The formula for pH is [tex]$pH =-\log \left[ H ^{+}\right]$[/tex], where [tex]$\left[ H ^{+}\right]$[/tex] is the hydrogen ion concentration.
The pH of a fruit juice is 3.2. What is the hydrogen ion concentration of the juice?
The hydrogen ion concentration [tex]$\left[ H ^{+}\right]$[/tex] is approximately how many moles per liter? (Round to the nearest tenth.)
Answer (1)
Substitute the given pH value into the formula: 3.2 = − lo g [ H + ] .
Multiply both sides by -1: − 3.2 = lo g [ H + ] .
Take the antilog (base 10) of both sides: 1 0 − 3.2 = [ H + ] .
Calculate and round to the nearest tenth: [ H + ] ≈ 0.0 .
Explanation
Understanding the Problem We are given the formula for pH: p H = − lo g [ H + ] , where [ H + ] is the hydrogen ion concentration. We are also given that the pH of a fruit juice is 3.2. Our goal is to find the hydrogen ion concentration [ H + ] .
Substituting the pH Value We substitute the given pH value into the formula: 3.2 = − lo g [ H + ]
Isolating the Logarithm To solve for [ H + ] , we first multiply both sides of the equation by -1: − 3.2 = lo g [ H + ]
Taking the Antilog Now, we take the antilog (base 10) of both sides of the equation to remove the logarithm: 1 0 − 3.2 = [ H + ]
Calculating the Hydrogen Ion Concentration Calculating 1 0 − 3.2 , we get approximately 0.000630957. We need to round this to the nearest tenth: [ H + ] ≈ 0.000630957 ≈ 0.0
Examples
Understanding pH and hydrogen ion concentration is crucial in many real-world applications. For example, in agriculture, knowing the pH of the soil helps farmers choose the right crops and optimize growing conditions. In medicine, maintaining the correct pH balance in the body is essential for various biological processes. In environmental science, monitoring the pH of water sources helps assess pollution levels and ensure water quality. The ability to calculate hydrogen ion concentration from pH values allows for precise control and management in these diverse fields.
