Chapter 5, Problem 5.69QP

(a)

Interpretation Introduction

Interpretation: The addition of $2.00\text{g}$ of $\text{Mg}$ metal in $95.0\text{mL}$ of $1.00\text{M}$ of $\text{HCl}$ in a coffee-cup calorimeter raised the temperature by $9.2°\text{C}$. The balanced net ionic equation of the reaction is to be written and $\Delta H_{\text{rxn}}$ is to be calculated.

Concept introduction: The heat of reaction or enthalpy of the reaction $\left(\Delta H_{\text{rxn}}\right)$ is defined as the amount of energy released or absorbed during formation of product. It is calculated by formula,

$q=n\times c_{\text{p}}\times \Delta T$

To determine: The balanced net ionic equation of the reaction.

Answer to Problem 5.69QP

Solution

The net ionic equation is,

$\text{Mg}\left(s\right)+2{\text{H}}^{+}\left(aq\right)\to {\text{Mg}}^{2+}\left(aq\right)+{\text{H}}_2\left(g\right)$

Explanation of Solution

Explanation

The balanced chemical equation is given as,

$\text{Mg}\left(s\right)+2\text{HCl}\left(aq\right)\to {\text{MgCl}}_2\left(aq\right)+{\text{H}}_2\left(g\right)$

The total ionic equation is given as,

$\text{Mg}\left(s\right)+2{\text{H}}^{+}\left(aq\right)+2{\text{Cl}}^{-}\left(aq\right)\to {\text{Mg}}^{2+}\left(aq\right)+2{\text{Cl}}^{-}\left(aq\right)+{\text{H}}_2\left(g\right)$

The net ionic equation is,

$\text{Mg}\left(s\right)+2{\text{H}}^{+}\left(aq\right)\to {\text{Mg}}^{2+}\left(aq\right)+{\text{H}}_2\left(g\right)$

(b)

Interpretation Introduction

To determine: The enthalpy of the reaction $\Delta H_{\text{rxn}}$.

Answer to Problem 5.69QP

Solution

The $\Delta H_{\text{rxn}}$ of the reaction is $\underset{\_}{2808.4J/mol}$.

Explanation of Solution

Explanation

The amount of $\text{Mg}$ metal added is $2.00\text{g}$.

The volume of $\text{HCl}$ is $95.0\text{mL}$.

The molarity of $\text{HCl}$ is $1.00\text{M}$.

Temperature change of the reaction $9.2°\text{C}$.

The molar heat capacity of $1.00\text{M}$ $\text{HCl}$ is $75.3\text{J}/\text{mol}\cdot °\text{C}$.

The total number of moles of $\text{Mg}$ are calculated by the formula,

$n_{\text{Mg}}=\frac{m}{M_1}$

Where,

• $m$ is the given mass of $\text{Mg}$.
• $M_1$ is the molar mass of $\text{Mg}$.

The molar mass of $\text{Mg}$ is $24.3\text{g}/\text{mol}$.

Substitute the molar mass and given mass of $\text{Mg}$ in the above formula,

$\begin{array}{c}{n}_{\text{Mg}}=\frac{2\text{g}}{24.3\text{g}/\text{mol}}\\ =0.082\text{mol}\end{array}$

The total number of moles of $1.00\text{M}$ $\text{HCl}$ are calculated by formula,

$n_{\text{HCl}}=M\times V$

Where,

• $M$ is the molarity of $\text{HCl}$.
• $V$ is the volume of $\text{HCl}$.

Convert $95.0\text{mL}$ into $\text{L}$.

$\begin{array}{c}95.0\text{mL}=\frac{95.0}{1000}\text{L}\\ =0.095\text{L}\end{array}$

Substitute the molarity and volume of $\text{HCl}$ in the above formula,

$\begin{array}{c}{n}_{\text{HCl}}=1.00\text{M}\times 0.095\text{L}\\ =0.095\text{mol}\end{array}$

The balanced chemical equation is given as,

$\text{Mg}\left(s\right)+2\text{HCl}\left(aq\right)\to {\text{MgCl}}_2\left(aq\right)+{\text{H}}_2\left(g\right)$

The above equation shows that $1\text{mol}$ if $\text{Mg}$ reacted with $2\text{mol}$ of $\text{HCl}$.

The number of moles of $\text{Mg}$ react with $0.095\text{mol}$ of $\text{HCl}$ is calculated by,

$N_{\text{Mg}}=\frac{n_{\text{HCl}}}{2}$

Substitute the number of moles of $\text{HCl}$.

$\begin{array}{c}{N}_{\text{Mg}}=\frac{0.095\text{mol}}{2}\\ =0.0475\text{mol}\end{array}$

The amount of heat absorbed or released is calculated by formula,

$q=m_{\text{HCl}}\times c\times \Delta T$ (1)

Where,

• $m_{\text{HCl}}$ is the mass of $\text{HCl}$ reacted with $\text{Mg}$.
• $C$ is the specific heat capacity of $\text{HCl}$.
• $\Delta T$ is the temperature change.

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

$m_{\text{HCl}}=n_{\text{HCl}}\times M_2$

Where,

• $M_2$ is the molar mass of $\text{HCl}$.

The molar mass of $\text{HCl}$ is $\begin{array}{l}=H+Cl\\ =1\text{g}/\text{mol}+35.5\text{g}/\text{mol}\\ =36.5\text{g}/\text{mol}\end{array}$

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

$\begin{array}{c}{m}_{\text{HCl}}=0.095\text{mol}\times 36.5\text{g}/\text{mol}\\ =3.46\text{g}\end{array}$

The specific heat capacity is calculated by formula

$c=\frac{c_{\text{p}}}{M_3}$

Where,

• $C_{\text{p}}$ is the given molar heat capacity.
• $M_3$ is the molar mass of water.

The molar mass of water is $\begin{array}{l}=2H+O\\ =2\times 1\text{g}/\text{mol}+1\times 16\text{g}/\text{mol}\\ =18\text{g}/\text{mol}\end{array}$

Substitute the values of molar heat capacity and molar mass of water in above formula.

$\begin{array}{c}c=75.3\text{J}/\text{mol}\cdot °\text{C}\times 18\text{g}/\text{mol}\\ =4.183\text{J/g}\cdot °\text{C}\end{array}$

Substitute the values of specific heat capacity, mass of $\text{HCl}$ and change in temperature in equation (1).

$\begin{array}{c}q=3.467\text{g}\times 4.183\text{J}/\text{g}\cdot °\text{C}\times 9.2°\text{C}\\ =133.4\text{J}\end{array}$

The $\Delta H_{\text{rxn}}$ of the reaction is calculated by formula,

$\Delta H_{\text{rxn}}=\frac{q}{N_{\text{Mg}}}$

Substitute the values of heat absorbed and number of moles of $\text{Mg}$.

$\begin{array}{c}\Delta H_{\text{rxn}}=\frac{133.4\text{J}}{0.0475\text{mol}}\\ =\underset{\_}{2808.4J/mol}\end{array}$

Therefore, the $\Delta H_{\text{rxn}}$ of the reaction is $\underset{\_}{2808.4J/mol}$.

Conclusion

1. a. The net ionic equation is,

$\text{Mg}\left(s\right)+2{\text{H}}^{+}\left(aq\right)\to {\text{Mg}}^{2+}\left(aq\right)+{\text{H}}_2\left(g\right)$

1. b. The $\Delta H_{\text{rxn}}$ of the reaction is $\underset{\_}{2808.4J/mol}$