\(5.00 \mathrm{~g}\) of solid sodium (Na) and \(30.0 \mathrm{~g}\) of liquid bromine \(\left(\mathrm{Br}_{2}\right)\) react to form solid \(\mathrm{NaBr}\). (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting? (c) What is the theoretical yield for this reaction in grams? (d) How many grams of excess reactant are left over at the end of the reaction? (e) When this reaction is actually performed, \(14.7 \mathrm{~g}\) of \(\mathrm{NaBr}\) is recovered. What is the percent yield of the reaction?

In chemistry, a balanced chemical equation is crucial for accurately representing a chemical reaction. It ensures that the law of conservation of mass is obeyed, which states that matter cannot be created or destroyed in a chemical reaction. In practical terms, this means the number of atoms of each element must be the same on both sides of the equation.

For instance, consider the reaction of solid sodium (Na) with liquid bromine (Br₂) to form solid sodium bromide (NaBr). The balanced chemical equation is:
\[2 \mathrm{Na} + \mathrm{Br}_{2} \rightarrow 2 \mathrm{NaBr}\]
Notice how there are two sodium atoms and two bromine atoms on each side of the equation, hence it is balanced. This step is foundational for all subsequent calculations in a chemical reaction, such as identifying the limiting reactant, theoretical yield, and percent yield.

The limiting reactant in a chemical reaction is the substance that is completely consumed first, thus determining the maximum amount of product that can be formed. Identifying the limiting reactant is a key step when predicting the quantities of products and reactants involved in a chemical reaction.

For our example reaction between sodium and bromine, we determine the limiting reactant by converting the given masses to moles and then comparing these to the mole ratios required by the balanced equation. In our case:
\[\begin{align*}\text{Moles of sodium:} & \frac{5.00 \mathrm{~g}}{22.99 \mathrm{~g/mol}} = 0.2174 \mathrm{~mol} \text{Moles of bromine:} & \frac{30.0 \mathrm{~g}}{159.8 \mathrm{~g/mol}} = 0.1879 \mathrm{~mol}\end{align*}\]
By comparing the mole ratio of sodium and bromine to the stoichiometric ratio from the balanced equation, we find that sodium, with fewer mole equivalents, is the limiting reactant. This is essential for accurately predicting the outcome of the reaction.

The percent yield is a measure of the efficiency of a chemical reaction, calculated by comparing the actual yield (the amount of product actually obtained) to the theoretical yield (the maximum amount of product that could be formed from the limiting reactant). Percent yield is expressed as a percentage and can be calculated using the formula:
\[\text{Percent yield} = \left( \frac{\text{Actual yield}}{\text{Theoretical yield}} \right) \times 100\% \]

In our example, we've established a theoretical yield of 22.37 g for sodium bromide. However, the actual experiment yielded only 14.7 g. Thus:
\[\text{Percent yield} = \left( \frac{14.7 \mathrm{~g}}{22.37 \mathrm{~g}} \right) \times 100\% = 65.7\% \]
A percent yield less than 100% can be due to factors such as incomplete reactions, loss of product during processing, or side reactions. Understanding percent yield helps in evaluating the effectiveness of a reaction and planning the quantities needed for a desired amount of product.