Question

What will be the mass percentage of the resulting solution prepared by mixing $\text{ 15 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$ $\text{ }\left( \text{w/w} \right)\text{ }$ 500 g aqueous solution of the area with $\text{ 25 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$$\text{ }\left( \text{w/w} \right)\text{ }$400 g aqueous solution of it?
A) $\text{ 18 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$
B) $\text{ 20 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$
C) $\text{ 25 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$
D) $\text{ 15 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$

Answer 1

Hint: Percentage by weight is a way of representing the concentration of the solution.it can be given by the symbol$\text{ }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$. -It is generally expressed as,
$\text{ Percent by weight }\left( \text{w/w} \right){\scriptstyle{}^{\text{0}}/{}_{\text{0}}}\text{ = }\dfrac{\text{gram of solute}}{\text{100 g of solution}}\text{ }$
Mass fraction or the weight fraction is defined as the ratio of the mass of a component in the mixture to the total mass or weight of the solution.

Complete Solution :
Solutions can be described in various concentration units such as normality, molarity, molality, etc. However, solutions can be sometimes expressed as the relative concentration percentage of solute to the solution. It is generally expressed as,
$\text{ Percent by weight }\left( \text{w/w} \right){\scriptstyle{}^{\text{0}}/{}_{\text{0}}}\text{ = }\dfrac{\text{gram of solute}}{\text{100 g of solution}}\text{ }$

- We have given the following data in question:
The mass percentage of $\text{ }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$ the first solution is equal to $\text{ 15 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$ .
The weight of the first aqueous solution is equal to 500 g.
Mass percentage of $\text{ }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$ the second solution is equal to $\text{ 25 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$
Weight of the first aqueous solution is equal to 400 g.

- We are interested in determining the mass percentage of the resulting solution.
We have given that $\text{ }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$of the first solution is 15. Thus we can write the $\text{ }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$as shown below,
$\begin{align}
  & \text{ 15 = }\dfrac{\text{500}}{\text{weight of solution (}{{\text{X}}_{\text{1}}}\text{)}}\text{ }\!\!\times\!\!\text{ 100 } \\
 & \Rightarrow {{\text{X}}_{\text{1}}}\text{ = }\dfrac{\left( 500 \right)\left( 100 \right)}{15} \\
 & \Rightarrow {{\text{X}}_{\text{1}}}=\text{ }\dfrac{{{\left( 10 \right)}^{4}}}{3}\text{ } \\
\end{align}$

- Similarly, the mole fraction $\text{ }{{\text{X}}_{\text{2}}}\text{ }$ for the second solution is calculated as follows, $\begin{align}
  & \text{ 25 = }\dfrac{\text{400}}{\text{weight of solution (}{{\text{X}}_{2}}\text{)}}\text{ }\!\!\times\!\!\text{ 100 } \\
 & \Rightarrow {{\text{X}}_{2}}\text{ = }\dfrac{\left( 400 \right)\left( 100 \right)}{25} \\
 & \Rightarrow {{\text{X}}_{2}}=\text{ 1600} \\
\end{align}$

- The total composition of the mixture would be equal to the ratio of the sum of the mass of the first and second solutions combined to the total eight of the solution. The total $\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$of the solution is also expressed in weight fraction. As follows, $\text{ Total}\left( \text{w/w} \right){\scriptstyle{}^{\text{0}}/{}_{\text{0}}}\text{ of mixture = weight fraction }\!\!\times\!\!\text{ 100 = }\dfrac{{{\text{W}}_{\text{comp1}}}\text{+ }{{\text{W}}_{\text{comp2}}}}{\text{weight of solution}}\text{ }$
Thus the total $\text{ }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$ composition of the solution prepared by combining the $\text{ 15 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$and $\text{ 25 }{\scriptstyle{}^{0}/{}_{0}}\text{ }$of the $\text{ }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }$composition is determined as follows,
$\begin{align}
  & \text{ Total }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ }=\text{ }\left[ \dfrac{500+400}{\dfrac{{{10}^{4}}}{3}+1600} \right]\text{ }\times \text{100} \\
 & \Rightarrow \text{Total }\left( \text{w/w} \right){\scriptstyle{}^{0}/{}_{0}}\text{ = }\dfrac{900}{33.3+16}\text{ = }\dfrac{900}{49.3}\simeq \text{ 18}{\scriptstyle{}^{0}/{}_{0}} \\
\end{align}$
Thus weight by weight percentage composition of the resulting solution is equal to\[\text{18}{\scriptstyle{}^{0}/{}_{0}}\].
So, the correct answer is “Option A”.

Note: Note that, the weight by weight concentration is used in solid solutions. The Sum of all the mass fraction or the weight fraction in the solution is always equal to unity. It is independent of the pressure, the temperature of the system.it is an intensive quantity. The weight fraction remains constant. Weight by weight ratios have great application in pharmaceutical industries.