AP Chemistry 4.5-4.6: Stoichiometry and Titration

Percent yield

Percent yield compares the experimentally obtained product with the stoichiometric maximum: $\%\text{ yield}=\frac{\text{actual yield}}{\text{theoretical yield}}\times100\%$.

Stoichiometry

Stoichiometry is the quantitative relationship between the amounts of reactants consumed and products formed in a chemical reaction. These relationships come from the coefficients of a balanced chemical equation.

Why must a chemical equation be balanced before stoichiometric calculations are performed?

A balanced equation gives the correct mole ratios among all reactants and products while conserving each element. These coefficients are the basis for every stoichiometric conversion.

What does the coefficient ratio in a balanced chemical equation represent?

It represents relative amounts in moles, molecules, formula units, or any equivalent counting unit. For example, $2NH_3:3H_2$ means 2 moles of ammonia form for every 3 moles of hydrogen consumed.

How are stoichiometric factors obtained from a balanced chemical equation?

Any pair of coefficients can form a mole ratio. For $N_2 + 3H_2 \rightarrow 2NH_3$, valid factors include $\frac{2\text{ mol }NH_3}{3\text{ mol }H_2}$ and $\frac{3\text{ mol }H_2}{1\text{ mol }N_2}$.

How can the number of product molecules be calculated from moles of a reactant?

Convert reactant moles to product moles using the balanced-equation ratio, then multiply by Avogadro’s number: $6.022\times10^{23}$ particles per mole.

How many moles of $I_2$ are required to react with $0.429$ mol Al in $2Al + 3I_2 \rightarrow 2AlI_3$?

Use the mole ratio: $0.429\text{ mol Al}\times\frac{3\text{ mol }I_2}{2\text{ mol Al}}=0.644\text{ mol }I_2$.

How many $CO_2$ molecules form when $0.75$ mol $C_3H_8$ combusts according to $C_3H_8+5O_2\rightarrow3CO_2+4H_2O$?

$0.75\text{ mol }C_3H_8\times\frac{3\text{ mol }CO_2}{1\text{ mol }C_3H_8}\times6.022\times10^{23}\frac{CO_2\text{ molecules}}{\text{mol}}\approx1.4\times10^{24}$ $CO_2$ molecules.

What is the standard mass-to-mass stoichiometry pathway for a chemical reaction?

Convert grams of the known substance to moles using its molar mass, use the balanced-equation mole ratio, then convert moles of the desired substance to grams using its molar mass.

How can the mass of one reactant needed to consume another reactant be calculated?

Convert the given reactant mass to moles, apply the balanced-equation mole ratio between the reactants, and convert the resulting moles to the requested mass.

What mass of NaOH is required to produce $16$ g of $Mg(OH)_2$ from $MgCl_2+2NaOH\rightarrow Mg(OH)_2+2NaCl$?

$16\text{ g }Mg(OH)_2\times\frac{1\text{ mol}}{58.3\text{ g}}\times\frac{2\text{ mol NaOH}}{1\text{ mol }Mg(OH)_2}\times\frac{40.0\text{ g}}{1\text{ mol}}\approx22\text{ g NaOH}$.

What mass of oxygen is consumed by $702$ g octane in $2C_8H_{18}+25O_2\rightarrow16CO_2+18H_2O$?

$702\text{ g }C_8H_{18}\times\frac{1\text{ mol}}{114.23\text{ g}}\times\frac{25\text{ mol }O_2}{2\text{ mol }C_8H_{18}}\times\frac{32.00\text{ g}}{1\text{ mol}}\approx2.46\times10^3\text{ g }O_2$.

How is solution molarity incorporated into a reaction-stoichiometry calculation?

First calculate moles of solute with $n=MV$, where $M$ is molarity in mol/L and $V$ is volume in liters. Then use the balanced-equation mole ratio to find the desired amount.

How does the sodium azide reaction demonstrate an applied stoichiometric calculation?

In $2NaN_3(s)\rightarrow3N_2(g)+2Na(s)$, the coefficient ratio determines how much nitrogen gas can be generated from a measured amount of sodium azide. This allows airbag systems to use an appropriate azide quantity for rapid inflation.

Stoichiometric amounts

Reactant amounts are stoichiometric when they are present in exactly the mole ratios required by the balanced chemical equation. If one reactant is present in less than this ratio, it may limit the reaction.

Limiting reactant

The limiting reactant is the reactant that is completely consumed first and therefore determines the maximum amount of product that can form.

Excess reactant

The excess reactant is supplied in more than the stoichiometric amount and remains partially unreacted after the limiting reactant is consumed.

Why can the reactant with the smaller starting mass not automatically be identified as the limiting reactant?

Limiting behavior depends on moles and the balanced-equation coefficients, not directly on mass. Each reactant must be converted to moles and compared with the required stoichiometric ratio.

How can the limiting reactant be identified by comparing product amounts?

Use each reactant separately to calculate the amount of product it could produce if completely consumed. The reactant that predicts the smaller product amount is the limiting reactant.

When $3.00$ mol $H_2$ reacts with $2.00$ mol $Cl_2$ according to $H_2+Cl_2\rightarrow2HCl$, which reactant is limiting and how much $H_2$ remains?

The reactants require a 1:1 ratio, so $Cl_2$ is limiting. Consuming $2.00$ mol $Cl_2$ uses $2.00$ mol $H_2$, leaving $1.00$ mol $H_2$ unreacted.

For $3Si+2N_2\rightarrow Si_3N_4$, which reactant limits when $2.00$ g Si and $1.50$ g $N_2$ react?

$2.00$ g Si is $0.0712$ mol and $1.50$ g $N_2$ is $0.0535$ mol. These amounts could produce $0.0237$ mol and $0.0268$ mol $Si_3N_4$, respectively, so Si is limiting.

How is theoretical yield determined when multiple reactants are provided?

Identify the limiting reactant first. Calculate the product amount from that reactant using the balanced-equation mole ratio; this is the theoretical yield.

What is the theoretical yield of a chemical reaction?

The theoretical yield is the maximum amount of product predicted by stoichiometry under specified conditions, assuming the limiting reactant reacts completely and no product is lost.

What is the actual yield?

The actual yield is the amount of product experimentally obtained. It is commonly lower than the theoretical yield because of side reactions, incomplete reactions, or product loss during recovery.

Why is the actual yield often less than the theoretical yield?

The reaction may have side reactions or fail to reach completion, and product may be lost during separation or collection. These effects reduce the recovered product.

What units may be used for actual and theoretical yield in a percent-yield calculation?

They may both be expressed as mass, moles, volume, or another appropriate quantity. The same units must be used for both values.

A reaction has a theoretical yield of $0.5072$ g Cu and an actual yield of $0.392$ g Cu. What is its percent yield?

$\%\text{ yield}=\frac{0.392}{0.5072}\times100\%=77.3\%$.

Can a percent yield ordinarily exceed $100\%$? What might an unusually high value indicate?

No; a value above $100\%$ is not physically consistent with the stated theoretical yield. It may indicate an impure or wet product, measurement error, or an incorrect limiting-reactant or stoichiometric calculation.

Quantitative chemical analysis

Quantitative chemical analysis determines the amount or concentration of a substance in a sample, often by measuring how much of it reacts or how much product forms.

Titration

Titration determines an analyte’s concentration by adding a solution of known concentration, the titrant, until it reacts completely with the analyte. The measured titrant volume and reaction stoichiometry are used to calculate the analyte amount.

Titrant versus analyte

The titrant is the solution of known concentration delivered from a buret. The analyte is the substance in the sample solution whose amount or concentration is being determined.

What role does a buret play in titration analysis?

A buret delivers and measures a variable volume of titrant accurately. The volume required to reach the endpoint is used with the titrant concentration and reaction stoichiometry.

What is the equivalence point of a titration?

The equivalence point is reached when stoichiometrically equivalent amounts of titrant and analyte have reacted according to the balanced equation.

What is the endpoint of a titration, and how does it relate to the equivalence point?

The endpoint is the experimentally observed signal—such as an indicator color change or cessation of bubbling—used to identify completion. A properly designed titration makes the endpoint very close to the equivalence point.

How can a titration endpoint be detected?

It may be detected by a visible change, commonly an indicator color change, or by monitoring a measurable solution property that changes predictably. Gas evolution that stops is another possible signal.

What information is needed to calculate an analyte concentration from a titration?

The titrant molarity, the volume of titrant delivered, the balanced-equation mole ratio, and the volume or other relevant amount of analyte sample are needed.

How would the acetic-acid concentration in vinegar be related to a potassium carbonate titration?

For $2CH_3CO_2H+K_2CO_3\rightarrow2CH_3CO_2K+CO_2+H_2O$, moles of acetic acid equal twice the moles of $K_2CO_3$ consumed. The observed bubbling results from produced $CO_2$.

Which major reaction types commonly serve as the basis for titration analysis?

Precipitation, acid–base, and redox reactions are common bases for titrations. In each case, a known reaction stoichiometry connects titrant amount to analyte amount.