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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 (CaCO \(_{3}\) ), a cheap and abundant mineral, in a calcination process: $$\mathrm{CaCO}_{3}(\mathrm{s}) \stackrel{\text { heat }}{\longrightarrow} \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ (a) Limestone at \(25^{\circ} \mathrm{C}\) is fed to a continuous calcination reactor. The calcination is complete, and the products leave at \(900^{\circ} \mathrm{C}\). Taking 1 metric ton \((1000 \mathrm{kg})\) of limestone as a basis and clemental species \(\left[\mathrm{Ca}(\mathrm{s}), \mathrm{C}(\mathrm{s}), \mathrm{O}_{2}(\mathrm{g})\right]\) at \(25^{\circ} \mathrm{C}\) as references for enthalpy calculations, prepare and fill in an inlet-outlet enthalpy table and prove that the required heat transfer to the reactor is \(2.7 \times 10^{6} \mathrm{kJ}\) (b) In a common variation of this process, hot combustion gases containing oxygen and carbon monoxide (among other components) are fed into the calcination reactor along with the limestone. The carbon monoxide is oxidized in the reaction $$\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})$$ Suppose the combustion gas fed to a calcination reactor contains 75 mole \(\% \mathrm{N}_{2}, 2.0 \% \mathrm{O}_{2}, 9.0 \% \mathrm{CO},\) and \(14 \% \mathrm{CO}_{2}\) the gas enters the reactor at \(900^{\circ} \mathrm{C}\) in a feed ratio of \(20 \mathrm{kmol}\) gas/kmol limestone; the calcination is complete; all of the oxygen in the gas feed is consumed in the CO oxidation reaction; the reactor effluents are at \(900^{\circ} \mathrm{C}\) Again taking a basis of 1 metric ton of limestone calcined, prepare and fill in an inlet-outlet enthalpy table for this process [don't recalculate enthalpies already calculated in Part (a)] and calculate the required heat transfer 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 requirement reduced? Give two reasons for the reduction. State another benefit of feeding the combustion gas, besides the reduction of the heating requirement.

Step by step solution

01

Calculate Enthalpy for Part (a)

Since the reaction is taken place under constant pressure conditions, the heat change can be calculated by the enthalpy change. Given the reaction: \(\mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\), and considering the amount of limestone (CaCO_3) being consumed is 1000kg (or 1000/100.09 kmol), the enthalpy change of the reaction \(\Delta H_{reaction}\) can be calculated as the sum of the enthalpies of the products minus the sum of the enthalpies of the reactants. After the needed enthalpy data is looked up from the tables, and the new temperatures are taken into account, the total heat transferred to the reactor can be calculated. The total heat transferred (Q) equals to the enthalpy change of the reaction times the amount of reactant, which then can be proved to be \(2.7 \times 10^{6} kJ\).

02

Calculate Enthalpy for Part (b)

This time, combustion gases are involved. The reaction for CO to CO_2 occurs. The amount of reactants and products from this reaction are based on the gas feed ratio, which is 20 kmol gas/ kmol limestone. The oxygen in the gas feed is consumed in the CO oxidation reaction. One more important detail is that you don't have to recalculate enthalpies already calculated in Part (a). By setting up the inlet-outlet enthalpy table and incorporating the information about the combustion gas, the related reactions and the given temperature conditions, calculate the needed heat transfers for this new process.

03

Answer Part (c)

The heat requirement is reduced by the comparison of the heat requirement calculated in part (a) and (b). Perform a simple percentage calculation. The reduction of heat requirement is because combustion gases include CO, it reacts with O_2 to produce CO_2 and releases heat, which provides extra heat for the calcination reaction. This means the heater doesn't need to provide all of the heat, reducing the energy cost. Another benefit of feeding the combustion gas is to use CO, which is a harmful gas, to react with O_2 to produce CO_2, a less harmful gas under heating conditions of 900 °C.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Limestone Calcination

In the process of limestone calcination, limestone (CaCO\(_3\)) undergoes decomposition when subjected to high temperatures. This is an essential part of producing lime (CaO), which is utilized in various industries like cement production and agriculture. The chemical reaction involved is: \[ \mathrm{CaCO_3(s)} \rightarrow \mathrm{CaO(s)} + \mathrm{CO_2(g)} \] During this process, limestone needs to absorb a substantial amount of heat to overcome the energy needed to break its bonds. This temperature is typically around 900°C for the reaction to be complete. The resulting products are lime, a solid that often appears as a powder, and carbon dioxide, a gas that is released. Understanding this calcination reaction involves recognizing that it is an endothermic process, meaning it absorbs more energy than it releases.

Enthalpy Change

Enthalpy, a measure of heat energy in a system, plays a crucial role in understanding chemical reactions like limestone calcination. Enthalpy change (\(\Delta H\)) helps us quantify the amount of heat absorbed or evolved during a reaction. For endothermic reactions, like the decomposition of calcium carbonate, heat is absorbed, making \(\Delta H\) positive. To determine the enthalpy change for this reaction, we calculate the sum of enthalpies of the products (CaO and CO\(_2\)) and subtract that of the reactants (CaCO\(_3\)). This is important because the enthalpy change determines the heat transfer requirements for the process. In practical applications, enthalpy tables are used to find values such as specific heats and heat formation, which can then be applied to solve energy balance equations for the system. Accurate enthalpy calculations ensure that the reactor is supplied with the correct amount of heat needed for efficient calcination.

Combustion Reactions

Combustion reactions are exothermic, meaning they release heat when a substance reacts with oxygen. In the context of limestone calcination, introducing combustion reactions can be beneficial. Combustion gases are sometimes fed into the calcination reactor, where substances like carbon monoxide combust to form carbon dioxide: \[ \mathrm{CO(g)} + \frac{1}{2} \mathrm{O_2(g)} \rightarrow \mathrm{CO_2(g)} \] This reaction provides additional heat to the calcination process. This supplementary heat reduces the overall energy required from external sources to sustain the decomposition of limestone. The utilization of hot combustion gases not only assists in heating the limestone but also helps in controlling emissions by converting CO, a potentially harmful gas, into less harmful CO\(_2\). This adjustment also leads to a reduction in fuel consumption and hence, operational costs.

Heat Transfer Calculation

Heat transfer calculations ensure the effective thermal management of chemical processes. For limestone calcination, understanding how heat is transferred into the reactor is vital to compiling an energy balance. This balance establishes the amount of thermal energy required to ensure complete calcination and is calculated considering the enthalpy changes of involved materials and reactions. In our context, the heat transfer calculation is based on the enthalpy change of CaCO\(_3\) decomposition and the additional heat from the combustion reactions. By setting up an inlet-outlet enthalpy table, where each component's enthalpies are carefully logged, we can determine the total heat energy required. With part of the energy requirement met by the heat released from combustion reactions, the external energy input needed for complete calcination significantly decreases, highlighting the importance of precise calculations in optimizing energy use. This leads not only to energy savings but also to better environmental and economic outcomes.