Question

What mass of \[{{KCl}}\](in grams) has to be dissolved in \[{{60g }}{{{H}}_{{2}}}{{O}}\] to obtain a \[{{20\% }}\]by mass solution?
A) 15
B) 1.5
C) 150
D) 11.5

Answer 1

Hint:Mass of the solution is the sum of the mass of solute and mass of solvent. Given mass, percent indicates \[{{20g}}\] of \[{{KCl}}\] in \[{{100g }}\] of solution. Using the mass percent formula calculate the mass of \[{{KCl}}\] dissolved in \[{{60g }}{{{H}}_{{2}}}{{O}}\].

Formula Used: \[{{Mass\% = }}\dfrac{{{{mass\ of\ solute}}}}{{{{mass\ of\ solution}}}} \times 100\% \]

Complete step-by-step answer:
Let us assume that \[xg\] of \[{{KCl}}\] dissolved in \[{{60g }}{{{H}}_{{2}}}{{O}}\] to obtain a \[{{20\% }}\] by the mass solution.

We can calculate the mass of \[{{KCl}}\] using the following \[{{Mass \% }}\] formula.
\[{{Mass \% = }}\dfrac{{{{mass\ of\ solute}}}}{{{{mass\ of\ solution}}}} \times 100\% \]
Mass percent solution = \[{{20\% }}\]
Mass of solute = \[xg\]
Mass of solution = Mass of solute + Mass of solvent.
Here, \[{{KCl}}\] is solute and its mass is assumed as \[xg\]. Water is solvent and its mass given to us is\[{{60g}}\].
So, the mass of solution = \[xg\]+\[{{60g}}\]
Now, substitute all the values in \[{{Mass \% }}\] the formula and calculate the mass of\[{{KCl}}\].
\[{{20\% = }}\dfrac{{{{xg}}}}{{{{xg + 60 g}}}} \times 100\% \]
Now, solve the equation for\[x\].
\[\Rightarrow {{20 = }}\dfrac{{{{100xg}}}}{{{{xg + 60 g}}}}\]
\[\Rightarrow {{20xg + 1200g = 100xg }}\]
\[\Rightarrow {{80xg = 1200g }}\]
\[{{x = 15g}}\]
Thus, \[{{15g}}\] of \[{{KCl}}\] has to be dissolved in \[{{60g }}{{{H}}_{{2}}}{{O}}\] to obtain a \[{{20\% }}\]by the mass solution.

Hence, the correct answer is option (A)15

Note:Solute is the substance that gets dissolved and the solvent is the substance in which substance gets dissolved. The solute is always present in fewer amounts than the solvent. The mass percent of the solution indicates that the mass of solute dissolved in a given mass of solution. In the given problem \[{{60g }} {{{H}}_{{2}}}{{O}}\] is a mass of solvent does not consider it as a mass of solution else end up with an incorrect answer.