To determine which reaction yields a salt with [tex]\( \text{pH} < 7 \)[/tex], we need to consider the properties of the acids and bases involved in each reaction. Specifically, we need to determine whether the acids or bases are strong or weak. The general rules for the pH of salts formed from acid-base reactions are as follows:
1. Strong acid + Strong base → Neutral salt (pH = 7)
2. Strong acid + Weak base → Acidic salt (pH < 7)
3. Weak acid + Strong base → Basic salt (pH > 7)
4. Weak acid + Weak base → Typically varies
Let's analyze each given reaction:
1. [tex]\( KOH + HBr \)[/tex]:
- [tex]\( KOH \)[/tex] is a strong base.
- [tex]\( HBr \)[/tex] is a strong acid.
- A reaction between a strong base and a strong acid will yield a neutral salt with [tex]\( \text{pH} = 7 \)[/tex].
2. [tex]\( HCOOH + KOH \)[/tex]:
- [tex]\( HCOOH \)[/tex] (formic acid) is a weak acid.
- [tex]\( KOH \)[/tex] is a strong base.
- A reaction between a weak acid and a strong base will yield a basic salt with [tex]\( \text{pH} > 7 \)[/tex].
3. [tex]\( Ca(OH)_2 + H_2SO_4 \)[/tex]:
- [tex]\( Ca(OH)_2 \)[/tex] is a strong base.
- [tex]\( H_2SO_4 \)[/tex] is a strong acid.
- A reaction between a strong base and a strong acid will yield a neutral salt with [tex]\( \text{pH} = 7 \)[/tex].
4. [tex]\( NH_3 + HNO_3 \)[/tex]:
- [tex]\( NH_3 \)[/tex] (ammonia) is a weak base.
- [tex]\( HNO_3 \)[/tex] is a strong acid.
- A reaction between a weak base and a strong acid will yield an acidic salt with [tex]\( \text{pH} < 7 \)[/tex].
Based on this analysis, the reaction that yields a salt with [tex]\( \text{pH} < 7 \)[/tex] is:
[tex]\( \boxed{4} \)[/tex] [tex]\( NH_3 + HNO_3 \)[/tex]
