Chapter 14, Problem 1ASA

(a)

Interpretation Introduction

Interpretation: In the given system, $\Delta t$ for water is to be determined.

Concept introduction:

Calorimetry is a technique used to measure how much heat is produced or absorbed during a chemical reaction. It is used to determine the specific heat of the metal. The expression for heat evolved or absorbed is as follows:

  $q=m\times S.H.\times \Delta t$

Here, $m$ is mass, $S.H.$ is specific heat capacity, and $\Delta t$ is the temperature change.

Answer to Problem 1ASA

  $\text{18}\text{.8}°\text{C}$

Explanation of Solution

The initial temperature is $23.0°\text{C}$ .

Final temperature is $41.8°\text{C}$ .

Expression for $\Delta t$ is,

  $\begin{array}{c}\Delta t=t_{\text{final}}-t_{\text{initial}}\\ =41.8°\text{C}-23.0°\text{C}\\ \text{=18}\text{.8}°\text{C}\end{array}$

Thus, $\Delta t$ for water is $\text{18}\text{.8}°\text{C}$ .

(b)

Interpretation Introduction

Interpretation: In the given system, $\Delta t$ for metal is to be determined.

Concept introduction:

Calorimetry is a technique used to measure how much heat is produced or absorbed during a chemical reaction. It is used to determine the specific heat of the metal. The expression for heat evolved or absorbed is as follows:

  $q=m\times C\times \Delta t$

Here, $m$ is mass, $C$ is specific heat capacity, and $\Delta t$ is the temperature change.

Answer to Problem 1ASA

  $-\text{57}\text{.7}°\text{C}$

Explanation of Solution

The initial temperature of metal is $99.5°\text{C}$ .

Final temperature is $41.8°\text{C}$ .

Expression for $\Delta t$ is,

  $\begin{array}{c}\Delta t=t_{\text{final}}-t_{\text{initial}}\\ =41.8°\text{C}-99.5°\text{C}°\text{C}\\ \text{=}-\text{57}\text{.7}°\text{C}\end{array}$

Thus, $\Delta t$ for metal is $-\text{57}\text{.7}°\text{C}$ .

(c)

Interpretation Introduction

Interpretation: The amount of heat flowed into the water is to be determined.

Concept introduction:

Calorimetry is a technique used to measure how much heat is produced or absorbed during a chemical reaction. It is used to determine the specific heat of the metal. The expression for heat evolved or absorbed is as follows:

  $q=m\times S.H.\times \Delta t$

Here, $m$ is mass, $S.H.$ is specific heat capacity, and $\Delta t$ is the temperature change.

Answer to Problem 1ASA

  $\text{3,907}\text{.98 J}$

Explanation of Solution

Amount of water is $49.73\text{ g}$

Specific heat of water is $4.18\text{J}/\text{g°C}$

  $\Delta t$ for water is $\text{18}\text{.8}°\text{C}$ .

Now, calculate heat flowing in water as follows:

  $\begin{array}{c}q=m\times S.H.\times \Delta t\\ =49.73\text{ g}\times 4.18\text{J}/\text{g°C}\times \text{18}\text{.8}°\text{C}\\ =\text{3,907}\text{.98 J}\end{array}$

Thus, heat flowed to water is $\text{3,907}\text{.98 J}$ .

(d)

Interpretation Introduction

Interpretation: The specific heat of metal is to be determined.

Concept introduction:

Calorimetry is a technique used to measure how much heat is produced or absorbed during a chemical reaction. It is used to determine the specific heat of the metal. The expression for heat evolved or absorbed is as follows:

  $q=m\times S.H.\times \Delta t$

Here, $m$ is mass, $S.H.$ is specific heat capacity, and $\Delta t$ is the temperature change.

Answer to Problem 1ASA

  $\text{0}\text{.457 }\text{J}/\text{g}°\text{C}$

Explanation of Solution

Amount of metal is $147.90\text{ g}$

  $\Delta t$ for metal is $-\text{57}\text{.7}°\text{C}$ . (Only value is taken not sign)

Heat given by metal is absorbed by water. Thus, heat given by metal is $\text{3,907}\text{.98 J}$ .

Now, calculate heat flowing in water as follows:

  $\begin{array}{c}{q}_{{\text{H}}_{\text{2}}\text{O}}=S.H{.}_{{\text{H}}_{\text{2}}\text{O}}\times m_{{\text{H}}_{\text{2}}\text{O}}\times \Delta t_{{\text{H}}_{\text{2}}\text{O}}=-S.H{.}_m\times m_m\times \Delta t_m\\ =-S.H{.}_m\times m_m\times \Delta t_m\\ \text{3,907}\text{.98 J}=-\left(147.90\text{ g}\times S.H{.}_m\times \left(-\text{57}\text{.7}°\text{C}\right)\right)\\ S.H{.}_m=\frac{\text{3,907}\text{.98 J}}{147.90\text{ g}\times \text{57}\text{.7}°\text{C}}\\ =\frac{\text{3,907}\text{.98 J}}{147.90\text{ g}\times \text{57}\text{.7}°\text{C}}\\ =\text{0}\text{.457 }\text{J}/\text{g}°\text{C}\end{array}$

Thus, the specific heat of metal is $\text{0}\text{.457 }\text{J}/\text{g}°\text{C}$

(e)

Interpretation Introduction

Interpretation: The specific heat of metal is to be determined.

Concept introduction:

The relation between molecular mass and specific metal is as follows:

  $MM\cong \frac{25}{S.H.\left(\text{J}/\text{g}°\text{C}\right)}$

Here, $MM$ is molecular formula, and $S.H$ is specific heat.

Answer to Problem 1ASA

  $\text{54}\text{.70 }\text{g}/\text{mol}$

Explanation of Solution

  $S.H{.}_m$ is $\text{0}\text{.457 }\text{J}/\text{g}°\text{C}$

Substitute values in the above formula

  $\begin{array}{c}MM\cong \frac{25}{\text{0}\text{.457}}\\ \cong \text{54}\text{.70 }\text{g}/\text{mol}\end{array}$

Thus, the approximate molecular formula of metal is $\text{54}\text{.70 }\text{g}/\text{mol}$ .