Chapter 11, Problem 135QP

(A)

Interpretation Introduction

Interpretation:

The combination of the given amount of $\text{KCl}$ and water will make $15.0$ percent by mass or not is to be identified.

Explanation of Solution

$\text{KCl}$ is an ionic compound and water is a polar solvent. Thus, $\text{KCl}$ is easily soluble in water to and the resulting force of attraction is ion-dipole force. The percent-by-mass is calculated by dividing the mass of the solute by the mass of the solution, and then multiplied by $100$ .

The relationship between percent by mass and mass of solute and solution is as follows:

$\text{Percent by mass}=\frac{\text{mass of solute in grams}}{\text{mass of solution in grams}}\times 100$ ……(1)

The amount of $\text{KCl}$ is $30\text{g}$ and the amount of water is $200\text{g}$ . So, the mass of the solution is:

$30\text{g}+200\text{g}=230\text{g}$

The percent by mass concentration of the solution is calculated by putting all the values in equation (1) as follows:

$\begin{array}{c}\text{Percent by mass}=\frac{\text{30 g}}{\text{230 g}}\times 100\\ =13\%\end{array}$

So, the given combination of $\text{KCl}$ and water will not form $15.0$ percent by mass solution of $\text{KCl}$ in water. The percent by mass concentration of the given response is $13\%$ .

(B)

Interpretation Introduction

Interpretation:

The combination of the given amount of $\text{KCl}$ and water will make $15.0$ percent by mass or not is to be identified.

Explanation of Solution

The combination given is $\text{30 mol KCl}$ dissolved in $200\text{g}$ of water. The molar mass of $\text{KCl}$ is $74.55{\text{g mol}}^{-1}$ . So, the mass of $\text{KCl}$ in gram is calculated as follows:

$\begin{array}{c}\text{Mass of KCl}=30\text{mol}\times 75.55{\text{g mol}}^{-1}\\ =2266.5\text{g}\end{array}$

The mass of the solution is:

$2266.5\text{g}+20\text{0 g}=2466.5\text{g}$ .

The percent by mass concentration of the solution is calculated by putting all the values in equation (1) as follows:

$\begin{array}{c}\text{Percent by mass}=\frac{\text{2266}\text{.5 g}}{\text{2466}\text{.5 g}}\times 100\\ =91.89\%\end{array}$

So, the given combination of $\text{KCl}$ and water will not form $15.0$ percent by mass solution of $\text{KCl}$ in water. The percent by mass concentration of the given response is $91.89\%$ .

(C)

Interpretation Introduction

Interpretation:

The combination from the given option of the amount of $\text{KCl}$ and water that makes $15.0$ percent by mass $\text{KCl}$ solution is to be identified.

Explanation of Solution

The combination given is $\text{170 g of KCl}$ dissolved in $30\text{g}$ of water. The mass of the solution is:

$170\text{g}+\text{30 g}=200\text{g}$ .

The percent by the mass concentration of the solution is calculated by putting all the values in equation (1) as follows:

$\begin{array}{l}\text{Percent by mass}=\frac{\text{170 g}}{\text{200 g}}\times 100\\ =85.0\%\end{array}$

So, the given combination of $\text{KCl}$ and water will not form $15.0$ percent by mass solution of $\text{KCl}$ in water. The percent by the mass concentration of the given response is $85.0\%$ .

(D)

Interpretation Introduction

Interpretation:

The combination of the given amount of $\text{KCl}$ and water will make $15.0$ percent by mass or not is to be identified.

Explanation of Solution

The combination given is $\text{30 mol KCl}$ dissolved in $170\text{ml}$ water. The molar mass of $\text{KCl}$ is $74.55{\text{g mol}}^{-1}$ and of water is $18.01{\text{g mol}}^{-1}$ . So, the mass of $\text{KCl}$ in grams is as follows:

$\begin{array}{l}\text{Mass of KCl}=30\text{mol}\times 75.55{\text{g mol}}^{-1}\\ =2266.5\text{g}\end{array}$

The mass of water is calculated as follows:

$\begin{array}{l}{\text{Mass of H}}_{\text{2}}\text{O}=170\text{mol}\times 18.01{\text{g mol}}^{-1}\\ =3061.7\text{g}\end{array}$

The mass of the solution is:

$2266.5\text{g}+\text{3061}\text{.7 g}=5328.2\text{g}$

The percent by the mass concentration of the solution is calculated by putting all the values in equation (1) as follows:

$\begin{array}{c}\text{Percent by mass}=\frac{\text{2266}\text{.5 g}}{\text{5328}\text{.2 g}}\times 100\\ =42.53\%\end{array}$

So, the given combination of $\text{KCl}$ and water will not form $15.0$ percent by mass solution of $\text{KCl}$ in water. The percent by the mass concentration of the given response is $42.53\%$ .

(E)

Interpretation Introduction

Interpretation:

The combination of the given amount of $\text{KCl}$ and water will make $15.0$ percent by mass or not is to be identified.

Explanation of Solution

The amount of $\text{KCl}$ is $30\text{g}$ and the amount of water is $170\text{g}$ . So, the mass of the solution is:

$30\text{g}+170\text{g}=200\text{g}$ .

The percent by the mass concentration of the solution is calculated by putting all the values in equation (1) as follows:

$\begin{array}{c}\text{Percent by mass}=\frac{\text{30 g}}{\text{200 g}}\times 100\\ =15\%\end{array}$

So, the given combination of $\text{KCl}$ and water will form $15.0$ percent by mass solution of $\text{KCl}$ in water. Hence, this is the right combination of $\text{KCl}$ and water.