Question

When $10g$ of $Al$ is used for reduction in each of the following alumino thermic reactions, which reaction would generate more heat and by how much ?
a. $2Al+C{r}_2{O}_3\to A{l}_2{O}_3+2Cr$
b. $2Al+F{e}_2{O}_3\to A{l}_2{O}_3+2Fe$

Standard heat of formation of $A{l}_2{O}_3$, $C{r}_2{O}_3$ and $F{e}_2{O}_3$ are $-1676kJ$, $-1141kJ$ and $-822.2kJ$, respectively.

• A. Reaction (b) produces more heat by $59.04kJ$
• B. Reaction (a) produces more heat by $59.04kJ$
• C. Reaction(a) and (b) produces equal heat
• D. None of these

Answer 1

The correct option is A Reaction (b) produces more heat by $59.04kJ$

Given,
$2Al+\frac{3}{2}{O}_2\to A{l}_2{O}_3;\Delta H_1=-1676kJ......\left(i\right)$

$2Cr+\frac{3}{2}{O}_2\to C{r}_2{O}_3;\Delta H_2=-1141kJ....\left(ii\right)$

$2Fe+\frac{3}{2}{O}_2\to F{e}_2{O}_3;\Delta H_3=-822.2kJ....\left(iii\right)$

To calculate
$\Delta H_a=?$

For $2Al+C{r}_2{O}_3\to A{l}_2{O}_3+2Cr....\left(iv\right)$

Subtract $\Delta H_2$ from $\Delta H_1$ to obtain $\Delta H_a$
$\Delta H_a=\Delta H_1-\Delta H_2$
$\Delta H_a=-1676-(-1141)$
$\Delta H_a=-535kJ$

$\Delta H_b=?$

For $2Al+F{e}_2{O}_3\to A{l}_2{O}_3+2Fe......\left(v\right)$

Subtract $\Delta H_3$ from $\Delta H_1$ to obtain $\Delta H_b$
$\Delta H_b=\Delta H_1-\Delta H_3$
$\Delta H_b=-1676-(-822.2)$
$\Delta H_b=-853.8kJ$

For reaction (iv)

$2\times 27g$ of $Al$ produces 535 kJ of heat

10g of $Al$ produces $\frac{535\times 10}{2\times 27}=99.07kJ$

For reaction (v)

$2\times 27g$ of Al produces 853.8 kJ of heat

10g of Al produces $\frac{853.8\times 10}{54}$
$=158.11kJ$

Reaction (ii) produces more heat by $=158.11-99.07$
$=59.04kJ$