Calculating the Energy Release of an Exothermic Mixing Process

Three moles of water and one mole of sulfuric acid are mixed isothermally at 0°C. How much heat must be absorbed or released to keep the mixture at 0°C?

Question

Calculating the Energy Release of an Exothermic Mixing Process

Three moles of water and one mole of sulfuric acid are mixed isothermally at 0°C. How much heat must be absorbed or released to keep the mixture at 0°C?

Accepted Answer

Water has amolecularweight of 18.015, and that of sulfuric acid is 98.078. Therefore, themixture will contain 3 × 18.015 + 1 × 98.078 = 152.12 g, and will have a composition of

[latex]\frac{98.078 g }{152.12 g } imes 100 \%=64.5 wt \% ext { sulfuric acid }[/latex]

From Fig. 8.1-1 the enthalpy of the mixture is about −315 kJ/kg. Therefore, when 3 mol water and 1 mol sulfuric acid are mixed isothermally,

[latex]\Delta_{ mix } \hat{H}=\hat{H}_{ mix }-w_{1} \hat{H}_{1}-w_{2} \hat{H}_{2}=-315 \frac{ kJ }{ kg }[/latex]

since [latex]\hat{H}_{1}\left(T=0^{\circ} C ight)=0 ext { and } \hat{H}_{2}\left(T=0^{\circ} C ight)=0[/latex], so that a total of −315 kJ/kg × 0.152 kg = −47.9 kJ of energy must be removed to keep the mixture at a constant temperature of 0°C.

Comment

Sulfuric acid and water are said to mix exothermically since energy must be released to the environment to mix these two components at constant temperature. The temperature rise that occurs when these two components are mixed adiabatically is considered in Illustration 8.4-1. Note also that to solve this problem we have, in effect, used an energy balance without explicitly writing a detailed balance equation. We will consider the balance equations (mass, energy, and entropy) for mixtures in Sec. 8.4.

Question 8.1.1: Calculating the Energy Release of an Exothermic Mixing Proce...

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