Chapter 15, Problem 45QAP

Interpretation Introduction

(a)

Interpretation:

The mass of the indicated solute in the given solution is to be calculated.

Concept Introduction:

The atomic mass of an element is defined as the sum of number of protons and number of neutrons. Molar mass of an element is determined from atomic mass of an element.

The number of moles is calculated by the formula,

$\text{Moles}=\frac{\text{Mass}\left(\text{g}\right)}{\text{Molar}\text{mass}}$

The molarity is calculated by the formula,

$\text{Molarity}=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solution}}$.

Answer to Problem 45QAP

The mass of the indicated solute in $\text{HCl}$ solution is $1193.7\text{g}$.

Explanation of Solution

The volume and molarity of $\text{HCl}$ solution is given to be $2.50\text{L}$ and $13.1\text{M}$ respectively.

The molar mass of $\text{HCl}$ is calculated as shown below.

$\begin{array}{c}\text{Molar}\text{mass}\text{of}\text{HCl}=\left(\text{Atomic}\text{mass}\text{of}\text{H}+\text{Atomic}\text{mass}\text{of}\text{Cl}\right)\\ =\left(1+35.45\right)\text{g}/\text{mol}\\ =36.45\text{g}/\text{mol}\end{array}$

The number of moles of a solute is calculated by the formula,

$\text{Number}\text{of}\text{moles}\text{of}\text{solute}=\text{Volume}\text{of}\text{solution}\times \text{Molarity}$

Substitute the values of volume of solution and molarity of $\text{HCl}$ solution in the above expression.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}\text{solute}=2.50\text{L}\times 13.1\text{M}\\ =32.75\text{moles}\end{array}$

The mass of $\text{HCl}$ is calculated by the formula,

$\text{Mass of HCl}=\text{Molar}\text{mass}\times \text{Number}\text{of}\text{moles}$

Substitute the values of molar mass and number of moles of $\text{HCl}$ in the above expression.

$\begin{array}{c}\text{Mass of HCl}=36.45\text{g}/\text{mol}\times 32.75\text{moles}\\ =1193.7\text{g}\end{array}$

Therefore, the mass of the indicated solute in $\text{HCl}$ solution is $1193.7\text{g}$.

Interpretation Introduction

(b)

Interpretation:

The mass of the indicated solute in the given solution is to be calculated.

Concept Introduction:

The atomic mass of an element is defined as the sum of number of protons and number of neutrons. Molar mass of an element is determined from atomic mass of an element.

The number of moles is calculated by the formula,

$\text{Moles}=\frac{\text{Mass}\left(\text{g}\right)}{\text{Molar}\text{mass}}$

The molarity is calculated by the formula,

$\text{Molarity}=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solution}}$.

Answer to Problem 45QAP

The mass of the indicated solute in $\text{NaOH}$ solution is $0.096\text{g}$.

Explanation of Solution

The volume and molarity of $\text{NaOH}$ solution is given to be $15.6\text{mL}$ and $0.155\text{M}$ respectively.

The conversion of units of volume into $\text{L}$ is done as,

$\begin{array}{c}15.6\text{mL}=\frac{15.6}{1000}\text{L}\\ =0.0156\text{L}\end{array}$

The molar mass of $\text{NaOH}$ is calculated as shown below.

$\begin{array}{c}\text{Molar}\text{mass}\text{of}\text{NaOH}=\left(\begin{array}{l}\text{Atomic}\text{mass}\text{of}\text{Na}+\text{Atomic}\text{mass}\text{of}\text{O}\\ +\text{Atomic}\text{mass}\text{of}\text{H}\end{array}\right)\\ =\left(23+16+1\right)\text{g}/\text{mol}\\ =40\text{g}/\text{mol}\end{array}$

The number of moles of a solute is calculated by the formula,

$\text{Number}\text{of}\text{moles}\text{of}\text{solute}=\text{Volume}\text{of}\text{solution}\times \text{Molarity}$

Substitute the values of volume of solution and molarity of $\text{NaOH}$ solution in the above expression.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}\text{solute}=0.0156\text{L}\times 0.155\text{M}\\ =0.0024\text{moles}\end{array}$

The mass of $\text{NaOH}$ is calculated by the formula,

$\text{Mass of NaOH in grams}=\text{Molar}\text{mass}\times \text{Number}\text{of}\text{moles}$

Substitute the values of molar mass and number of moles of $\text{NaOH}$ in the above expression.

$\begin{array}{c}\text{Mass of NaOH}=40\text{g}/\text{mol}\times 0.0024\text{moles}\\ =0.096\text{g}\end{array}$

Therefore, the mass of the indicated solute in $\text{NaOH}$ solution is $0.096\text{g}$.

Interpretation Introduction

(c)

Interpretation:

The mass of the indicated solute in the given solution is to be calculated.

Concept Introduction:

The atomic mass of an element is defined as the sum of number of protons and number of neutrons. Molar mass of an element is determined from atomic mass of an element.

The number of moles is calculated by the formula,

$\text{Moles}=\frac{\text{Mass}\left(\text{g}\right)}{\text{Molar}\text{mass}}$

The molarity is calculated by the formula,

$\text{Molarity}=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solution}}$.

Answer to Problem 45QAP

The mass of the indicated solute in ${\text{HNO}}_3$ solution is $17.098\text{g}$.

Explanation of Solution

The volume and molarity of ${\text{HNO}}_3$ solution is given to be $135\text{mL}$ and $2.01\text{M}$ respectively.

The conversion of units of volume into $\text{L}$ is done as,

$\begin{array}{c}135\text{mL}=\frac{135}{1000}\text{L}\\ =0.135\text{L}\end{array}$

The molar mass of ${\text{HNO}}_3$ is calculated as shown below.

$\begin{array}{c}\text{Molar}\text{mass}\text{of}{\text{HNO}}_3=\left(\begin{array}{l}\text{Atomic}\text{mass}\text{of}\text{H}+\text{Atomic}\text{mass}\text{of}\text{N}\\ +3\left(\text{Atomic}\text{mass}\text{of}\text{O}\right)\end{array}\right)\\ =1+14+3\left(16\right)\text{g}/\text{mol}\\ =63\text{g}/\text{mol}\end{array}$

The number of moles of a solute is calculated by the formula,

$\text{Number}\text{of}\text{moles}\text{of}\text{solute}=\text{Volume}\text{of}\text{solution}\times \text{Molarity}$

Substitute the values of volume of solution and molarity of ${\text{HNO}}_3$ solution in the above expression.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}\text{solute}=0.135\text{L}\times 2.01\text{M}\\ =0.2714\text{moles}\end{array}$

The mass of ${\text{HNO}}_3$ is calculated by the formula,

${\text{Mass of HNO}}_3=\text{Molar}\text{mass}\times \text{Number}\text{of}\text{moles}$

Substitute the values of molar mass and number of moles of ${\text{HNO}}_3$ in the above expression.

$\begin{array}{c}{\text{Mass of HNO}}_3=63\text{g}/\text{mol}\times 0.2714\text{moles}\\ =17.098\text{g}\end{array}$

Therefore, the mass of the indicated solute in ${\text{HNO}}_3$ solution is $17.098\text{g}$.

Interpretation Introduction

(d)

Interpretation:

The mass of the indicated solute in the given solution is to be calculated.

Concept Introduction:

The atomic mass of an element is defined as the sum of number of protons and number of neutrons. Molar mass of an element is determined from atomic mass of an element.

The number of moles is calculated by the formula,

$\text{Moles}=\frac{\text{Mass}\left(\text{g}\right)}{\text{Molar}\text{mass}}$

The molarity is calculated by the formula,

$\text{Molarity}=\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{Volume}\text{of}\text{solution}}$.

Answer to Problem 45QAP

The mass of the indicated solute in ${\text{CaCl}}_2$ solution is $240.6\text{g}$.

Explanation of Solution

The volume and molarity of ${\text{CaCl}}_2$ solution is given to be $4.21\text{L}$ and $0.515\text{M}$ respectively.

The molar mass of ${\text{CaCl}}_2$ is calculated as shown below.

$\begin{array}{c}\text{Molar}\text{mass}\text{of}{\text{CaCl}}_2=\left(\text{Atomic}\text{mass}\text{of}\text{Ca}+2\left(\text{Atomic}\text{mass}\text{of}\text{Cl}\right)\right)\\ =\left(40+2\left(35.45\right)\right)\text{g}/\text{mol}\\ =110.9\text{g}/\text{mol}\end{array}$

The number of moles of a solute is calculated by the formula,

$\text{Number}\text{of}\text{moles}\text{of}\text{solute}=\text{Volume}\text{of}\text{solution}\times \text{Molarity}$

Substitute the values of volume of solution and molarity of ${\text{CaCl}}_2$ solution in the above expression.

$\begin{array}{c}\text{Number}\text{of}\text{moles}\text{of}\text{solute}=4.21\text{L}\times 0.515\text{M}\\ =2.17\text{moles}\end{array}$

The mass of ${\text{CaCl}}_2$ is calculated by the formula,

$\text{Mass of}{\text{CaCl}}_2=\text{Molar}\text{mass}\times \text{Number}\text{of}\text{moles}$

Substitute the values of molar mass and number of moles of ${\text{CaCl}}_2$ in the above expression.

$\begin{array}{c}{\text{Mass of CaCl}}_2=110.9\text{g}/\text{mol}\times 2.17\text{moles}\\ =240.6\text{g}\end{array}$

Therefore, the mass of the indicated solute in ${\text{CaCl}}_2$ solution is $240.6\text{g}$.