Lime $($calcium oxide$)$ is widely used in the production of cement, steel, medicines insecticides, plant and animal food, soap, rubber, and many other familiar materials It is usually produced by heating and decomposing limestone $(CaC{O}_3),$ a cheap and abundant minerat, in a culcination proces:

atem out $CaC{O}_3(s)={?}^{\text{c}\text{a}\text{O}}Ca(s)+C{O}_2(s)$

$($a$)$ Limestone at $25C$ is fod to a continuous calcination reactor. The calcination is complete, and the products leave at $900C.$ Taking I metric ton $(1000kg)$ of limestone as a basis and elemental species $Ca(s),C(s),O_2((g))$ at $25C$ as references for enthalpy calculations prepare and fill in an inlet$-$outlet enthalpy table and prove that the required hear transter to the reactor is $2\mathrm{.}710kJ$

$($b$)\sqrt[\phantom{2}]{n\text{a}\text{c}\text{o}\text{m}\text{m}\text{o}\text{n}}$ variation of this process, hot combustion gases containing oxygen and carbon monoxide $($among other components$)$ are fed into the calcination reactor along with the lime$-$

stone. The carbon monoxide is oxidized in the reaction

$CO(s)+1O_2(s)C{O}_2(s)$

Suppose

$8=0\mathrm{.}35an$

the combustion gas fed to a calcination reactor contaios $75$ mole $\%N_2,2\mathrm{.}0\%O_2,9\mathrm{.}0\%CO$ and $14\%C{O}_2$ :

the gas enters the reactor at $900C$ in a teed ratio of $20km$ ol gas$/$kmol limestone$,$

the calcination is complete,

all of the oxygen in the gas feed is consumed in the CO oxidation reaction:

the reactor etfuents are at gorr.

$($Gavila$,$

Again taking a basis of $1$ metric ton of limestone calcined, prepare and fill in an inlet$-$outlet enthalpy table for this process $[$don$\text{'}$t recalculate enthalpies already calculated in part $($a$)]$ and calculale the required heat cransfer to the reactor.

$($c$)$ You should have found that the heat that must be transferred to the reactor is significantly lower with the combustion gas in the feed than it is without the gas. By what percentage is the heat