Chapter 15, Problem 7PE

Interpretation Introduction

Interpretation:

The amount of energy required to raise the temperature of $75\text{g}$ of solid zinc from $22°\text{C}$ to $555°\text{C}$ is to be calculated.

Concept introduction:

The amount of energy required to change the state of a substance is known as enthalpy. It is the different in the energy of final and initial state of a substance. The negative and positive sign of enthalpy indicates the energy released and energy absorbed, respectively, during the phase change.

Answer to Problem 7PE

The amount of energy required to raise the temperature of $75\text{g}$ of solid zinc from $22°\text{C}$ to $555°\text{C}$ is $26\text{kJ}$.

Explanation of Solution

The mass of solid zinc is $75\text{g}$.

The melting temperature of the solid zinc is $420°\text{C}$.

The required initial temperature is $22°\text{C}$.

The required final temperature is $555°\text{C}$.

The amount of energy required to raise the temperature of zinc from $22°\text{C}$ to $420°\text{C}$ is calculated by the formula shown below.

${\text{q}}_{\text{1}}=\text{mc}\left({\text{T}}_2-{\text{T}}_1\right)$…(1)

Where,

• $\text{m}$ is the mass of the sample.

• $\text{c}$ is the specific heat of zinc.

• ${\text{T}}_{\text{2}}$ is the final temperature $\left(420°\text{C}\right)$.

• ${\text{T}}_{\text{1}}$ is the initial temperature $\left(22°\text{C}\right)$.

The specific heat of zinc (solid) is $0.39\text{J}/\text{g}\cdot °\text{C}$.

Substitute the mass, final, initial temperature and specific heat of zinc in equation (1).

$\begin{array}{rll}{\text{q}}_{\text{1}}& =& \left(75\text{g}\right)\left(0.39\text{J}/\text{g}\cdot °\text{C}\right)\left(420°\text{C}-22°\text{C}\right)\\ & =& \left(1.16415\times {10}^4\text{J}\right)\left(\frac{1\text{kJ}}{1000\text{J}}\right)\\ & \approx & 12\text{kJ}\end{array}$

The amount of energy required for phase transformation is calculated by the formula shown below.

${\text{q}}_{\text{2}}=\text{m}\Delta {\text{H}}_{\text{fus}}$…(2)

Where,

• is the heat of fusion.

The heat of fusion of zinc is $112\text{J}/\text{g}$.

Substitute the mass and heat of fusion in equation (2).

$\begin{array}{rll}{\text{q}}_{\text{2}}& =& \left(75\text{g}\right)\left(112\text{J}/\text{g}\right)\\ & =& \left(8.4\times {10}^3\text{J}\right)\left(\frac{1\text{kJ}}{1000\text{J}}\right)\\ & =& 8.4\text{kJ}\end{array}$

The amount of energy required to raise the temperature of zinc from $420°\text{C}$ to $555°\text{C}$ is calculated by the formula shown below.

${\text{q}}_{\text{3}}=\text{mc}\left({\text{T}}_2-{\text{T}}_1\right)$…(3)

Where,

• $\text{m}$ is the mass of the sample.

• $\text{c}$ is the specific heat of zinc (liquid).

• ${\text{T}}_{\text{2}}$ is the final temperature $\left(555°\text{C}\right)$.

• ${\text{T}}_{\text{1}}$ is the initial temperature $\left(420°\text{C}\right)$.

The specific heat of zinc (liquid) is $0.51\text{J}/\text{g}\cdot °\text{C}$.

Substitute the mass, final, initial temperature and specific heat of zinc in equation (3).

$\begin{array}{rll}{\text{q}}_{\text{3}}& =& \left(75\text{g}\right)\left(0.51\text{J}/\text{g}\cdot °\text{C}\right)\left(555°\text{C}-420°\text{C}\right)\\ & =& \left(5.164\times {10}^3\text{J}\right)\left(\frac{1\text{kJ}}{1000\text{J}}\right)\\ & \approx & 5.2\text{kJ}\end{array}$

The total amount of energy sample gained when temperature is changed from $22°\text{C}$ to $555°\text{C}$ is shown below.

$\text{q}={\text{q}}_1+{\text{q}}_2+{\text{q}}_3$

Substitute the value of energies in the above equation.

$\begin{array}{rll}\text{q}& =& 12\text{kJ}+8.4\text{kJ}+5.2\text{kJ}\\ & =& 25.6\text{kJ}\\ & \approx & 26\text{kJ}\end{array}$

Therefore, the amount of energy required to raise the temperature of $75\text{g}$ of solid zinc from $22°\text{C}$ to $555°\text{C}$ is $26\text{kJ}$.

Conclusion

The amount of energy required to raise the temperature of $75\text{g}$ of solid zinc from $22°\text{C}$ to $555°\text{C}$ is $26\text{kJ}$.