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 3.1. What is the hydrogen ion concentration of the juice?
The hydrogen ion concentration [tex]$\left[ H ^{+}\right]$[/tex] is approximately ______ moles per liter. (Round to the nearest tenth.)
Answer (1)
Substitute the given pH value into the formula: 3.1 = − lo g [ H + ] .
Multiply both sides by -1: − 3.1 = lo g [ H + ] .
Take the antilog (base 10) of both sides: [ H + ] = 1 0 − 3.1 .
Calculate 1 0 − 3.1 and round to the nearest tenth: 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 3.1. Our goal is to find the hydrogen ion concentration [ H + ] .
Substituting the pH Value We substitute the given pH value into the formula: 3.1 = − lo g [ H + ] .
Isolating the Logarithm To solve for [ H + ] , we first multiply both sides of the equation by -1: − 3.1 = lo g [ H + ] .
Taking the Antilog Next, we take the antilog (base 10) of both sides of the equation to isolate [ H + ] : [ H + ] = 1 0 − 3.1 .
Calculating the Hydrogen Ion Concentration Now, we calculate the value of 1 0 − 3.1 . The result of this calculation is approximately 0.0007943. We are asked to round the result to the nearest tenth, so we round 0.0007943 to 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 determine the best crops to grow. 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 safety. The ability to calculate hydrogen ion concentration from pH values allows for precise control and management in these diverse fields.
