Consider the unbalanced equation for the reaction of solid lead with silver nitrate: $$ \mathrm{Pb}(s)+\mathrm{AgNO}_{3}(a q) \longrightarrow \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Ag}(s) $$ (a) Balance the equation. (b) How many moles of silver nitrate are required to completely react with \(9.3 \mathrm{~mol}\) of lead? (c) How many moles of Ag are formed by the complete reaction of \(28.4\) mol of \(\mathrm{Pb}\) ?

Balancing chemical equations is a foundational skill in chemistry that ensures the law of conservation of matter is adhered to. This law states that matter cannot be created or destroyed. When balancing equations, our goal is to make sure the number of atoms of each element is equal on both the reactant and product sides.

For instance, when balancing the equation \[ \text{Pb}(s) + \text{AgNO}_{3}(aq) \longrightarrow \text{Pb(NO}_{3})_{2}(aq) + \text{Ag}(s) \], we observe each element or compound to ensure that they match up. Starting with the most complex molecule, typically a good practice, we work through each element to make sure it balances. The process might involve placing coefficients — whole numbers placed in front of compounds — to ensure the number of atoms of each element in the reactants equals those in the products. In our case, we ended up with the balanced equation \[ \text{Pb}(s) + 2\text{AgNO}_{3}(aq) \longrightarrow \text{Pb(NO}_{3})_{2}(aq) + 2\text{Ag}(s) \].

The mole-to-mole ratio is derived from the coefficients of a balanced chemical equation. It tells us how many moles of one substance will react with or produce a certain number of moles of another substance. A clear understanding of mole-to-mole ratios is crucial for precisely predicting the amounts of reactants or products involved in a chemical reaction.

In the solved exercise, the balanced equation indicates a mole-to-mole ratio of 1 mole of Pb to 2 moles of AgNO3 (\(1:\text{Pb}=2:\text{AgNO}_{3}\)) for the reactants and 1 mole of Pb to 2 moles of Ag (\(1:\text{Pb}=2:\text{Ag}\)) for the products. Using this ratio, it is straightforward to predict that to react with 9.3 moles of \(\text{Pb}\), one would need 18.6 moles of \(\text{AgNO}_{3}\).

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction, using the mole-to-mole ratios derived from a balanced equation. It tells us how much product can be formed from given reactants or how much reactants are needed to produce a certain amount of product, based on those proportions.

By following reaction stoichiometry, we can, for example, determine that 28.4 moles of Pb will produce 56.8 moles of Ag, using the molecule-to-molecule ratio expected from the reaction.

Considering Conversion Factors

In a real-world scenario, such calculations often incorporate additional steps to convert between units, such as grams to moles, using the molar mass as a conversion factor. This enables precise measurements in the lab and industrial processes.

When solving stoichiometry problems, students should follow a structured approach to avoid mistakes and ensure accuracy:

1. Start by writing down the unbalanced chemical equation.
2. Balance the equation using coefficients to get equal numbers of atoms of each element on both sides.
3. Determine the mole ratios from the balanced equation.
4. Use conversion factors as needed, such as molar masses, to translate between grams and moles or liters, if dealing with gases at STP (Standard Temperature and Pressure).
5. Apply the mole ratios to calculate the moles (or mass or volume) of reactants or products as required by the problem.

Utilizing Dimensional Analysis

Dimensional analysis, a mathematical method that employs conversion factors to move from one unit to another, is an indispensable tool in solving stoichiometry problems. This method prevents missteps by ensuring that units cancel properly and calculations are consistent with the mole ratios.