Consider the following data on some weak acids and weak bases:
Use this data to rank the following solutions in order of increasing pH. In other words, select a '1' next to the solution that will have the lowest pH, a '2 the solution that will have the next lowest pH, and so on.
Answer (1)
C 5 H 5 N H B r - 1
N H 4 Cl - 2
N a Cl - 3
N a CN - 4
Explanation
Problem Analysis We are given the K a values for hypochlorous acid (HClO) and hydrocyanic acid (HCN), as well as the K b values for ammonia ( N H 3 ) and pyridine ( C 5 H 5 N ). We need to rank the following solutions in order of increasing pH: 0.1 M NaCN, 0.1 M N H 4 Cl , 0.1 M C 5 H 5 N H B r , and 0.1 M NaCl.
Solution Analysis First, let's analyze each solution:
0.1 M NaCN: NaCN is the salt of a weak acid (HCN) and a strong base (NaOH). Therefore, it will form a basic solution due to the hydrolysis of C N − ions.
0.1 M N H 4 Cl : N H 4 Cl is the salt of a weak base ( N H 3 ) and a strong acid (HCl). Therefore, it will form an acidic solution due to the hydrolysis of N H 4 + ions.
0.1 M C 5 H 5 N H B r : C 5 H 5 N H B r is the salt of a weak base ( C 5 H 5 N ) and a strong acid (HBr). Therefore, it will form an acidic solution due to the hydrolysis of C 5 H 5 N H + ions.
0.1 M NaCl: NaCl is the salt of a strong acid (HCl) and a strong base (NaOH). Therefore, it will form a neutral solution.
Calculating Acid and Base Dissociation Constants To compare the acidity of N H 4 Cl and C 5 H 5 N H B r , we need to compare the K a values of their conjugate acids, N H 4 + and C 5 H 5 N H + , respectively. Similarly, to determine the basicity of NaCN, we need to find the K b of C N − .
We can calculate these values using the relationship K w = K a t im es K b , where K w = 1.0 t im es 1 0 − 14 .
Calculations of Constants
Calculate K b for C N − :
K b = K a K w = 4.9 t im es 1 0 − 10 1.0 t im es 1 0 − 14 = 2.04 t im es 1 0 − 5
Calculate K a for N H 4 + :
K a = K b K w = 1.8 t im es 1 0 − 5 1.0 t im es 1 0 − 14 = 5.56 t im es 1 0 − 10
Calculate K a for C 5 H 5 N H + :
K a = K b K w = 1.7 t im es 1 0 − 9 1.0 t im es 1 0 − 14 = 5.88 t im es 1 0 − 6
Comparing Acidities and Basicities Now we can compare the K a values of N H 4 + and C 5 H 5 N H + . Since the K a of C 5 H 5 N H + ( 5.88 t im es 1 0 − 6 ) is greater than the K a of N H 4 + ( 5.56 t im es 1 0 − 10 ), C 5 H 5 N H B r will be more acidic than N H 4 Cl . Therefore, C 5 H 5 N H B r will have a lower pH than N H 4 Cl .
Since NaCl is a neutral salt, its pH will be around 7.
NaCN is a basic salt, so it will have the highest pH among the given solutions.
Final Ranking Therefore, the ranking of the solutions in order of increasing pH is:
0.1 M C 5 H 5 N H B r
0.1 M N H 4 Cl
0.1 M NaCl
0.1 M NaCN
Examples
Understanding the pH of salt solutions is crucial in various applications. For instance, in agriculture, the pH of the soil affects nutrient availability for plants. If the soil is too acidic, adding a basic salt like NaCN (though not practical due to its toxicity) could theoretically raise the pH. In reality, safer alternatives like calcium carbonate are used. Similarly, in biological experiments, maintaining the correct pH is essential for enzyme activity and cell function. Knowing whether a salt will create an acidic, basic, or neutral solution helps in preparing the appropriate buffer solutions.
