For which of the following aqueous solutions at the same temperature will the pH be highest, that is, the solution will be the most strongly basic, assuming complete dissociation of strong electrolytes?

Introduction / Context:
This chemistry question tests understanding of pH, strong and weak acids and bases, and the effect of polybasic bases on hydroxide ion concentration. Learners must recognise that pH is determined by the concentration of hydrogen ions or hydroxide ions in solution, not just by the molarity of the compound. The comparison includes strong bases, a strong acid, and a weak acid, all at the same molarity, so the key is to determine which produces the greatest hydroxide ion concentration.

Given Data / Assumptions:
- All solutions have the same volume, 50.0 mL, and the same molarity, 0.0500 M.
- The solutes are Ca(OH)2, NaOH, HNO3, and HNO2.
- Ca(OH)2 and NaOH are strong bases, HNO3 is a strong acid, and HNO2 is a weak acid.
- We assume complete dissociation for strong electrolytes in dilute solution and standard conditions for pH calculations.

Concept / Approach:
pH is related to hydrogen ion concentration by the relation pH = minus log10[H plus]. For bases, it is often easier to think in terms of hydroxide ion concentration and then relate pOH and pH. A strong base such as NaOH dissociates completely to give one hydroxide ion per formula unit. A strong base like Ca(OH)2 dissociates to give two hydroxide ions per formula unit, making its effect on pH stronger at the same molarity. Strong acids give high hydrogen ion concentration, which lowers pH, and weak acids only partly dissociate. The solution with the highest pH will be the one with the highest hydroxide ion concentration, which is the Ca(OH)2 solution.

Step-by-Step Solution:
Step 1: For 0.0500 M NaOH, which is a strong base, the dissociation NaOH gives Na plus and OH minus. Therefore, [OH minus] is 0.0500 M.
Step 2: For 0.0500 M Ca(OH)2, which is also treated as a strong base in such questions, the dissociation Ca(OH)2 gives Ca2 plus and 2 OH minus. Therefore, [OH minus] is 2 multiplied by 0.0500 M, which is 0.1000 M.
Step 3: A higher hydroxide ion concentration corresponds to a higher pOH but a lower [H plus], and therefore a higher pH, since pH plus pOH equals 14 at 25 degree celsius.
Step 4: For the strong acid HNO3 at 0.0500 M, complete dissociation gives [H plus] equal to 0.0500 M, which produces a low pH, not a high pH.
Step 5: For the weak acid HNO2 at 0.0500 M, [H plus] will be less than 0.0500 M because the acid does not fully dissociate, but the solution will still be acidic and have a pH lower than neutral, not the highest pH among the options.
Step 6: Comparing all cases, 0.0500 M Ca(OH)2 gives the highest hydroxide ion concentration, 0.1000 M, and hence the highest pH value.

Verification / Alternative check:
An alternative way is to compare the basic strength qualitatively. Strong polybasic bases such as Ca(OH)2 supply more than one hydroxide ion per formula unit, effectively doubling the basic effect compared with a monobasic base of the same molarity. Strong acids like HNO3 clearly lower pH, and weak acids like HNO2 lower pH less but still produce acidic solutions. Therefore, the Ca(OH)2 solution must be the most basic among the four, confirming that its pH is highest.

Why Other Options Are Wrong:
- 50.0 mL of 0.0500 M NaOH: This is a strong base but provides only 0.0500 M hydroxide ions, which is lower than the 0.1000 M provided by Ca(OH)2 at the same molarity.
- 50.0 mL of 0.0500 M HNO3: This is a strong acid that gives a high hydrogen ion concentration, so its pH is low, not high.
- 50.0 mL of 0.0500 M HNO2: This weak acid provides some hydrogen ions but still yields an acidic solution, so it cannot have the highest pH among the options.

Common Pitfalls:
Students often compare only the molarity of the compounds and forget to account for the number of hydroxide ions per formula unit in polybasic bases. Another common mistake is to think that any strong electrolyte at the same molarity will have the same impact on pH, which is not correct because the stoichiometry of ion production matters. Misclassifying HNO2 as a strong acid can also lead to errors. Keeping track of how many ions of each type are produced per mole of solute helps avoid these mistakes.

Final Answer:
50.0 mL of 0.0500 M calcium hydroxide Ca(OH)2 produces the highest hydroxide ion concentration and therefore has the highest pH among the given solutions.