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In the thermite reaction $$\ce{2Al(s) + Fe2O3(s) -> 2Fe(l) + Al2O3(s)}$$ what is the maximum temperature attainable by the products? Assume reactants at 25°C and 1 atm and that all heat capacities remain constant.

I started by using Hess's law to find the enthalpy change of the reaction. I couldn't find a heat of formation for liquid iron so I assume I have to find that out. I just wrote out the equation $\small\ce{Fe(s) + heat + enthalpy Of Fusion -> Fe(s)}$ and figured the heat of formation for liquid iron at 25°C is around -302.71kJ/mol.

To find the max temperature I used $ \small \Delta H(reaction) = \Delta T * Cp(products)$. I am coming out with an equation like -14445 kJ/mol = 0.147 kJ/(mol K) * maxT. This gives me a negative temperature, so I assume it is wrong. Even if I were to take the absolute value, the answer seems awfully high. I was expecting something around a few thousand degrees not near ten thousand.

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Thermodynamics will never give a complete picture here: the actual heat will be dominated by the kinetics of the reaction and the kinetics of heat transfer to the environment. Thermodynamic calculations will give an absolute upper limit at best. –  matt_black Oct 30 '12 at 19:58
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3 Answers 3

According to Wikipedia the maximum temperature is approximately 2500 °C, limited by the boiling point of aluminum, which is 2519 °C. The article provides some discussion of how the temperature is limited, and how to calculate it using Hesse's law.

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This gives me a negative temperature, so I assume it is wrong.

Remember that the energy given off as an exothermic reaction progresses is absorbed by the surroundings. The chemical potential energy stored in aluminum and rust is converted into kinetic energy. You are interested in $\Delta H_{surr}$, which should be $-\Delta H_{sys}$. The "system" in this case is the electrons of the materials engaged in various bonding patterns, and the "surroundings" are the bulk materials.

I was expecting something around a few thousand degrees not near ten thousand.

I would agree. Both aluminum oxide and iron melt and then boil below 10000 oC. Are you sure you are determining the $\Delta _f H^o$ of $\ce{Fe}(l)$ correctly? Melting is an endothermic process (absorbs heat from the surroundings).

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well for one I used a ridiculous number for the melting point of iron. That combined with fixing what is negative and what is not in each circumstance I am getting around 5000C which is more reasonable but still seems high. I could have just made another simple error –  Steve Oct 29 '12 at 3:50
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I am coming out with an equation like -14445 kJ/mol = 0.147 kJ/(mol K) * maxT

It is wrong. $C_p$ is temperature dependent, so you have to use a more sophisticated equation with integrals. Moreover, parts for heating liquid and solid phases will be different.

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This question is assuming Cp is not temperature dependent in the given temperature ranges –  Steve Oct 29 '12 at 12:18
    
Well... It is wrong. And again, one have to count at least the fact, that the reaction gives partially melted products, that also reduces overall effect. –  permeakra Oct 29 '12 at 15:20
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