Known that in the process of smelting a certain metal in a blast furnace, the reactions involved are as follows:

$\mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO}=2 \mathrm{Fe}+3 \mathrm{CO}_{2}(1)$

$\mathrm{C}+\mathrm{O}_{2}=\mathrm{CO}_{2}(2)$

$\mathrm{C}+0.5\mathrm{O}_{2}=\mathrm{CO}(3)$

The $\Delta_{f} H m^{\circ}$ of each substance involved above are as follows:

$\Delta_{f} H m^{\ominus}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)=-824.25 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

$\Delta_{f} H m^{\ominus}\left(\mathrm{CO}_{2}\right)=-393.52 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

$\Delta_{f} H m^{\ominus}(\mathrm{CO})=-110.53 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

It is now known that at the working temperature of the blast furnace, in the tail gas of the reaction between $\mathrm{CO}$ and $\mathrm{Fe}_{2} \mathrm{O}_{3}$, $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=0.40$. If every $1 \mathrm{~mol} \mathrm{Fe}$ is produced, $400.00 \mathrm{~kJ}$ of heat will be dissipated from the furnace wall to the air. The system has no other heat sources or material exchange, and the system is a constant pressure system. If the furnace temperature is kept constant, please calculate the $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)$ in the products of coke combustion, the correct option is:
已知高炉冶炼某金属的过程中,涉及的反应如下:

$\mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO}=2 \mathrm{Fe}+3 \mathrm{CO}_{2}(1)$

$\mathrm{C}+\mathrm{O}_{2}=\mathrm{CO}_{2}(2)$

$\mathrm{C}+0.5\mathrm{O}_{2}=\mathrm{CO}(3)$

上述涉及到的各物质的 $\Delta_{f} H m^{\circ}$ 如下:

$\Delta_{f} H m^{\ominus}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)=-824.25 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

$\Delta_{f} H m^{\ominus}\left(\mathrm{CO}_{2}\right)=-393.52 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

$\Delta_{f} H m^{\ominus}(\mathrm{CO})=-110.53 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

现已知在高炉的工作温度下, $\mathrm{CO}$ 与 $\mathrm{Fe}_{2} \mathrm{O}_{3}$ 反应的尾气中, $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=0.40$ 。若每生
成 $1 \mathrm{~mol} \mathrm{Fe}$, 将有 $400.00 \mathrm{~kJ}$ 的热从炉壁散到空气中。体系无其他热源与物质交换，且体系为恒压体系。若维持炉温不变, 请计算焦炭燃烧的
产物中的 $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)$，下列选项正确的是：
All other options are incorrect
3.01
6.31
1.22
1.00
3.36
5.50
3.57
5.88
其他选项均不正确
3.01
6.31
1.22
1.00
3.36
5.50
3.57
5.88
$\Delta r H m^{\circ}(1)=3 \times \Delta_{f} H m^{\circ}\left(\mathrm{CO}_{2}\right)-3 \times \Delta_{f} H m^{\circ}(\mathrm{CO})-\Delta_{f} H m^{\circ}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)=-24.72 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

<Checkpoint>[$\Delta r H m^{\circ}(1)=-24.72 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$](1)</Checkpoint>

Let $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=x$ 。

From this, it can be seen that whenever there is $1 \mathrm{~mol} \mathrm{CO}_{2}$ in the combustion products, $x \mathrm{~mol} \mathrm{CO}$ will be generated. Therefore, $1 \mathrm{~mol}$ of reaction $\mathrm{(2)}$
and $x \mathrm{~mol}$ of reaction $\mathrm{(3)}$ will occur.

In addition, assuming that $y \mathrm{~mol}$ of reaction $\mathrm{(1)}$ occurs, then in the exhaust gas, $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=(x-3 y) /(1+3 y)=0.40$ and heat is dissipated
$800.00 y \mathrm{~kJ}$ 。

<Checkpoint>[In the exhaust gas, $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=(x-3 y) /(1+3 y)=0.40$ and heat is dissipated $800.00 y \mathrm{~kJ}$ ](1)</Checkpoint>

Since the furnace temperature remains unchanged, the sum of the total enthalpy change of the three reactions is 0. Among them, the enthalpy changes of reaction $\mathrm{(2)}$ and reaction $\mathrm{(3)}$ are the enthalpy of formation of $\mathrm{CO_2}$ and $\mathrm{CO}$:
$\mathrm{-393.52 - 110.53x - 24.72y + 800.00y = 0 }$

<Checkpoint>[Thermal equilibrium: $\mathrm{-393.52 - 110.53x - 24.72y + 800.00y = 0 }$](1)</Checkpoint>

The above two equations can be solved simultaneously to obtain:

$x=6.3$

<Checkpoint>[$\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=6.3$ ](1)</Checkpoint>
$\Delta r H m^{\circ}(1)=3 \times \Delta_{f} H m^{\circ}\left(\mathrm{CO}_{2}\right)-3 \times \Delta_{f} H m^{\circ}(\mathrm{CO})-\Delta_{f} H m^{\circ}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)=-24.72 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$

<Checkpoint>[$\Delta r H m^{\circ}(1)=-24.72 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$](1)</Checkpoint>

设 $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=x$ 。

由此可知每当燃烧产物中有 $1 \mathrm{~mol} \mathrm{CO}_{2}$, 则将生成 $x \mathrm{~mol} \mathrm{CO}$ 。因此将发生 $1 \mathrm{~mol}$ 反应$\mathrm{(2)}$
和 $x \mathrm{~mol}$ 反应$\mathrm{(3)}$。

另假设发生了 $y \mathrm{~mol}$ 反应$\mathrm{(1)}$, 则尾气中 $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=(x-3 y) /(1+3 y)=0.40$ 并散热
$800.00 y \mathrm{~kJ}$ 。

<Checkpoint>[尾气中 $\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=(x-3 y) /(1+3 y)=0.40$ 并散热 $800.00 y \mathrm{~kJ}$ ](1)</Checkpoint>

由炉温不变可知，三个反应的总焓变和为0。其中反应$\mathrm{(2)}$和反应$\mathrm{(3)}$的焓变即为$\mathrm{CO_2}$和$\mathrm{CO}$的生成焓:
$\mathrm{-393.52 - 110.53x - 24.72y + 800.00y = 0 }$

<Checkpoint>[热平衡: $\mathrm{-393.52 - 110.53x - 24.72y + 800.00y = 0 }$](1)</Checkpoint>

上述两式联立可得:

$x=6.3$

<Checkpoint>[$\mathrm{p}(\mathrm{CO}) / \mathrm{p}\left(\mathrm{CO}_{2}\right)=6.3$ ](1)</Checkpoint>