The Limiting Reactant

In chemical reactions with two or more reactants, the reaction will continue until one of the reactants is used up. When that reactant is gone, the reaction stops. No more product can form. A limiting reactant (or limiting reagent) is used up first. It is the reactant that limits the amount of product that can be made. Consider the reaction of sodium metal with water to form hydrogen gas  

In the reaction of sodium hydroxide, NaOH, with hydrochloric acid, HC1 (aq), the balanced equation shows that each mole of NaOH reacts with the exact same number of moles of HC1 (aq). They react in a 1 to 1 mole ratio, the number of moles of both being identical. 

If NaOH and HCl(aq) are combined in anything other than a 1 to 1 mole ratio, one reactant will be in excess. The other will be the limiting reactant. Whenever starting amounts of two reactants are given in a stoichiometry problem, before you can calculate amounts of product you will first have to learn which reactant is the limiting reactant. It will govern how much product forms. 

To show how to analyze a limiting reactant problem, three different starting mixtures of NaOH and HCl(aq) follow. See how the limiting reactant is determined in each mixture. 

To determine which is the limiting reactant, choose one of the reactants and determine how many moles of the other it will consume. Let s choose NaOH and ask the question How many moles of HCl will be consumed by 0.35 mole of NaOH Even without doing a mole-to-mole conversion, the 1-to-l mole ratio in the balanced equation indicates that 

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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... 

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... 

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. 

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. 

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. 

The enormous value of K means that for all practical purposes this reaction goes to completion, consuming the limiting reactant, H+ or OH-. 

After reaction, the activity of a 25.0-mL water sample is 745 counts per minute (cpm), caused by the presence of Tl+-204 ions. The activity of Tl-204 is 5.53 X 105 cpm per gram of thallium metal. Assuming that 02 is the limiting reactant in the above equation, calculate its concentration in moles per liter. 

A 20 m3 working volume of a bioreactor is used for producting penicillin. What would be the sugar concentration (S0) you choose if oxygen transfer rate is not the limiting reactant Given data ... 

Besides mass transfer limitations, it is very important in electrochemical promotion experiments to compute the maximum mass-balance allowable rate enhancement. This is intimately related to the conversion of the limiting reactant under open circuit conditions, as the conversion of the latter cannot exceed 100%. In this respect keeping the open circuit conversion as low as possible (normally by using a small amount of catalyst) allows the system to exhibit a pronounced rate enhancement ratio. 

The limiting reactant in a reaction is the reactant that governs the maximum yield of product. A limiting reactant is like a part in short supply in a motorcycle factory. Suppose there are eight wheels and seven motorcycle frames. Because each frame requires two wheels, there are enough wheels for only four motorcycles, so the wheels play the role of the limiting reactant. When all the wheels have been used, three frames remain unused, because they were present in excess. 

In some cases, we must determine by calculation which is the limiting reactant. For example, from the equation... 

The limiting reactant is the reactant that will be completely used up. All other reactants are in excess. Because the limiting reactant is the one that limits the amounts of products that can be formed, the theoretical yield is calculated from the amount of the limiting reactant. 

Step 3 If the actual amount of the second reactant is greater than the amount needed (the value calculated in step 2), then the second reactant is present in excess in this case, the first reactant is the limiting reactant. If the actual amount of the second reactant is less than that calculated, then all of it will react so it is the limiting reactant and the first reactant is in excess. 

Calculate the theoretical molar yield of one of the products for each reactant separately, by using the procedure in Toolbox L.l. This method is a good one to use when there are more than two reactants. The reactant that would produce the smallest amount of product is the limiting reactant. 

Step 1 Convert the mass of each reactant into moles, if necessary, by using the molar masses of the substances. Step 2 Select one of the products. For each reactant, calculate how many moles of the product it can form. Step 3 The reactant that can produce the least amount of product is the limiting reactant. 

EXAMPLE M.2 Sample exercise Identifying the limiting reactant... 

Calcium carbide, CaC2, reacts with water to form calcium hydroxide and the flammable gas ethyne (acetylene). This reaction was once used for lamps on bicycles, because the reactants are easily transported, (a) Which is the limiting reactant when 1.00 X 102 g of water reacts with 1.00 X 102 g of calcium carbide (b) What mass of ethyne can he produced (c) What mass of excess reactant remains after reaction is complete Assume that the calcium carbide is pure and that all the ethyne produced is collected. The chemical equation is... 

Step 3 Determine which reactant is Because 3.12 mol H20 is required and 5.55 mol the limiting reactant. H20 is supplied, all the calcium carbide can react ... 

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