Calculate the \(\mathrm{pH}\) of a solution made by mixing \(50 \mathrm{~mL}\) of \(0.01 \mathrm{M}\) \(\mathrm{Ba}(\mathrm{OH})_{2}\) with \(50 \mathrm{~mL}\) water. Assume complete ionisation.

When a strong base like barium hydroxide e(e(e(₂)) is diluted with water, the concentration of thehydroxide (e(₂)) ions in the solution decreases. This dilution is a critical step in calculating the e(_{) of the solution, as the number ofhydroxide ions directly affects the acidity or basicity of thesolution. In the given exercise, diluting 50 mL of 0.01 M2) solution with an equal volume of water results in ae(2) concentration of 0.005 M. However, since e(2) produces twohydroxide ions, the actualhydroxide ion concentration is . It's essential to remember that thenumber of hydroxide ions contributes to the basicity of thesolution and thus influences the e() value.}

Hydroxide ion concentration is a measure of the number ofhydroxide ions (e(^-) present per liter of solution. In the context of the e(^2-), a strong base typically found in laboratory and industrialsettings, it is important to understand that each formula unit of e(^2-)dissociates to release twohydroxide ions into the solution, effectively doubling thehydroxide ion concentration compared to the initial molarity of thestrong base. Therefore, after dilution in the example, theconcentration of hydroxide ions is not merely the diluted molarity of e(^2-), but rather the diluted molarity multiplied by two (). This concept is crucial for accurately determiningthe e(P(OH)) and, by extension, the e(PH) of the solution.

The relationship between e(OH) and e() is fundamental to understandingacidity and basicity in solutions. The pOH is a measure of thealkalinity of a solution, where a lower e(OH) indicates ahigher concentration ofhydroxide ions and a more basic solution. Conversely, pH measures the acidity, with a lower pHindicating a higher concentration of hydrogen ions (e(⁺)) anda more acidic solution. The two values are inversely related and alwaysadd up to 14 in aqueous solutions at room temperature. Thisrelationship is concise and is expressed by the formula e() + e(OH) = 14. In other words, to findthe pH of a solution when you have the pOH (as demonstrated in the exercise), you subtractthe pOH from 14. For example, with a e() value of 2 for the solution, the pH is calculated to be.

Logarithm plays a crucial role in various applications inchemistry, particularly in the calculation of pH and e(OH), which are measures of acidity and basicity, respectively. ThepH and pOH scales are logarithmic, meaning each unit changerepresents a tenfold change in hydrogen or hydroxide ionconcentration. The logarithmic scale is used because it allows us toconveniently express a wide range of ion concentrations in a smallnumeric range. Specifically, the pH is calculated as the negative base10 logarithm of the hydrogen ion concentration (e()) and the pOH is the negativelogarithm of the hydroxide ion concentration (e([OH^-])). In the exercise, afterdetermining thehydroxide ion concentration, we apply the logarithmic formula tofind the e(OH) as e(OH) = -e([OH^-]) = 2, which succinctlytransforms the hydroxide ion concentration into an easilyinterpretable scale.