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Question: What mass of \[{{KCl}}\](in grams) has to be dissolved in \[{{60g }}{{{H}}_{{2}}}{{O}}\] to obtain a...

What mass of KCl{{KCl}}(in grams) has to be dissolved in 60gH2O{{60g }}{{{H}}_{{2}}}{{O}} to obtain a 20%{{20\% }}by mass solution?
A) 15
B) 1.5
C) 150
D) 11.5

Explanation

Solution

Mass of the solution is the sum of the mass of solute and mass of solvent. Given mass, percent indicates 20g{{20g}} of KCl{{KCl}} in 100g{{100g }} of solution. Using the mass percent formula calculate the mass of KCl{{KCl}} dissolved in 60gH2O{{60g }}{{{H}}_{{2}}}{{O}}.

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

Complete step-by-step answer:
Let us assume that xgxg of KCl{{KCl}} dissolved in 60gH2O{{60g }}{{{H}}_{{2}}}{{O}} to obtain a 20%{{20\% }} by the mass solution.

We can calculate the mass of KCl{{KCl}} using the following Mass%{{Mass \% }} formula.
Mass%=mass of solutemass of solution×100%{{Mass \% = }}\dfrac{{{{mass\ of\ solute}}}}{{{{mass\ of\ solution}}}} \times 100\%
Mass percent solution = 20%{{20\% }}
Mass of solute = xgxg
Mass of solution = Mass of solute + Mass of solvent.
Here, KCl{{KCl}} is solute and its mass is assumed as xgxg. Water is solvent and its mass given to us is60g{{60g}}.
So, the mass of solution = xgxg+60g{{60g}}
Now, substitute all the values in Mass%{{Mass \% }} the formula and calculate the mass ofKCl{{KCl}}.
20%=xgxg+60g×100%{{20\% = }}\dfrac{{{{xg}}}}{{{{xg + 60 g}}}} \times 100\%
Now, solve the equation forxx.
20=100xgxg+60g\Rightarrow {{20 = }}\dfrac{{{{100xg}}}}{{{{xg + 60 g}}}}
20xg+1200g=100xg\Rightarrow {{20xg + 1200g = 100xg }}
80xg=1200g\Rightarrow {{80xg = 1200g }}
x=15g{{x = 15g}}
Thus, 15g{{15g}} of KCl{{KCl}} has to be dissolved in 60gH2O{{60g }}{{{H}}_{{2}}}{{O}} to obtain a 20%{{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 60gH2O{{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.