What is the pH of a [tex]$3.60 \times 10^{-6} M$[/tex] solution of the strong acid [tex]$HClO_4$[/tex]?
[tex]$\begin{array}{l}
HClO_4(aq)+H_2 O(\ell) \rightarrow ClO_4^{-}(aq)+H_3 O^{+}(aq) \
{\left[HClO_4\right]_0=3.60 \times 10^{-6}}
\end{array}$[/tex]
Answer (2)
Determine the hydronium ion concentration: [ H 3 O + ] = 3.60 × 1 0 − 6 M .
Apply the pH formula: p H = − l o g 10 [ H 3 O + ] .
Substitute the concentration: p H = − l o g 10 ( 3.60 × 1 0 − 6 ) .
Calculate the pH: p H ≈ 5.44 .
5.44
Explanation
Problem Analysis and Strategy We're asked to find the pH of a $3.60
\times 10^{-6} M so l u t i o n o f p erc h l or i c a c i d ( HClO_4 ) . S in ce HClO_4 i s a s t ro n g a c i d , i t co m pl e t e l y d i ssoc ia t es in w a t er , m e anin g t h eco n ce n t r a t i o n o f h y d ro ni u mi o n s ( H_3O^+ ) w i ll b ee q u a lt o t h e ini t ia l co n ce n t r a t i o n o f t h e a c i d . T h e p H i s t h e n c a l c u l a t e d u s in g t h e f or m u l a pH = -log_{10}[H_3O^+]$.
Determining Hydronium Ion Concentration Since H Cl O 4 is a strong acid, it dissociates completely in water: H Cl O 4 ( a q ) + H 2 O ( l ) → H 3 O + ( a q ) + Cl O 4 − ( a q ) The concentration of H 3 O + is equal to the initial concentration of H Cl O 4 , which is $3.60
\times 10^{-6} M$.
Calculating the pH Now we can calculate the pH using the formula: p H = − l o g 10 [ H 3 O + ] Substituting the concentration of H 3 O + :
p H = − l o g 10 ( 3.60 × 1 0 − 6 ) Calculating the logarithm: p H ≈ 5.44
Final Answer Therefore, the pH of the solution is approximately 5.44.
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. This concept is also used in food science to preserve food and control microbial growth.
The pH of a 3.60 × 1 0 − 6 M solution of perchloric acid (HClO₄) is approximately 5.44, as the acid fully dissociates to yield an equal concentration of hydronium ions. This is calculated using the formula for pH, p H = − lo g 10 ([ H 3 O + ]) . Hence, the solution remains slightly acidic despite the low concentration.
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