If \(150 \mathrm{~mL}\) of \(0.055 \mathrm{M} \mathrm{HNO}_{3}\) are needed to completely neutralize \(1.48 \mathrm{~g}\) of an impure sample of sodium hydrogen carbonate (baking soda), what percent of the sample is baking soda?

Understanding a balanced chemical equation is crucial in the study of chemistry, as it represents the law of conservation of mass. It illustrates that atoms are neither created nor destroyed in a chemical reaction. In our sample exercise, the balanced equation \( HNO_3 + NaHCO_3 \rightarrow NaNO_3 + CO_2 + H_2O \) ensures that the number of atoms for each element is the same on both sides of the equation.

When working with chemical reactions, always check the balance of your equation first. This will tell you the stoichiometric ratios needed to calculate reactants and products – essential knowledge for subsequent calculations in the problem.

Molarity, symbolized as \(M\), measures the concentration of a solution and is defined as the number of moles of solute per liter of solution. It is a fundamental concept when dealing with chemical solutions, as it allows us to relate the volume of a solution to the amount of substance in moles. The formula \( n_{HNO_3} = M_{HNO_3} \times V_{HNO_3} \) demonstrates this calculation. Here, knowing the molarity and volume of \(HNO_3\) solution enables us to find the moles of \(HNO_3\) used in the reaction.

Keep in mind, the volume needs to be in liters for the calculation to work correctly. If provided in milliliters, as in our problem, you must convert to liters by dividing by 1000.

Once the moles of a substance are known, mole-to-mass conversion allows us to determine its mass, which is vital in quantitative chemistry. This step utilizes the substance's molar mass. The relationship is given by \( m = n \times M_{molar} \) where \(m\) is the mass, \(n\) is the number of moles, and \(M_{molar}\) is the molar mass.

In the given exercise, after finding the moles of \(NaHCO_3\), we multiply by its molar mass (84.01 g/mol) to calculate the mass. This step is essential in moving from the abstract quantity (moles) to a tangible quantity (grams) that we can measure.

The percent purity of a chemical compound is a measure of its composition in terms of pure substance. It's particularly important in industry where the quality of materials matters. Calculated using the formula \( \text{Percent purity} = (\frac{m_{pure}}{m_{impure}}) \times 100\% \) where \(m_{pure}\) is the mass of the pure substance and \(m_{impure}\) is the mass of the impure sample.

In our problem, to find the purity of the baking soda sample, we calculate the mass of pure \(NaHCO_3\) and express it as a percentage of the initial mass of the sample provided in the problem. This tells us how much of the original sample is the desired compound.

The neutralization reaction between an acid and a base is a specific type of double displacement reaction, where an acid reacts with a base to produce a salt and water. This reaction invariably involves the transfer of protons from the acid to the base. In the context of our example, nitric acid \(HNO_3\) reacts with sodium hydrogen carbonate \(NaHCO_3\) following the equation shown above.

Understanding the stoichiometry of neutralization reactions is key for calculations, as it often involves a 1:1 mole ratio for monoprotic acids and bases, simplifying calculations. For multiprotic acids or bases, the ratio might differ, which is essential to consider when balancing equations.