Question

What is the mass percent of sucrose in a solution obtained by mixing 225.0 g of an aqueous solution that is 6.25% sucrose by mass with 135.0 g of an aqueous solution that is 8.20% sucrose by mass?

Answer 1

Hint: Here there are two different masses of solutes in the solution. Firstly, we will find the mass percent of solute individually and then find out the mass percent of sucrose in the solution. As there is two mass percent of solute they will have to be added to get the mass of solute. Also, the mass of each aqueous solution will be added to get the total mass of the solution.

Complete Step By Step Answer:
6.25 % Sucrose by mass has a mass of 225.0 g and 8.20 % sucrose by mass has a mass of 135.0 g.
We will initially find the mass of each percent by the mass of sucrose.
 $6.25\mathrm{\%}Sucrosebymass={\displaystyle \frac{6.25}{100}}\times \text{ 225}\text{.0 = 14}\text{.06 g}$
 $8.20\mathrm{\%}Sucrosebymass\text{ = }{\displaystyle \frac{8.20}{100}}\times \text{ 135}\text{.0 = 11}\text{.07 g}$
Now, add the mass of both the mass percent to find the total mass of the solute in grams.
 $Total\text{ m}ass\text{ of Sucrose (Solute })\text{ = 14}\text{.06 + 11}\text{.07 = 25}\text{.13 g}$
For the total mass of solution add both the masses of aqueous solution (gram) present.
 $TotalMass\text{ of Aqueous Solution = 225}\text{.0 + 135}\text{.0 = 360 g}$
We know that mass percent is given by the ratio of the mass of solute and mass of solution into 100.
 $\Rightarrow Mass\mathrm{\%}={\displaystyle \frac{Mass\text{ of solute}}{Mass\text{ of solution}}}\times \text{ 100 }$
Put the values of solute and solution in the above formula we get,
 $\Rightarrow Mass\mathrm{\%}={\displaystyle \frac{25.13}{360}}\times \text{ 100 }$
 $\Rightarrow Mass\mathrm{\%}={\displaystyle \frac{\text{2513}}{360}}$
 $\Rightarrow Mass\mathrm{\%}=\text{ 6}\text{.9805}\mathrm{\%}$
The mass percent should be rounded off to get a whole number value.
 $\Rightarrow Mass\mathrm{\%}\approx \text{ 7}\text{.0 }\mathrm{\%}$
Therefore, mass percent of Sucrose in a solution = 7.0 %.

Note:
Mass percent is also referred to as percent by weight i.e. w/w %. The mass percent can be stated as the molar mass of the element can be taken in 1 mole of the compound. The mass percentage can be determined by using these masses of the elements.