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To calculate the pH of a solution, we need to understand that pH is a measure of the hydrogen ion concentration in the solution. It is calculated using the formula: \[pH = -\log_{10}([\text{H}^+])\]For example, with a given pH of 2.56, you can find the concentration \[[\text{H}^+] = 10^{-2.56} = 2.75 \times 10^{-3} \text{mol/L}\]This formula shows that the pH is inversely related to the hydrogen ion concentration; the more acidic the solution, the higher the concentration of hydrogen ions. This step is crucial because it links the pH value directly to the amount of acid in solution, which is necessary for subsequent calculations in acid-base reactions.

Molarity, or molar concentration, is key for determining the amount of a substance in a given volume of solution. It is defined as the number of moles of solute per liter of solution. The formula for molarity \(M\) is:\[M = \frac{\text{moles of solute}}{\text{liters of solution}}\]For hydrochloric acid in our example, the concentration found from the pH helps us calculate molarity directly. With a hydrogen ion concentration of \[2.75 \times 10^{-3} \, \text{mol/L}\]and knowing the solution volume is 0.125 L, you find the moles of HCl by multiplying these values:\[\text{Moles of HCl} = 2.75 \times 10^{-3} \, \text{mol/L} \times 0.125 \, \text{L} = 3.44 \times 10^{-4} \, \text{mol}\]This molarity is then used to understand the concentration of HCl available to react with another substance.

Chemical stoichiometry involves using balanced chemical equations to determine the relationships between reactants and products in a reaction. In acid-base reactions like the one between hydrochloric acid and sodium bicarbonate, stoichiometry dictates how much of each substance is needed or produced. The balanced equation:\[\text{HCl} + \text{NaHCO}_3 \rightarrow \text{NaCl} + \text{CO}_2 + \text{H}_2\text{O}\]shows a 1:1 molar ratio. This means that one mole of HCl reacts with one mole of NaHCOeutraliUsing the calculated moles of HCl \(3.44 \times 10^{-4} \, \text{mol}\), you can determine that an equal amount of NaHCOeutronis required to neutralize the acid. This simple stoichiometric ratio makes calculations straightforward, ensuring all reactants are consumed without excess.

A neutralization reaction occurs when an acid reacts with a base to produce salt and water. In the exercise, HCl is neutralized by NaHCO₃:\[\text{HCl} + \text{NaHCO}_3 \rightarrow \text{NaCl} + \text{CO}_2 + \text{H}_2\text{O}\]This process results in the formation of water, sodium chloride (table salt), and carbon dioxide gas. Neutralization reactions are essential in various applications, such as antacid tablets to relieve indigestion by neutralizing stomach acid. For our example, understanding the reaction helps in calculating the required mass of the base. By using the stoichiometric ratio (1:1), we've determined that the moles of NaHCO₃ needed are the same as the HCl moles. Finally, it allows us to compute the precise mass of NaHCO₃:\[\text{Mass} = 3.44 \times 10^{-4} \, \text{mol} \times 84.006 \, \text{g/mol} = 0.0289 \, \text{g}\]Here, the reaction completes, demonstrating the beauty of chemistry in balancing reactants to achieve neutralization.