The equation for the pH of a substance is [tex]$pH = -\log [H^+]$[/tex], where [tex]$H^+$[/tex] is the concentration of hydrogen ions. Which equation models the concentration of hydrogen ions ([tex]$H^+$[/tex]) of a solution whose pH is 7.2?
A. [tex]$[H^+] = \log 7.2$[/tex]
B. [tex]$[H^+] = -\log 7.2$[/tex]
C. [tex]$[H^+] = 10^{-7.2}$[/tex]
D. [tex]$[H^+] = 10^{7.2}$[/tex]
Answer (2)
Substitute the given pH value into the equation: 7.2 = − lo g [ H + ] .
Multiply both sides by -1: − 7.2 = lo g [ H + ] .
Convert the logarithmic equation to exponential form: [ H + ] = 1 0 − 7.2 .
The equation that models the concentration of hydrogen ions is [ H + ] = 1 0 − 7.2 .
Explanation
Understanding the Problem The problem states that the pH of a substance is given by the equation p H = − lo g [ H + ] , where [ H + ] is the concentration of hydrogen ions. We are given that the pH of a solution is 7.2, and we need to find the equation that models the concentration of hydrogen ions [ H + ] .
Substituting the pH Value We substitute p H = 7.2 into the equation p H = − lo g [ H + ] to get 7.2 = − lo g [ H + ] .
Isolating the Logarithm To isolate the logarithm, we multiply both sides of the equation by -1: − 7.2 = lo g [ H + ]
Converting to Exponential Form Now, we rewrite the logarithmic equation in exponential form. Recall that lo g a b = c is equivalent to a c = b . In our case, the base of the logarithm is 10, so we have: 1 0 − 7.2 = [ H + ]
Final Equation Therefore, the equation that models the concentration of hydrogen ions is [ H + ] = 1 0 − 7.2 .
Examples
Understanding pH is crucial in many real-world applications. For example, in agriculture, knowing the pH of the soil helps farmers choose the right crops and fertilizers. In medicine, maintaining the correct pH balance in our blood is vital for our health. In environmental science, monitoring the pH of lakes and rivers helps assess water quality and the impact of pollution. The relationship between pH and hydrogen ion concentration, as described by the equation p H = − lo g [ H + ] , allows scientists and professionals to quantify acidity and alkalinity in various substances and make informed decisions.
To find the hydrogen ion concentration ([H^+]) corresponding to a pH of 7.2, we substitute this value into the pH equation. After isolating the logarithm and converting it to exponential form, we find that [H^+] = 10^{-7.2}. Therefore, the correct answer is option C: [H^+] = 10^{-7.2}.
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