Question

Acid rain has been measured with a pH of 1.5. Calculate the hydrogen ion concentration of this rain.

Short answer

The hydrogen ion concentration is approximately 3.16 x 10^-2 mol/L.

Step-by-step solution

Understanding pH

The pH scale is a measure of how acidic or basic a solution is. It is calculated as the negative logarithm (base 10) of the hydrogen ion concentration ([H^+] ) in a solution. Mathematically, it's expressed as: \[\text{pH} = -\log([H^+])\]Given the problem, we need to find the hydrogen ion concentration when the pH is 1.5.

Setting Up the Equation

We begin with the formula for pH: \[\text{pH} = -\log([H^+])\]Substitute the given pH value into the equation: \[1.5 = -\log([H^+])\]

Solving for Hydrogen Ion Concentration

To isolate [H^+], solve the equation by exponentiating both sides using base 10. This effectively 'undoes' the logarithm. So:\[[H^+] = 10^{-1.5}\]Calculate the power of 10 to find the hydrogen ion concentration.

Calculating the Concentration

Using a calculator, compute 10^{-1.5}. This calculation results in:\[[H^+] \approx 3.16 \times 10^{-2} \text{ mol/L}\]

Key concepts

Understanding the pH Scale

The pH scale is an essential tool used to measure the acidity or basicity of a solution. Ranging from 0 to 14, the scale helps us determine if a solution is acidic, neutral, or basic. If a solution has a pH of 7, it's considered neutral, like pure water. Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic or alkaline.
At one end of the scale, a pH of 0 represents a very strong acid, whereas a pH of 14 indicates a very strong base. The scale is logarithmic, which means each whole pH value below 7 is ten times more acidic than the next higher value. For example, a pH of 1 is ten times more acidic than a pH of 2, making it critical to understand this scale when studying acid rain.
When you come across the term "acid rain" with a pH of 1.5, it indicates a highly acidic solution. Such acidity can have damaging effects on the environment, which is why it’s important to measure and understand the severity of its pH level.

Hydrogen Ion Concentration in Solutions

Hydrogen ion concentration is a direct measure of acidity in a solution. It's denoted as \([H^+]\) and is crucial in calculating the pH. Solutions with a high concentration of hydrogen ions are acidic, whereas those with lower concentrations are basic.
In chemical terms, the more hydrogen ions \([H^+]\) present, the stronger the acid. For example, in acid rain with a low pH, there's a high concentration of hydrogen ions. Calculating the hydrogen ion concentration requires understanding the relationship between pH and \([H^+]\).
Remember the formula \(\text{pH} = -\log([H^+])\). This equation helps us work backwards from a known pH value to find the hydrogen ion concentration. In our example of acid rain with a pH of 1.5, by reversing the equation, we found \([H^+] \approx 3.16 \times 10^{-2} \text{ mol/L}\). This demonstrates a high acidity level, showcased by the abundance of hydrogen ions.

The Role of Logarithms in pH Calculations

Logarithms are mathematical tools used to solve equations involving exponential relationships. In the context of pH calculations, they allow us to express small amounts of hydrogen ions in a solution in a manageable number format. This is because the concentrations of hydrogen ions can be minuscule, making raw numbers unwieldy.
The logarithm scale of base 10 transforms these tiny concentrations into the pH scale, which is much easier to interpret. For the pH scale, we use the formula: \(\text{pH} = -\log([H^+])\). The negative sign indicates that as the concentration of hydrogen ions increases, the pH value decreases.
When you're solving for the hydrogen ion concentration, you're essentially reversing this process. By using the inverse operation of the logarithm (exponentiation) on pH, you can derive \([H^+]\). This shows the power of logarithms in simplifying chemistry problems and helping us comprehend quantities that span several orders of magnitude.