Chapter 6, Problem 6.94QP

The combustion of what volume of ethane (C₂H₆), measured at 23.0°C and 752 mmHg, would be required to heat 855 g of water from 25.0°C to 98.0°C?

Interpretation Introduction

Interpretation:

The volume of ethane that is required to heat the mass of water has to be given.

Concept Introduction:

The change in enthalpy that is associated with the formation of one mole of a substance from its related elements being in standard state is called standard enthalpy of formation

(${\text{ΔH}}_{\text{f}}\text{°}$).  The standard enthalpy of formation is used to determine the standard enthalpies of compound and element.

The standard enthalpy of reaction is the enthalpy of reaction that takes place under standard conditions.

The equation for determining the standard enthalpies of compound and element can be given by,

${\text{ΔH°}}_{\text{reaction}}\text{=}{\displaystyle \sum {\text{nΔH°}}_{\text{f}}\text{(products)}}\text{-}{\displaystyle \sum {\text{mΔH°}}_{\text{f}}\text{(reactants)}}$

Specific heat:

Specific heat can be defined as quantity of heat required to raise the temperature of $\text{1}\text{g}$ substance by $\text{1°C}$.  The relationship between heat and change in temperature can be expressed by the equation given below.

$\text{q=cmΔT}$

Where $\text{q=}$ Heat added

c= Specific heat

$\text{m=}$ Mass

$\text{ΔT=}$ Change in temperature.

The unit of specific heat is $\text{J}{\text{g}}^{\text{-1}}\text{.°C}$ .

Answer to Problem 6.94QP

The volume of ethane that is required to heat the mass of water is $\text{4}\text{.10}\text{L}\text{.}$

Explanation of Solution

The combustion reaction is given as,

${\text{C}}_{\text{2}}{\text{H}}_{\text{6(l)}}\text{+}\frac{\text{7}}{\text{2}}{\text{O}}_{\text{2(g)}}\stackrel{}{\to }{\text{2CO}}_{\text{2(g)}}{\text{+3H}}_{\text{2}}{\text{O}}_{\left(\text{l}\right)}$

The heat released during the combustion is calculated as,

$\begin{array}{l}{\text{ΔH°}}_{\text{rxtn}}\text{=}\left[{\text{2ΔH°}}_{\text{f}}\left({\text{CO}}_{\text{2}}\right){\text{+3ΔH°}}_{\text{f}}\left(\text{H}{\text{2}}_{}\text{O}\right)\right]\text{-}\left[{\text{ΔH°}}_{\text{f}}\left({\text{C}}_{\text{2}}{\text{H}}_{\text{6}}\right)\text{+}\frac{\text{7}}{\text{2}}{\text{ΔH°}}_{\text{f}}\left({\text{O}}_{\text{2}}\right)\right]\\ \\ {\text{ΔH°}}_{\text{rxtn}}\text{=}\left[\left(\text{2}\right)\left(\text{-393}\text{.5kJ/mole}\right)\text{+}\left(\text{3}\right)\left(\text{-285}\text{.8}\text{kJ/mole}\right)\right]\text{-}\left[\left(\text{1}\right)\left(\text{-84}\text{.7}\text{kJ/mole}\right)\text{+}\frac{\text{7}}{\text{2}}\left({\text{O}}_{\text{2}}\right)\right]\\ \\ {\text{ΔH°}}_{\text{rxtn}}\text{=}\text{-1560}\text{kJ/mole}\end{array}$

The heat requires to raise the temperature of water to $\text{98°C}$ is calculated as,

$\begin{array}{l}\text{q}\text{=}{\text{m}}_{{\text{H}}_{\text{2}}\text{O}}{\text{s}}_{{\text{H}}_{\text{2}}\text{O}}\text{Δt}\\ \\ \text{q}\text{=}\left(\text{855}\text{g}\right)\left(\text{4}\text{.184}\text{J/g°C}\right)\left(\text{98}\text{.0-25}\text{.0}\right)\text{°C}\\ \\ \text{q}\text{=}\text{2}{\text{.61×10}}^{\text{5}}\text{J}\\ \\ \text{q}\text{=}\text{261}\text{kJ}\end{array}$

The combustion of one mole of ethane yields $\text{1560}\text{kJ}$ , the number of moles of ethane is calculated as,

$\begin{array}{l}\text{Number}\text{of}\text{moles of ethane}\text{=}\text{261}\text{kJ×}\frac{\text{1}\text{mole}\text{ethane}}{\text{1560}\text{kJ}}\\ \\ \text{Number}\text{of}\text{moles of ethane}\text{=}\text{0}\text{.167}\text{mole}\end{array}$

The volume of ethane is calculated using the ideal gas equation,

$\begin{array}{l}\text{PV}\text{=}\text{nRT}\\ \\ {\text{V}}_{\text{ethane}}\text{=}\frac{\text{nRT}}{\text{P}}\\ \\ {\text{V}}_{\text{ethane}}\text{=}\frac{\left(\text{0}\text{.167}\text{mole}\right)\left(\text{0}\text{.0821}\frac{\text{L}\text{.atm}}{\text{mole}\text{.K}}\right)\left(\text{296}\text{K}\right)}{\left(\text{752}\text{mm}\text{Hg×}\frac{\text{1}\text{atm}}{\text{760}\text{mm}\text{Hg}}\right)}\\ \\ {\text{V}}_{\text{ethane}}\text{=}\text{4}\text{.10L}\end{array}$

The volume of ethane that is required to heat the mass of water is $\text{4}\text{.10}\text{L}\text{.}$

Conclusion

The volume of ethane that is required to heat the mass of water was calculated as $\text{4}\text{.10}\text{L}\text{.}$