Textbook Problem

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Ethanol, C₂H_sOH, boils at 78.29 °C. How much energy, in joules, is required to raise the temperature of 1.00 kg of ethanol from 20.0 °C to the boiling point and then to change the liquid to vapor at that temperature? (The specific heat capacity of liquid ethanol is 2.44 J/g · K, and its enthalpy of vaporization is 855 J/g.)

Interpretation Introduction

Interpretation:

The energy needed to raise the temperature of ethanol to its boiling point and then to vaporize has to be calculated.

Concept Introduction:

Heat energy required to raise the temperature of 1g of substance by 1K.

Energy gained or lost can be calculated using the below equation.

  $\text{q=C×m×ΔT}$

Where,

  q= energy gained or lost for a given mass of substance (m)

  C =specific heat capacity,

  $\Delta T$= change in temperature.

Explanation of Solution

Given,

  Boiling point of ethanol= $\text{78}{\text{.29}}^{\text{0}}\text{C}$

  Specific heat capacity=$\text{2}\text{.44JK/g}$ 

  Heat of vaporization=$\text{855J/g}$

  Mass=$\text{1Kg}$ =$\text{1000g}$

  ${\text{q}}_{\text{1}}\text{=}$ To increase the temperature from ${\text{20}}^{\text{0}}\text{C}$ to $\text{78}{\text{.29}}^{\text{0}}\text{C}$

  $\text{q=C×m×ΔT}$

Substitute for the equation as

  ${\text{q}}_{\text{1}}\text{=}$$\text{2}\text{.44JK/g×1000g(351}\text{.29K-293K)}$ 

  ${\text{q}}_{\text{1}}\text{=}$$\text{142227}\text{.6J}$ 

  ${\text{q}}_{\text{2}}\text{=}$ Vaporize from $\text{78}{}^{}$