The equation for the pH of a substance is [tex]$pH =-\log \left[ H ^{+}\right]$[/tex], where [tex]$H +$[/tex] is the concentration of hydrogen ions. What is the approximate pH of a solution if the concentration of hydrogen ions is [tex]$5.0 \times 10^{-4}$[/tex] moles per liter?
A. 2.7
B. 3.0
C. 3.3
D. 3.6
Answer (1)
Substitute the concentration of hydrogen ions into the pH equation: p H = − lo g [ 5.0 × 1 0 − 4 ] .
Use properties of logarithms to simplify: p H = − ( lo g [ 5.0 ] + lo g [ 1 0 − 4 ]) = − ( lo g [ 5.0 ] − 4 ) .
Approximate lo g [ 5.0 ] as 0.7: p H = − ( 0.7 − 4 ) .
Calculate the final pH value: p H = − ( − 3.3 ) = 3.3 . The approximate pH of the solution is 3.3 .
Explanation
Understanding the Problem We are given the formula for calculating the pH of a substance: p H = − lo g [ H + ] , where H + is the concentration of hydrogen ions. We are also given that the concentration of hydrogen ions for a particular solution is 5.0 × 1 0 − 4 moles per liter. Our goal is to find the approximate pH of this solution.
Substituting the Given Value To find the pH, we substitute the given concentration of hydrogen ions into the pH equation: p H = − lo g [ 5.0 × 1 0 − 4 ]
Using Logarithmic Properties Using the properties of logarithms, we can rewrite the expression as: p H = − ( lo g [ 5.0 ] + lo g [ 1 0 − 4 ]) Since lo g [ 1 0 − 4 ] = − 4 , we have: p H = − ( lo g [ 5.0 ] − 4 )
Approximating the Logarithm We know that lo g [ 5.0 ] is approximately 0.7 (more precisely, it's about 0.699). Substituting this value into the equation, we get: p H = − ( 0.7 − 4 ) p H = − ( − 3.3 ) p H = 3.3
Final Answer Therefore, the approximate pH of the solution is 3.3.
Examples
The concept of pH is widely used in environmental science to measure the acidity or alkalinity of water bodies, which is crucial for aquatic life. For example, if a lake has a pH of 6.5, it is slightly acidic, which might affect the survival of certain fish species. In agriculture, pH levels in soil affect nutrient availability for plants. Understanding pH helps farmers optimize soil conditions for better crop yields. In medicine, the pH of blood is tightly regulated to ensure proper bodily functions; deviations can indicate underlying health issues.
