Question

When limestone is heated, quicklime is formed according to the equation, $CaC{O_3}\left( s \right) \rightleftharpoons CaO\left( s \right) + C{O_2}\left( s \right)$
The experiment was carried out in the temperature range $800 - {900^ \circ }C$ . Equilibrium constant ${K_p}$ follow the relation, $\log {K_p} = 7.282 - 8500/T$
Where, $T$ is the temperature in Kelvin. At what temperature the decomposition will give $C{O_2}$ at $1atm$ ?

Answer 1

As we know the partial pressure of a gas is directly proportional to the number of moles of gas at constant temperature. We can use this to calculate the partial pressure of each component in a reaction.

Complete step by step solution:
In the given question it is given that when limestone is heated, quicklime is formed according to the equation,
$CaC{O_3}\left( s \right) \rightleftharpoons CaO\left( s \right) + C{O_2}\left( s \right)$
The experiment was carried out in the temperature range $800 - {900^ \circ }C$ . Equilibrium constant ${K_p}$ follow the relation, $\log {K_p} = 7.282 - 8500/T$
Where, $T$ is the temperature in Kelvin.
The decomposition gives $C{O_2}(g)$ at 1 atm
${K_p} = {P_{C{O_2}}} = 1$
Now , we can calculate the temperature by putting the value of ${K_p}$ in above relation $\log {K_p} = 7.282 - 8500/T$
$\log 1 = 7.282 - \dfrac{{8500}}{T}$
On solving the above equation, we will get the temperature at which the decomposition will give $C{O_2}$ at $1atm$ .
$0 = 7.282 - \dfrac{{8500}}{T}$
$\Rightarrow$ $7.282 = \dfrac{{8500}}{T}$
$T = 1167.26K$
Now, we get the required temperature at which the decomposition will give $C{O_2}$ at $1atm$ . The temperature is $1167.26K$

Additional information:
Limestone: It is a type of carbonate. It is composed primarily of calcium carbonate $\left( {CaC{O_3}} \right)$ in the form of mineral calcite.
Quicklime: it is a white, caustic and alkaline crystalline solid at room temperature. The chemical formula of quicklime is $CaO$ . it is also known as burnt lime.

Note:
The temperature for decomposition of $CaC{O_3}$ will give $C{O_2}$ at $1atm$ is very high; this indicates that more heat is required for this process. The process is endothermic because temperature is required for the decomposition.