Find the final temperature if the reaction of Eq. (2.7-1) is carried out adiabatically at constant pressure beginning at 298.15 K. Assume that a stoichiometric mixture is present before the reaction and that the reaction proceeds to completion. Assume that the heat capacity of water vapor is

Question

Find the final temperature if the reaction of [latex]Eq. (2.7-1): 2H_{2}(g)+O_{2}(g)\longrightarrow 2H_{2}O(l)[/latex] is carried out adiabatically at constant pressure beginning at 298.15 K. Assume that a stoichiometric mixture is present before the reaction and that the reaction proceeds to completion. Assume that the heat capacity of water vapor is constant and equal to its value at 2000 K.

Accepted Answer

The reaction as written in [latex]Eq. (2.7-1): 2H_{2}(g)+O_{2}(g)\longrightarrow 2H_{2}O(l)[/latex] includes liquid water as the product. In our case the water produced will be a vapor, so we calculate ΔH° at 298.15K for the gaseous product:

[latex]\Delta H°(298.15K)=2\Delta _{f}H°(H_{2}O(g))-0-0[/latex]

[latex]=2(-241.818kJmol^{-1})=-483.636kJmol^{-1}=-483636Jmol^{-1}[/latex]

[latex]C_{P}(products)=2(51.18JK^{-1}mol^{-1})=102.36JK^{-1}mol^{-1}[/latex]

[latex]\int_{298.15K}^{T_{2}}{(102.36JK^{-1}mol^{-1})} dT-483636Jmol^{-1}=0[/latex]

[latex](102.36JK^{-1}mol^{-1})(T_{2}-298.15K)=483636Jmol^{-1}[/latex]

[latex]T_{2}=5023K\approx 5000K[/latex]

This result might be inaccurate because of the actual dependence of the heat capacity of water vapor on temperature.

Question 2.32: Find the final temperature if the reaction of Eq. (2.7-1) is...

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