Question

(a) What is the \(\mathrm{pH}\) of \(6.14 \times 10^{-3} \mathrm{M}\) HI? Is the solution neutral, acidic, or basic? (b) What is the \(p O H\) of \(2.55 M B a(O H)_{2} ?\) Is the solution neutral, acidic, or basic?

Short answer

The pH of 6.14 \times 10^{-3} M HI is 2.21 (acidic). The pOH of 2.55 M Ba(OH)_2 is -0.71 (basic).

Step-by-step solution

- Calculate the \(\text{pH}\) of \(6.14 \times 10^{-3} M HI\)

Since \(HI\) is a strong acid, it fully dissociates in water. Thus, the concentration of \([H^+]\) is equal to \(6.14 \times 10^{-3} M\). The \(\text{pH}\) is calculated using the formula: \[ \text{pH} = -\text{log}[H^+] \] Substituting the values, \[ \text{pH} = -\text{log}(6.14 \times 10^{-3}) = 2.21 \] The solution is acidic because \( \text{pH} < 7 \).

- Calculate the \(pOH\) of \(2.55 M Ba(OH)_2\)

Since \(Ba(OH)_2\) is a strong base, it fully dissociates in water to give \(Ba^{2+} \text{ and } 2OH^-\). Thus, the concentration of \([OH^-]\) is twice the concentration of \(Ba(OH)_2\): \[ [OH^-] = 2 \times 2.55 M = 5.10 M \] The \( pOH\) is calculated using the formula: \[ pOH = -\text{log}[OH^-] \] Substituting the values, \[ pOH = -\text{log}(5.10) = -0.71 \] This result is unconventional (since \(pOH\) typically ranges from 0 to 14) but mathematically valid, indicating a highly basic solution. The solution is basic because \([OH^-] > [H^+]\).

Key concepts

Strong Acids

Strong acids, like HI (hydroiodic acid), fully dissociate in water. This means that if you have a concentration of a strong acid, all of the acid molecules split into ions in the solution. In our example, HI dissociates completely, so the concentration of hydrogen ions \([H^+]\) is the same as the initial concentration of the acid. Because dissociation is complete, we can directly calculate the pH. Understanding how strong acids behave is crucial for pH calculations. We use the formula \[\text{pH} = -\text{log}[H^+] \] to compute the pH, which tells us how acidic the solution is. Knowing that a pH value less than 7 means the solution is acidic is useful for quick analysis of any solution's properties.

Strong Bases

Let's talk about strong bases, using our example of Ba(OH)\(_2\). Similar to strong acids, strong bases completely dissociate in water. For Ba(OH)\(_2\), it splits entirely to form Ba\(^2+\) and OH\(^-\) ions. Since each molecule of Ba(OH)\(_2\) releases 2 OH\(^-\) ions, the concentration of OH\(^-\) is twice the concentration of the base. This is key to understanding why strong bases can have such a significant impact on a solution's pH and pOH. To find the pOH, you can use \[ pOH = -\text{log}[OH^-] \] Calculated pOH values help in determining how basic a solution is.

Acidic and Basic Solutions

Knowing whether a solution is acidic or basic is essential for many chemical processes. To determine this, we often look at the pH and pOH values. A pH less than 7 means the solution is acidic, while a pH greater than 7 means it's basic. As for pOH, it gives a complementary perspective: pOH less than 7 is basic, and pOH greater than 7 is acidic. Since pH and pOH are interconnected, knowing one allows you to find the other using the relationship: \[ pH + pOH = 14 \] For example, if you have a strong acid like HI, it will make the solution acidic by lowering the pH. Conversely, a strong base like Ba(OH)\(_2\) will increase the OH\(^-\) concentration, leading to a lower pOH and thus, a higher pH, indicating a basic solution. This simple yet powerful understanding helps in quickly assessing and categorizing solutions in chemistry.