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 (2)
Substitute the given concentration of hydrogen ions into the pH formula: p H = − lo g [ 5.0 × 1 0 − 4 ] .
Use logarithm properties to rewrite the expression: p H = − ( lo g [ 5.0 ] + lo g [ 1 0 − 4 ]) .
Simplify the expression using lo g [ 1 0 − 4 ] = − 4 and lo g [ 5.0 ] ≈ 0.7 : p H = − ( 0.7 − 4 ) .
Calculate the 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 Value To find the pH, we substitute the given concentration of hydrogen ions into the formula: p H = − lo g [ 5.0 × 1 0 − 4 ]
Using Logarithm Properties Using the properties of logarithms, we can rewrite the expression as: p H = − ( lo g [ 5.0 ] + lo g [ 1 0 − 4 ])
Calculating the pH We know that lo g [ 1 0 − 4 ] = − 4 . Also, we can approximate lo g [ 5.0 ] using a calculator or knowing that it's approximately 0.7 (more precisely, it's about 0.699). So, we have: p H = − ( lo g [ 5.0 ] − 4 ) p H = − ( 0.699 − 4 ) p H = − ( − 3.301 ) p H = 3.301
Final Answer Therefore, the approximate pH of the solution is 3.3.
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. Different plants thrive at different pH levels. Similarly, in medicine, maintaining the correct pH balance in our blood is vital for our health. A deviation from the normal pH range can indicate various medical conditions. In environmental science, pH is a key indicator of water quality, affecting aquatic life and the safety of drinking water. The calculation we performed is fundamental to these applications.
The approximate pH of the solution with a hydrogen ion concentration of 5.0 × 1 0 − 4 moles per liter is calculated to be 3.3 . Therefore, the correct choice is C. 3.3 .
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