For the reaction ; $$ 2 \mathrm{Na}_{3} \mathrm{PO}_{4(\mathrm{aq})}+3 \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2(\mathrm{aq})} \longrightarrow \mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2(\mathrm{~s})}+6 \mathrm{NaNO}_{3(\mathrm{aq})} $$ Suppose that a solution containing \(32.8 \mathrm{~g}\) of \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) and \(26.1 \mathrm{~g}\) of \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) is mixed. How many \(\mathrm{g}\) of \(\mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) are formed?

Understanding the nature of chemical reactions is pivotal when dealing with stoichiometry problems. A chemical reaction analysis involves interpreting the balanced chemical equation to decipher the relationship between reactants and products. This underpins many calculations in chemistry, including those required to solve quantitative problems.

For instance, let's examine the reaction given in the exercise: \[2 \mathrm{Na}_{3} \mathrm{PO}_{4(\mathrm{aq})}+3 \mathrm{Ba}(\mathrm{NO}_{3})_{2(\mathrm{aq})} \longrightarrow \mathrm{Ba}_{3}(\mathrm{PO}_{4})_{2(\mathrm{~s})}+6 \mathrm{NaNO}_{3(\mathrm{aq})}\]
A balanced chemical equation is represented by coefficients before each compound, which indicate the molar ratios in which reactants combine and products are formed. This specific equation tells us that two moles of sodium phosphate \((\mathrm{Na}_{3} \mathrm{PO}_{4})\) react with three moles of barium nitrate \((\mathrm{Ba}(\mathrm{NO}_{3})_{2})\) to produce one mole of barium phosphate \((\mathrm{Ba}_{3}(\mathrm{PO}_{4})_{2})\) and six moles of sodium nitrate \((\mathrm{NaNO}_{3})\).

This stoichiometric relationship is the foundation for determining the amount of products formed in a reaction and identifying the limiting reactant, as demonstrated in the solution steps provided for the exercise.

In any chemical reaction, the limiting reactant is the substance that is completely consumed first, thus determining the maximum amount of product that can be formed. Identifying the limiting reactant is crucial in predicting the extent of chemical reactions and optimizing the use of reactants.

Following the steps of the given solution, after we calculate the moles of the reactants, we must compare the stoichiometric ratio of the reactants from the balanced chemical equation. In simple terms, you need to check which reactant is present in the smallest stoichiometric amount. This is done by converting the given masses of reactants to the corresponding moles and applying the molar ratios from the balanced equation.
\[\text{Required moles of } \mathrm{Ba}(\mathrm{NO}_{3})_{2} \text{ for 0.200 moles } \mathrm{Na}_{3}\mathrm{PO}_{4} = (0.200 \text{ moles } \mathrm{Na}_{3}\mathrm{PO}_{4}) \times \left(\frac{3 \text{ moles } \mathrm{Ba}(\mathrm{NO}_{3})_{2}}{2 \text{ moles } \mathrm{Na}_{3}\mathrm{PO}_{4}}\right) = 0.300 \text{ moles}.\]
Since the available moles of barium nitrate \((\mathrm{Ba}(\mathrm{NO}_{3})_{2})\) are less than the required stoichiometric amount, it is the limiting reactant. Calculating the limiting reactant accurately is imperative, as any error will lead to incorrect values for the amount of products formed.

Molar mass determination is the process of calculating the mass of one mole of a substance. It is a fundamental concept in chemistry that enables the conversion between mass and moles, serving as a bridge between the macroscopic world we observe and the microscopic world of atoms and molecules.

As demonstrated in the exercise solution, the molar mass is calculated by summing the masses of all the atoms in the molecule. For example, the molar mass of sodium phosphate \((\mathrm{Na}_{3}\mathrm{PO}_{4})\) was found using the formula:\[\text{Molar mass of } \mathrm{Na}_{3}\mathrm{PO}_{4} = 3(22.99 \text{ g/mol for Na}) + 30.97 \text{ g/mol for P} + 4(16.00 \text{ g/mol for O}) = 163.94 \text{ g/mol}.\]
Once you have the molar mass, you can convert the given mass of a substance to moles, which is a step towards using the stoichiometric relationships from the balanced chemical equation and subsequently determining the mass of the product formed.

Molar mass values must be precise since all subsequent calculations depend on these figures. When performing your calculations, be attentive to the rounding of atomic masses and ensure that you maintain consistency in your significant figures to achieve accurate results.