Question

1 mole of $F{{e}_{2}}{{O}_{3}}$ and 2 moles of Al are mixed at temperature 25℃ and the reaction is completed to give :
$F{{e}_{2}}{{O}_{3}}\left( s \right)+2A{{l}_{2}}{{O}_{3}}\left( s \right)+2F{{e}_{2}}\left( l \right);\Delta H=-850kJ$
The liberated heat is retained within the products whose combined specific heat over a wide temperature range is about $0.8J{{g}^{-1}}{{K}^{-1}}$. The melting point of iron is 1530℃. Show that the quantity of heat liberated is sufficient to raise the temperature of the product to the melting point of iron in order to get it wielded.

Answer 1

Use the formula for heat liberated which is $q=mc\Delta T$. Basically the heat released is proportional to the change in temperature. Here, c is the specific heat capacity i.e. the heat capacity per unit mass of a substance. In this there is a decrease of temperature of the system, as it is an endothermic reaction.

Complete step by step answer:
- In this question are given a reaction of wielding the rusted iron:
$F{{e}_{2}}{{O}_{3}}\left( s \right)+2Al\left( s \right)\to A{{l}_{2}}{{O}_{3}}\left( s \right)+2F{{e}_{2}}\left( l \right);\Delta H=-850kJ$
-We are required to find if the heat liberated is sufficient to raise the temperature of the product to the melting point of iron.
- First write down the information given to us in the question:
Initial temperature, ${{T}_{1}}$ = 25℃ , convert the temperature in standard form = 25 + 273 =298K
Final temperature, ${{T}_{2}}$ = 1530℃ = 1530 + 273 = 1803K
Enthalpy change, $\Delta H$= -850 kJ
Heat capacity, $c$= $0.8J{{g}^{-1}}{{K}^{-1}}$
We know that Specific heat capacity or also known as specific heat is the per unit mass heat capacity of any material, it is represented by the symbol c
- It depends on the material and phase of the material.
- In order to find the heat liberated at the increase in temperature we will use the following formula: $q=mc\Delta T$
where q is the heat liberated, m is the total mass of the product, c is the heat capacity and $\Delta T$ is the change in temperature.
- Here m = mass of$A{{l}_{2}}{{O}_{3}}$+ 2 (mass of Fe)
= 2×Al +3×O + 2×Fe
= 2×26 + 3×16 + 2×55.84
=211.68 g
- For $\Delta T$= ${{T}_{2}}$ - ${{T}_{1}}$
=1530 – 298
= 1505K
-Now putting all the values in the above equation
$q=mc\Delta T$
= 211.68 × 0.8 × 1505
= 254862 J = 254.862 kJ
- As heat required is less than heat released, we can conclude that the quantity of heat liberated is sufficient to raise the temperature of the product to the melting point of iron in order to get it wielded.

Note:
-Always convert the units into standard form while solving the questions.
-In the equation mass m is the total of mass of the product.
- In this there is a decrease of temperature of the system, as it is an endothermic reaction.
-Endothermic reactions are those reactions in which heat is liberated.