If \(380 \mathrm{~mL}\) of \(0.35 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) are added to 500 . \(\mathrm{mL}\) of \(0.65\) \(M \mathrm{HCl}\), will the mixture be acidic or basic? Find the \(\mathrm{pH}\) of the resulting solution.

When working with solutions in chemistry, molarity is a crucial concept. Molarity (M) refers to the concentration of a solution. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution. The formula to determine molarity is simple: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
For instance, in the original exercise, we had a solution of \text{Ba(OH)}_2 with a molarity of 0.35 M and a volume of 380 mL (which is 0.380 L). By multiplying these values, we found the number of moles of \text{Ba(OH)}_2. Remember to always convert the volume into liters before calculating molarity.
This simple concept allows us to quantify how strong a solution is and is often the first step in solving many chemistry problems.

In any chemical reaction, the limiting reagent is the substance that gets completely consumed first and thus determines the maximum amount of product that can be formed. Identifying the limiting reagent involves comparing the mole ratios of the reactants based on the balanced chemical equation.
In our example, we were dealing with \text{Ba(OH)}_2 and \text{HCl} in an acid-base reaction. By calculating the moles of each reactant, we determined that \text{OH}^- (from \text{Ba(OH)}_2) was the limiting reagent because it had fewer moles compared to \text{HCl}. \[ \text{moles of } \text{OH}^- = 0.266 \text{ and } \text{moles of } \text{HCl} = 0.325 \]
With the limiting reagent fully reacting, the remaining excess of the second reagent can be calculated to understand the reaction's outcome further.

Acid-base reactions are common in chemistry and involve the transfer of protons (H+ ions) from the acid to the base. In aqueous solutions:

• Acids release H+ ions (protons).
• Bases release OH- (hydroxide) ions.

When acids and bases react, they neutralize each other to produce water and a salt. In the exercise, \text{HCl}, a strong acid, reacted with \text{Ba(OH)}_2, a strong base. The balanced reaction is: \[ \text{Ba(OH)}_2 + 2 \text{HCl} \rightarrow \text{BaCl}_2 + 2 \text{H}_2\text{O} \]
The resulting mixture still contained an excess of \text{HCl}, which kept the solution acidic. Knowing the remaining moles of \text{HCl} helped in calculating the final concentration of H+ ions, leading to the determination of pH.

In chemistry, logarithms are frequently used to describe the concentrations of hydronium ions (H+) in a solution. pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution, defined as: \[ \text{pH} = - \text{log}[\text{H}^+] \]
Here, \text{log} refers to the base-10 logarithm. A decrease in one pH unit corresponds to a tenfold increase in H+ ion concentration.
In our problem, once we calculated the H+ concentration from the remaining HCl as 0.067 M, we found the pH using the logarithm: \[ \text{pH} = - \text{log}(0.067) \]
This gives us a pH of approximately 1.17, indicating a strongly acidic solution. Understanding how to manipulate and interpret logarithms is essential in accurately determining pH values in chemistry.