Rank The Following Solutions From Lowest To Highest PH. A) 0.10 M HC4H7O2 (Ka = 1.5 × 10−5) B) 0.50 M HCN (Ka = 4.9 × 10−10)
The Correct Answer and Explanation is :
Ranking the Solutions from Lowest to Highest pH
We are given two weak acid solutions with their respective concentrations and acid dissociation constants (( K_a )):
- A) 0.10 M HC₄H₇O₂ (Ka = ( 1.5 \times 10^{-5} ))
- B) 0.50 M HCN (Ka = ( 4.9 \times 10^{-10} ))
To determine their pH values, we need to calculate the hydrogen ion concentration ([H^+]) for each solution using the weak acid dissociation formula:
[
[H^+] = \sqrt{K_a \times C_a}
]
where:
- ( K_a ) = acid dissociation constant
- ( C_a ) = initial concentration of the acid
Step 1: Calculate [H⁺] for HC₄H₇O₂
[
[H^+] = \sqrt{(1.5 \times 10^{-5}) \times (0.10)}
]
[
[H^+] = \sqrt{1.5 \times 10^{-6}}
]
[
[H^+] \approx 1.22 \times 10^{-3} \text{ M}
]
[
\text{pH} = -\log(1.22 \times 10^{-3}) \approx 2.91
]
Step 2: Calculate [H⁺] for HCN
[
[H^+] = \sqrt{(4.9 \times 10^{-10}) \times (0.50)}
]
[
[H^+] = \sqrt{2.45 \times 10^{-10}}
]
[
[H^+] \approx 1.57 \times 10^{-5} \text{ M}
]
[
\text{pH} = -\log(1.57 \times 10^{-5}) \approx 4.80
]
Final Ranking (Lowest to Highest pH)
- 0.10 M HC₄H₇O₂ (pH ≈ 2.91)
- 0.50 M HCN (pH ≈ 4.80)
Explanation
- The pH of a weak acid is determined by both its ( K_a ) value and its concentration.
- HC₄H₇O₂ has a larger ( K_a ) (( 1.5 \times 10^{-5} )), meaning it ionizes more than HCN, leading to a lower pH.
- HCN has a much smaller ( K_a ) (( 4.9 \times 10^{-10} )), meaning it ionizes very little, resulting in a higher pH.
- Since lower pH means more acidic, HC₄H₇O₂ is the more acidic solution compared to HCN.
Thus, HC₄H₇O₂ has the lowest pH, followed by HCN with a higher pH.