g\text{ }methanol}{100g\text{ }solution}=149.7g\text{ }methanol`

This implies that the solution will also contain:

`\begin{gathered} Mass\text{ }of\text{ }solution=Mass\text{ }of\text{ }water-mass\text{ }of\text{ }methanol \\ \\ 998g=Mass\text{ }of\text{ }water-149.7g \\ \\ Mass\text{ }of\text{ }water=998g-149.7g=848.30g \end{gathered}`

To get the mole % of methanol, you must determine how many moles of methanol and of water the solution contains.

`\begin{gathered} Moles\text{ }of\text{ }methanol=\frac{mass}{molar\text{ }mass}=\frac{149.7g}{32.04g\text{/}mol}=4.67\text{ }mol \\ \\ Moles\text{ }of\text{ }water=\frac{848.30g}{18.02g\text{/}mol}=47.08\text{ }mol \end{gathered}`

Hence, the mole % of methanol will be:

`\begin{gathered} Mole\text{ }\%\text{ }methanol=\frac{moles\text{ }of\text{ }methanol}{Total\text{ }mole}*100\%=\frac{4.67\text{ }mol}{\placeholder{⬚}} \\ \\ Mole\text{ }\%\text{ }methanol=\frac{4.67\text{ }mol}{4.67\text{ }mol+47.08\text{ }mol}*100\%=9.02\% \end{gathered}`

Hence, the mole % methanol of the aqueous solution is 9.02%.

(e) Mass %

The mass % of methanol in the aqueous solution has been given in the question to be 15.0%.

Also, you can calculate it from the masses of methanol and water above as follows:

`\begin{gathered} Mass\text{ }\%\text{ }methanol=\frac{mass\text{ }of\text{ }methanol}{Total\text{ }mass}*100\% \\ \\ Mass\text{ }\%\text{ }methanol=(149.7g)/(998g)*100\%=15.0\% \end{gathered}`