What is the pH of [tex]$5.22 \times 10^{-3} M HClO _4( H ^{+})$[/tex] solution?
A. none of these
B. 5.22
C. [tex]$1.92 \times 10^{-12}$[/tex]
D. 0.438
E. 2.28
Answer (2)
The pH of a 5.22 × 1 0 − 3 M HClO₄ solution is approximately 2.28, indicating an acidic solution. This is calculated using the formula p H = − lo g 10 [ H + ] . Therefore, the correct answer is option E: 2.28.
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Determine the hydrogen ion concentration: Since H Cl O 4 is a strong acid, [ H + ] = 5.22 × 1 0 − 3 M .
Apply the pH formula: p H = − lo g 10 [ H + ] .
Substitute the hydrogen ion concentration: p H = − lo g 10 ( 5.22 × 1 0 − 3 ) .
Calculate the pH: p H ≈ 2.28 .
The pH of the solution is 2.28 .
Explanation
Understanding the Problem We are given a solution of H Cl O 4 (perchloric acid) with a concentration of $5.22
\times 10^{-3} M . W e n ee d t o f in d t h e p Ho f t hi sso l u t i o n . S in ce HClO_4 i s a s t ro n g a c i d , i t co m pl e t e l y d i ssoc ia t es in w a t er , m e anin g t h eco n ce n t r a t i o n o f H^+ i o n s in t h eso l u t i o ni se q u a lt o t h eco n ce n t r a t i o n o f t h e a c i d . T h e p H i sc a l c u l a t e d u s in g t h e f or m u l a pH = -\log_{10}[H^+]$.
Determining the Hydrogen Ion Concentration Since H Cl O 4 is a strong acid, it completely dissociates in water:
[ H + ] = [ H Cl O 4 ] = 5.22 × 1 0 − 3 M
Applying the pH Formula Now we can calculate the pH using the formula:
p H = − lo g 10 [ H + ]
Substituting the value of [ H + ] :
p H = − lo g 10 ( 5.22 × 1 0 − 3 )
Calculating the pH Value Calculating the pH:
p H = − lo g 10 ( 5.22 × 1 0 − 3 ) ≈ 2.2823
Rounding to two decimal places, we get:
p H ≈ 2.28
Final Answer Therefore, the pH of the 5.22 × 1 0 − 3 M H Cl O 4 solution is approximately 2.28.
Examples
Understanding pH is crucial in many real-world applications. For instance, in agriculture, knowing the pH of the soil helps farmers determine the best crops to grow and the necessary soil treatments. In medicine, maintaining the correct pH balance in the body is vital for various biological processes. Similarly, in environmental science, monitoring the pH of water sources helps assess pollution levels and ensure water safety. The ability to calculate pH, as demonstrated in this problem, is a fundamental skill in these fields.
