Question

If you had 325 grams of 5.0% by mass solution of citric acid, how many grams would be the acid and how many grams would be water? How many moles of citric acid would it contain?

Answer 1

We know that the mass percent of a solution is defined by the number of parts by mass of one component (solute or solvent) per 100 parts by mass of the solution. Here, we have to use the formula of mass percent, that is,
${\text{Mass}}\,\;{\text{percent}} = \dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{solute}}}} {{{\text{Mass}}\,{\text{of}}\,{\text{solution}}}} \times 100$

Complete step by step answer:
First, we have to calculate the mass of citric acid using the formula of mass percent. The mass of the solution is 325 g and mass percent is 5%.
$5 = \dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{citric}}\,{\text{acid}}}} {{325}} \times 100$
$\Rightarrow {\text{Mass}}\,{\text{of}}\,{\text{citric}}\,{\text{acid}} = \dfrac{{5 \times 325}} {{100}} = 16.25\,{\text{g}}$
Now, we can calculate the mass of solvent. We know that the mass of the solution is the summation of mass of solute and solvent.
Mass of solution=Mass of solute + Mass of solvent
$\Rightarrow 325\;{\text{g}} = 16.25\,{\text{g}} + {\text{Mass}}\,{\text{of}}\,{\text{solvent}}$
$\Rightarrow {\text{Mass}}\,{\text{of}}\,{\text{solvent}} = 325 - 16.25 = 308.75\,{\text{g}} \approx {\text{309}}\,{\text{g}}$
Now, we have to calculate the moles of citric acid. To calculate the number of moles, we have to use the below formula.
Number of moles=$\dfrac{{{\text{Mass}}}} {{{\text{Molar}}\,{\text{mass}}}}$
Here, we need to calculate the molar mass of citric acid $\left( {{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{8}}}{{\text{O}}_{\text{7}}}} \right)$
Molar mass of ${{\text{C}}_{\text{6}}}{{\text{H}}_{\text{8}}}{{\text{O}}_{\text{7}}} = 6 \times 12 + 8 \times 1 + 16 \times 7 = 72 + 8 + 112 = 192\,{\text{g}}\,{\text{mo}}{{\text{l}}^{ - 1}}$
The mass of citric acid is 16.25 g.
So,
The number of moles of citric acid=$\dfrac{{16.25\,{\text{g}}}} {{192\,{\text{g}}\,{\text{mo}}{{\text{l}}^{ - 1}}}} = 0.0845\,{\text{mol}}$
Hence,
Mass of water is 309 g
Mass of citric acid is 16.25 g
Moles of citric acid is 0.0845.

Note: It is to be remembered that both mass percent and volume percent are used to express concentration of the solution. Both are simply ratios and have no units. Concentration of a solution can also be expressed in terms of weight/volume (W/V). For example, 10% solution KCl (W/V) means that 10 g of the salt is dissolved in 100 mL of the solution.