Lead ions can be precipitated from solution with \(\mathrm{NaCl}\) according to the reaction: $$ \mathrm{Pb}^{2+}(a q)+2 \mathrm{NaCl}(a q) \longrightarrow \mathrm{PbCl}_{2}(s)+2 \mathrm{Na}^{+}(a q) $$ When \(135.8 \mathrm{~g}\) of \(\mathrm{NaCl}\) are added to a solution containing \(195.7 \mathrm{~g}\) of \(\mathrm{Pb}^{2+}, \mathrm{a} \mathrm{PbCl}_{2}\) precipitate forms. The precipitate is filtered and dried and found to have a mass of \(252.4 \mathrm{~g}\). Determine the limiting reactant, theoretical yield of \(\mathrm{PbCl}_{2}\), and percent yield for the reaction.

Stoichiometry is the section of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It is founded on the law of conservation of mass which states that in a chemical reaction, matter is neither created nor destroyed. Consequently, the amount of each element must be the same in the reactants and products.

To solve stoichiometry problems, one must first write the balanced chemical equation for the reaction. Then, using the coefficients from the balanced equation, which indicate the mole ratios in the reaction, solve for the unknown quantities. For example, the equation \(\mathrm{Pb}^{2+}(aq) + 2 \mathrm{NaCl}(aq) \longrightarrow \mathrm{PbCl}_{2}(s) + 2 \mathrm{Na}^{+}(aq)\) implies that one mole of \(\mathrm{Pb}^{2+}\) reacts with two moles of \(\mathrm{NaCl}\). These ratios are the foundation of all subsequent calculations.

The theoretical yield is a term that refers to the maximum amount of product that could be formed in a chemical reaction, assuming that every molecule of reactants converts perfectly to product without any loss.

To calculate the theoretical yield, you first need to determine the limiting reactant—the reactant that will be completely used up first, limiting the amount of product that can be formed. Once the limiting reactant is known, you can use the stoichiometric ratios from the balanced chemical equation to find the maximum possible amount of product.

Example

In the given reaction, after finding the moles of \(\mathrm{PbCl}_{2}\) that could be formed based on the limiting reactant's moles, you would then convert these moles to grams using the molar mass of \(\mathrm{PbCl}_{2}\). This gives us the theoretical yield, which is essential for determining the efficiency of the reaction.

Percent yield is a measurement of how efficient a chemical reaction is. It compares the actual yield (the amount of product actually produced) to the theoretical yield (the maximum amount that could theoretically be produced).

The formula for calculating percent yield is straightforward: \[\text{Percent Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100\%\] For the exercise at hand, after determining the actual yield of \(\mathrm{PbCl}_{2}\) to be 252.4 g (the amount that was actually produced in the experiment) and calculating the theoretical yield (as explained in the previous section), you would use these values to find the percent yield of the reaction. A percent yield above 100% is generally not possible and indicates an error in the experiment or calculations, while a percent yield under 100% reflects the losses and inefficiencies that occur in practical settings.

A chemical reaction is a process that involves the transformation of one set of chemical substances to another. During a reaction, bonds between atoms are broken and formed, creating new substances with different properties from the original substances.

In the chemical equation provided, \(\mathrm{Pb}^{2+}(aq) + 2 \mathrm{NaCl}(aq) \longrightarrow \mathrm{PbCl}_{2}(s) + 2 \mathrm{Na}^{+}(aq)\), lead ions \(\mathrm{Pb}^{2+}\) react with sodium chloride \(\mathrm{NaCl}\) to form a precipitate of lead(II) chloride \(\mathrm{PbCl}_{2}\) along with sodium ions in solution. This precipitation reaction is an example of a double displacement reaction in which cations and anions switch partners. The solid \(\mathrm{PbCl}_{2}\) that forms is insoluble in the aqueous solution, thus precipitates out which can be collected by filtration.