Chapter 5, Problem 42QP

Interpretation Introduction

Interpretation:

The final temperature of the combined solution of $\text{HCl}$ and $\text{NaOH}$ in given system is to be calculated.

Concept Introduction:

The first law of thermodynamics states that the energy released by a system must be absorbed by the system.

$q_{surr}=-q_{sys}$

Heat absorbed or released by a system is calculated by multiplying the mass of the substance with its specific heat and the change in temperature of the system.

The sign of heat change is positive, if heat is absorbed by the system, and negative, if heat is released by the system.

The specific heat (s) of a substance is the amount of heat required to raise the temperature of 1 g of the substance by $\text{1 }°\text{C}$ .

The heat released by the system in the given system is calculated by the formula $q=C_{\text{P}}\Delta T$.

Here, $q$ is the heat change, $C_{\text{P}}$ is the heat capacity of calorimeter, and $\Delta T$ is the change in temperature of the system.

The heat absorbed by the substance in the given system is calculated by the expression: $q=ms\left(T_2-T_1\right)$.

Here, $q$ is the heat change, $m$ is the mass of substance, $s$ is the specific heat capacity of substance, $T_1$ is the initial temperature, and $T_2$ is the final temperature of the system.

The conversion of volume from $\text{mL}$ into liter is done as follows:

$1\text{mL}={10}^{-3}\text{L}$

The conversion of heat from $\text{J}$ into $\text{kJ}$ is as:

$1\text{J}={10}^{-3}\text{kJ}$

The number of moles of solute present in the given solution is calculated by the formula,

$\begin{array}{c}\text{M}=\frac{\text{n}}{\text{V}}\\ \text{n}=\text{MV}\end{array}$

Here, $\text{M}$ is the molarity of the given solution, $\text{n}$ is the number of moles of solute present in the given solution, and $\text{V}$ is the volume of solution in liters.