Chapter 11, Problem 138QP

(a)

Interpretation Introduction

Interpretation:

Whether the statement, “ $0.0500\text{ mol}$ of ${\text{K}}_2{\text{SO}}_4$ completely reacts with $0.0250\text{ mol}$ of ${\text{AgNO}}_3$ �, describes the given reaction or not is to be determined and, if not, the statement is to be modified such that it does.

Explanation of Solution

The reaction between silver nitrate and potassium sulphate forms the precipitate of aluminium sulphate and soluble potassium nitrate.

$2{\text{AgNO}}_3(aq)+{\text{K}}_2{\text{SO}}_4(aq)\to {\text{Ag}}_2{\text{SO}}_4(s)+2{\text{KNO}}_3(aq)$

So, from the mole ratio of the above balanced equation, it can be conclude that $2\text{mol}$ of ${\text{AgNO}}_3$ will react with $1\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ to give $1\text{mol}$ of ${\text{Ag}}_2{\text{SO}}_4$ and $2\text{mol}$ of ${\text{KNO}}_3$ precipitates, which are soluble in water.

The moles of ${\text{AgNO}}_3$ present in $25\text{mL}$ of $1\text{M}{\text{AgNO}}_3$ solution is:

$\begin{array}{c}{\text{mol AgNO}}_3=\text{25}\text{.0 }\cancel{\text{mL}}{\text{ AgNO}}_3\times \frac{1\cancel{\text{L}}}{1000\cancel{\text{mL}}}\times \frac{1.00\text{mol}}{\cancel{\text{L}}{\text{ AgNO}}_3}\\ =0.0250{\text{mol AgNO}}_3\end{array}$

The moles of ${\text{K}}_2{\text{SO}}_4$ present in $25\text{mL}$ of $2\text{M}{\text{K}}_2{\text{SO}}_4$ solution is:

$\begin{array}{c}{\text{mol K}}_2{\text{SO}}_4=\text{25}\text{.0 }\cancel{\text{mL}}{\text{ K}}_2{\text{SO}}_4\times \frac{1\cancel{\text{L}}}{1000\cancel{\text{mL}}}\times \frac{2.00\text{mol}}{\cancel{\text{L}}{\text{ K}}_2{\text{SO}}_4}\\ =0.0500{\text{mol K}}_2{\text{SO}}_4\end{array}$

So, from the mole ratio of the reaction, it can be stated that $0.0250{\text{mol AgNO}}_3$ will react with $0.0125{\text{mol K}}_2{\text{SO}}_4$ $\left(0.0250{\text{mol K}}_2{\text{SO}}_4\text{/2}\right)$ .

The given statement, “ $0.0500\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ completely reacts with $0.0250\text{mol}$ of ${\text{AgNO}}_3$ �, is incorrect because a sufficient amount of ${\text{AgNO}}_3$ is not present in $25\text{mL}$ of $1\text{M}{\text{AgNO}}_3$ to react completely with $0.0500\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ .

The corrected statement is “ $0.0125\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ completely reacts with $0.0250\text{mol}$ of ${\text{AgNO}}_3$ solution�.

(b)

Interpretation Introduction

Interpretation:

Whether the statement, “ $0.0125\text{mol}$ of ${\text{Ag}}_2{\text{SO}}_4$ should be formed as a precipitate�, describes the given reaction or not is to be determined and, if not, the statement is to be modified such that it does.

Explanation of Solution

From the above calculation it is clear that given statement is correct. From the mole ratio of the balanced equation $1$ , it can be concluded that $1\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ will produce $1\text{mol}$ of ${\text{Ag}}_2{\text{SO}}_4$ . Since $0.0125\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ takes part in the reaction, it will produce $0.0125\text{mol}$ of ${\text{Ag}}_2{\text{SO}}_4$ . Hence, the statement is correct.

(c)

Interpretation Introduction

Interpretation:

Whether the statement, “ $0.100\text{mol}$ of aqueous ${\text{KNO}}_3$ should be produced�, describes the given reaction or not is to be determined and, if not, the statement is to be modified such that it does.

Explanation of Solution

The given statement, “ $0.100\text{mol}$ of aqueous ${\text{KNO}}_3$ should be produced�, is incorrect. According to reaction $1$ , the number of moles of ${\text{KNO}}_3$ produced will be:

$\begin{array}{c}{\text{mol KNO}}_3=0.0250\cancel{{\text{mol AgNO}}_3}\times \frac{2{\text{ mol KNO}}_3}{2\cancel{{\text{mol AgNO}}_3}}\\ =0.0250{\text{ mol KNO}}_3\end{array}$

The corrected statement is “ $0.0250\text{mol}$ of aqueous ${\text{KNO}}_3$ will be produced�.

(d)

Interpretation Introduction

Interpretation:

Whether the statement, “the final reaction mixture will contain the products and unreacted ${\text{AgNO}}_3$ �, describes the given reaction or not is to be determined and, if not, the statement is to be modified such that it does.

Explanation of Solution

The given statement is incorrect because all of the ${\text{AgNO}}_3$ will be consumed during the course of the reaction and unreacted ${\text{K}}_2{\text{SO}}_4$ will remain in the solution.

The corrected statement is “the final reaction mixture will contain the products and unreacted ${\text{K}}_2{\text{SO}}_4$ �.

(e)

Interpretation Introduction

Interpretation:

Whether the statement, “ $0.0250\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ remains unreacted�, describes the given reaction or not is to be determined and, if not, the statement is to be modified such that it does.

Explanation of Solution

The given statement is incorrect because the unreacted ${\text{K}}_2{\text{SO}}_4$ will be of $0.0375\text{mol}$ $\left(0.0500\text{mol}-0.0125\text{mol}\right)$ , and not $0.0250\text{mol}$ .

Therefore, the corrected statement is “ $0.0375\text{mol}$ of ${\text{K}}_2{\text{SO}}_4$ remains unreacted�.