- #1
marellasunny
- 255
- 3
QUESTION: Say I have the following equilibrium reaction
[tex]CO+\frac{1}{2}O_2\leftrightharpoons CO_2[/tex]
The stoichiometric mixture of CO and $O_2$ in a closed vessel, initially at 1 atm and 300K, is exploded. Calculate the composition of the products of combustion at 2500K and the gas pressure.
Take $K_p$=27.5. Take $\alpha$ as the degree of dissociation.
$$$$
MY ATTEMPT AT AN ANSWER:
I use the ICE method to find out the reactant and product composition
$$CO+\frac{1}{2}O_2\leftrightharpoons CO_2$$
The reaction quotient can be given as Q=0/0.5=0. Therefore, the products must have plus sign.
Then I get the final composition(/concentration) as
$$CO=[1-\alpha] $$
$$O_2=[1-\alpha/2]$$
$$CO_2=[\alpha]$$
then, $$ K_p= \frac{\alpha}{[1-\alpha][1-\alpha/2]^{0.5} } $$
I would then use the IDEAL GAS LAW to find the product mixture
i.e $$ p_RV=n_RRT_R$$ $$p_pV=n_PRT_p$$
I would then substitute these values into the expression for $K_P$.
MY QUERY:
1.Is my calculation for [itex]K_P[/itex] correct? I take [itex]CO_2[/itex] as the product and CO and [itex]O_2[/itex] as the reactants.
2.I am not able to figure out what is the number of moles of the products [itex]n_P[/itex] and the number of moles of the reactants [itex]n_R[/itex].The book's solution gives [itex]n_R[/itex]=3/2 and [itex]n_P=1+\alpha/2[/itex].
The author solves with the initial species as [itex]CO_2[/itex] and obtains the compositions [itex]CO_2=(1-\alpha)[/itex];[itex]CO=\alpha[/itex];[itex]O_2=\alpha/2[/itex], which is confusing given that the question states the reaction starts with CO and O2 in a closed vessel.
[tex]CO+\frac{1}{2}O_2\leftrightharpoons CO_2[/tex]
The stoichiometric mixture of CO and $O_2$ in a closed vessel, initially at 1 atm and 300K, is exploded. Calculate the composition of the products of combustion at 2500K and the gas pressure.
Take $K_p$=27.5. Take $\alpha$ as the degree of dissociation.
$$$$
MY ATTEMPT AT AN ANSWER:
I use the ICE method to find out the reactant and product composition
$$CO+\frac{1}{2}O_2\leftrightharpoons CO_2$$
The reaction quotient can be given as Q=0/0.5=0. Therefore, the products must have plus sign.
Then I get the final composition(/concentration) as
$$CO=[1-\alpha] $$
$$O_2=[1-\alpha/2]$$
$$CO_2=[\alpha]$$
then, $$ K_p= \frac{\alpha}{[1-\alpha][1-\alpha/2]^{0.5} } $$
I would then use the IDEAL GAS LAW to find the product mixture
i.e $$ p_RV=n_RRT_R$$ $$p_pV=n_PRT_p$$
I would then substitute these values into the expression for $K_P$.
MY QUERY:
1.Is my calculation for [itex]K_P[/itex] correct? I take [itex]CO_2[/itex] as the product and CO and [itex]O_2[/itex] as the reactants.
2.I am not able to figure out what is the number of moles of the products [itex]n_P[/itex] and the number of moles of the reactants [itex]n_R[/itex].The book's solution gives [itex]n_R[/itex]=3/2 and [itex]n_P=1+\alpha/2[/itex].
The author solves with the initial species as [itex]CO_2[/itex] and obtains the compositions [itex]CO_2=(1-\alpha)[/itex];[itex]CO=\alpha[/itex];[itex]O_2=\alpha/2[/itex], which is confusing given that the question states the reaction starts with CO and O2 in a closed vessel.