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The perturbed invariant manifolds

Why do reactions stop?

Rarely in nature are the reactants present in the exact ratios specified by Rarely in nature are the reactants present in the exact ratios specified by the balanced chemical equation. Generally, one or more reactants are in the balanced chemical equation. Generally, one or more reactants are in excess and the reaction proceeds until all of one reactant is used up.

excess and the reaction proceeds until all of one reactant is used up.

When a reaction is carried out in the laboratory, the same principle When a reaction is carried out in the laboratory, the same principle applies. Usually, one or more of the reactants are in excess, while one is applies. Usually, one or more of the reactants are in excess, while one is limited. The amount of product depends on the reactant that is limited.

limited. The amount of product depends on the reactant that is limited.

Limiting and

Limiting and excess reactantsexcess reactants Recall the reaction from theRecall the reaction from the Launch Lab. After the colorless solution formed, adding more sodium Launch Lab. After the colorless solution formed, adding more sodium hydrogen sulfite had no effect because there was no more potassium hydrogen sulfite had no effect because there was no more potassium permanganate available to react with it. Potassium permanganate was a permanganate available to react with it. Potassium permanganate was a limiting reactant. As the name implies, the

limiting reactant. As the name implies, the limiting reactantlimiting reactant limits the limits the extent of the reaction and, thereby, determines the amount of product extent of the reaction and, thereby, determines the amount of product formed. A portion of all the

formed. A portion of all the other reactants remainother reactants remains after the reactions after the reaction

1.3

1.3

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Determining the limiting reactant

Determining the limiting reactant The calculations you did inThe calculations you did in the previous section were based on having the reactants present in the the previous section were based on having the reactants present in the ratio described by the

ratio described by the balanced chemical equationbalanced chemical equation. When this is . When this is not thenot the case, the first thing you must do is determine which reactant is limiting.

case, the first thing you must do is determine which reactant is limiting.

Consider the reaction shown in

Consider the reaction shown in Figure 11.5,Figure 11.5, in which three mole- in which three mole-cules of nitrogen (

cules of nitrogen (NN22) and three molecules of hydrogen () and three molecules of hydrogen (HH22) react to) react to form ammonia (N

form ammonia (NHH33). In the ). In the first step of the reaction, all first step of the reaction, all the nitrogenthe nitrogen molecules and hydrogen molecules are separated into individual atoms.

molecules and hydrogen molecules are separated into individual atoms.

These atoms are available for reassembling into ammonia molecules, These atoms are available for reassembling into ammonia molecules,  just as the too

 just as the tools inls inFigure 11.4Figure 11.4 are available to be assembled into tool are available to be assembled into tool kits. How many molecules of ammonia can be produced from the kits. How many molecules of ammonia can be produced from the avail-able atoms? Two ammonia molecules can be assembled from the able atoms? Two ammonia molecules can be assembled from the

hydro-Three nitrogen molecules

(two nitrogen atoms, six hydrogen atoms) (two nitrogen atoms, six hydrogen atoms)

Two nitrogen molecules

 Figure 11.5 Figure 11.5 If you check all the atoms present before and after the reaction, If you check all the atoms present before and after the reaction, you will find thatyou will find that some of the

some of the nitrogen molecules are unchanged. These nitrogen molecules are the excess reactant.nitrogen molecules are unchanged. These nitrogen molecules are the excess reactant.

Interactive Figure

Interactive Figure To see an animationTo see an animation of limiting reactants, visit

of limiting reactants, visitglencoe.comglencoe.com..

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Moles of reactants

Moles of reactants Identifying the limiting Identifying the limiting reactant involvreactant involves find-es find-ing the number of moles of each reactant. You can do this by convertfind-ing ing the number of moles of each reactant. You can do this by converting the masses of chlorine and sulfur to moles. Multiply each mass by a the masses of chlorine and sulfur to moles. Multiply each mass by a con- version f

 version factor that ractor that relates moelates moles and massles and mass—the inve—the inverse of morse of molar mass.lar mass.

100.0 g C

Using mole ratios The next step involves determining whether theThe next step involves determining whether the two reactants are in the correct mole ratio, as given in

two reactants are in the correct mole ratio, as given in the balancedthe balanced chemical equation. The coefficients in

chemical equation. The coefficients in the balanced chemical equationthe balanced chemical equation indicate that 4 mol of chlorine is

indicate that 4 mol of chlorine is needed to react with 1 needed to react with 1 mol of sulfur.mol of sulfur.

This 4:1 ratio from the

This 4:1 ratio from the equation must be compareequation must be compared with td with the actual ratiohe actual ratio of the moles of available reactants just calculated above. To determine of the moles of available reactants just calculated above. To determine the actual ratio of moles, divide the number of available moles of the actual ratio of moles, divide the number of available moles of chlo-rine by the number of available moles of sulfur.

rine by the number of available moles of sulfur.

1.410 mol C

1.410 mol Cll22 available available

__

__

0.7797 mol S

0.7797 mol S88 available available ==

1.808 mol C

1.808 mol Cll22 available available

__

__

1 mol S

1 mol S88 available available

Only 1.808 mol of chlorine is available for every 1 mol of sulfur, instead Only 1.808 mol of chlorine is available for every 1 mol of sulfur, instead of the 4 mol of chlorine required by the balanced chemical equation.

of the 4 mol of chlorine required by the balanced chemical equation.

Therefore, chlorine is the limiting reactant.

Therefore, chlorine is the limiting reactant.

Calculating the amount of product formed

Calculating the amount of product formed After determin-After determin-ing the limitdetermin-ing reactant, the amount of product in

ing the limiting reactant, the amount of product in moles can be calcu-moles can be calcu-lated by multiplying the given number of moles of the limiting reactant lated by multiplying the given number of moles of the limiting reactant

Careers In chemistry Careers In chemistry

Pharmacist

Pharmacist Knowledge of drugKnowledge of drug composition, modes of action, and composition, modes of action, and possible harmful interactions with possible harmful interactions with other substances allows a other substances allows a pharma-cist to counsel

cist to counsel patients on their care.patients on their care.

Pharmacists also mix chemicals to Pharmacists also mix chemicals to form powders, tablets, ointments, form powders, tablets, ointments, and solutions. For more information and solutions. For more information on chemistry careers, visit

on chemistry careers, visit glencoe.com

glencoe.com..

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