Reactant, limiting

Let A and B be two reactants of a chemical reaction taking place in a batch reactor. Using Eq. 2.3.6, at any time t, the molar contents of the two reactants are related by 

If reactant A is indeed the limiting reactant, Aa(0 vanishes before Ais(t), therefore, the following relation should be satisfied  

Note that because the stoichiometric coefficients of reactants are negative, absolute values are used. Similarly, for steady-flow reactors, using Eq. 2.3.15, the species molar flow rates of the two reactants are related by 

Equation 2.5.2 is the mathematical condition for stoichiometric proportion of the reactants in the reactor feed. 

When multiple chemical reactions take place, the chemical reaction whose stoichiometric coefficients are used in Eqs. 2.5.1a and 2.5.1b is the stoichiometric relation that ties the reactants fed to the desirable product. This is illustrated in Example 2.11. 

What is the yield of NH4CI (in grams) if 0.238 mol of CI2 and 1.627 g of NH3 are available for the following reaction Which reactant is the limiting reactant  

The NH3is the limiting reactant because less product is obtained from it. The yield for the reaction is 3.833 g because it is the lesser of the two amounts. 

When a chemist carries out a reaction, the reactants usually are not present in stoichiometric amonnts. Becanse the goal of a reaction is usually to produce the maximum quantity of a useful compound from the starting materials, an excess of one reactant is commonly supplied to ensure that the more expensive or more important reactant is converted completely to the desired product. Consequently, some of the reactant supplied in excess will be left over at the end of the reaction. The reactant used up first in a reaction is called the limiting reactant, because the amount of this reactant limits the amount of product that can form. When all the limiting reactant has been consumed, no more product can be formed. Excess reactants are those present in quantities greater than necessary to react with the quantity of the limiting reactant. 

The concept of a limiting reactant applies to everyday tasks, too, such as making ham sandwiches. Suppose you want to make the maximum number of ham sandwiches possible, each of which will consist of two shces of bread and one slice of ham. If you have eight slices of bread and six slices of ham, how many sandwiches can you make The answer is four, because after making four sandwiches you will be out of bread. You will have two slices of ham left over, but without additional bread you will be unable to make any more sandwiches. In this case, bread is the limiting reactant and ham is the excess reactant. 

In problems involving limiting reactants, the first step is to determine which is the hmiting reactant. After the limiting reactant has been identified, the rest of the problem can be solved using the approach outlined in Section 3.6. Consider the formation of methanol (CH3OH) from carbon 

We can use the stoichiometric conversion factors to determine how many moles of H2 are necessary for all the CO to react. From the balanced equation, we have 1 mol CO 2 mol H2. Therefore, the amount of H2 necessary to react with 5 mol CO is 

Because there are only 8 moles of H2 available, there is insufficient H2 to react with all the CO. Therefore, H2 is the limiting reactant and CO is the excess reactant. H2 will be used up first, and when it is gone, the formation of methanol will cease and there will be some CO left over, as shown in Fignre 3.6(b). To determine how much CO will be left over when the reaction is complete, we mnst first calculate the amount of CO that will react with all 8 moles of H2  

Consider the chemical reaction between compounds A and B, aA + bB cC, and let the rate equation be 

Both reactants A and B will get completely converted into products if the reactants A and B are present in the exact stoichiometric mole ratio. 

Cbo is the minimum initial concentration of B required for the complete conversion of A. 

Assume that reactant B is made available very much in excess of the minimum quantity required, that is, Cbo Cm- Then reactant A, but not reactant B, will get completely converted into product. Even after complete conversion of A, a large amount of B will remain unconverted in the reaction vessel. As reactant B is present in excess, change in concentration of B is negligible compared to the initial concentration of B, Cbo and hence Cb can be treated as a constant for all practical purposes, that is, Cg = Cgg- The rate Equation 2.9 gets reduced to 

Reactant A is called the limiting reactant and it is the concentration of A, C, that controls the rate of reaction. Consider a second-order reaction between A and B with the rate equation expressed as 

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Fischer esterification is reversible and the position of equilibrium lies slightly to the side of products when the reactants are simple alcohols and carboxylic acids When the Fis cher esterification is used for preparative purposes the position of equilibrium can be made more favorable by using either the alcohol or the carboxylic acid m excess In the following example m which an excess of the alcohol was employed the yield indicated IS based on the carboxylic acid as the limiting reactant... 

C is the concentration of limiting reactant in mol/L, c is the chemiluminescence quantum yield in ein/mol, and P is a photopic factor that is determined by the sensitivity of the human eye to the spectral distribution of the light. Because the human eye is most responsive to yellow light, where the photopic factor for a yellow fluorescer such as fluorescein can be as high as 0.85, blue or red formulations have inherently lower light capacities. 

For simulation on the IBM 360/65 computer, the reaction was represented as first order to oxygen, the limiting reactant, and by the usual Arrhenius form dependency on temperature. Since the changes here were rapid, various transport processes had significant roles. The following set of differential equations was used to describe the transient system ... 

In cases where the reactants involved are not present in the proper stoichiometric ratios, the limiting reactant will have to be determined and the excess amounts of the other reactants calculated. It is safe to assume that unconsumed reactants and inert components exit with the products in their original forms. Consider the following example. 

To simplify calculations, but also by convention, the amount of excess reactant in a reaction is defined on the basis of the reaction going to completion for the limiting reactant. In the case of methane (CH4) burned with excess air, the volume of air needed to combust the methane is calculated as though there is complete combustion of the methane, converting it entirely to carbon dioxide and water. 

Assume that the reaction between A and B is second order and is represented by A -i- B —> products where A is the limiting reactant. The rate expression is... 

Selectivity is defined as the ratio of the desired product to the amount of limiting reactant tliat has undergone chemical change. That is... 

A limiting reactant is that reactant which is present in the smallest stoichiometric amount. In industrial reactions, the reactants are not necessarily supplied in the exact proportions demanded by the stoichiometry of the equation. Under these... 

The degree of completion of a reaction refers to the fraction of the limiting reactant that has been converted into products. 

Examine the stoichiometry of the chemical reaction, and identify the limiting reactant and excess reactants. 

Choose a basis of 100 lb of ethane (limiting reactant). The stoichiometric equation is... 

In situations such as this, a distinction is made between the excess reactant (Sb) and the limiting reactant, I2. The amount of product formed is determined (limited) by the amount of limiting reactant With 3.00 mol of 1 only 2.00 mol of Sbl3 is obtained, regardless of how large an excess of Sb is used. 

Under these conditions, the theoretical yield of product is the amount produced if the limiting reactant is completely consumed. In the case just cited, the theoretical yield of Sbl3 is 2.00 mol, the amount formed from the limiting reactant, I2. 

Often you will be given the amounts of two different reactants and asked to determine which is the limiting reactant, to calculate the theoretical yield of the product and to find how much of the excess reactant is unused. To do so, it helps to follow a systematic, four-step procedure. 

Choose the smaller of the two amounts calculated in (1) and (2). This is the theoretical yield of product the reactant that produces the smaller amount is the limiting reactant. The other reactant is in excess only part of it is consumed. 

To illustrate how this procedure works, suppose you want to make grilled cheese sandwiches from 6 slices of cheese and 18 pieces of bread. The available cheese is enough for six grilled cheese sandwiches the bread is enough for 9. Clearly, the cheese is the limiting reactant there is an excess of bread. The theoretical yield is 6 sandwiches. Six grilled cheese sandwiches use up 12 slices of bread. Since there are 18 pieces available, 6 pieces of bread are left over. 

Determine the limiting reactant and the theoretical yield when... 

Because 1.20 mol is the smaller amount of product, that is the theoretical yield of Sbl3. This amount of Sbl3 is produced by the antimony, so Sb is the limiting reactant. 

The reactant that yields the smaller amount (3.17 g) of Sbl3 is I2. Hence I2 is the limiting reactant. The smaller amount, 3.17 g of Sbl3, is the theoretical yield. 

Click Coached Problems for a self-study module on limiting reactants. 

The theoretical yield is the maximum amount of product that can be obtained. In calculating the theoretical yield, it is assumed that the limiting reactant is 100% converted to product. In the real world, that is unlikely to happen. Some of the limiting reactant may be consumed in competing reactions. Some of the product may be lost in separating it from the reaction mixture. For these and other reasons, the experimental yield is ordinarily less than the theoretical yield. Put another way, the percent yield is expected to be less than 100% ... 

The dependence of reaction rate on concentration is readily explained. Ordinarily, reactions occur as the result of collisions between reactant molecules. The higher the concentration of molecules, the greater the number of collisions in unit time and hence the faster the reaction. As reactants are consumed, their concentrations drop, collisions occur less frequently, and reaction rate decreases. This explains the common observation that reaction rate drops off with time, eventually going to zero when the limiting reactant is consumed. 

Make a table like the one above and determine the number of moles of acetic acid (HAc) and acetate ion (Ac-) after the reaction is complete. Since the stoichiometric ratios are 1 1, the limiting reactant is the one with the smaller number of moles. 

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