Calculating PH Of A Solution With H3O+ Concentration Of 5.2 X 10^-8 M

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When dealing with chemical solutions, pH is a crucial concept to understand, as it dictates the acidity or basicity of a solution. In this comprehensive guide, we will delve into the calculation of pH for a solution, specifically focusing on a scenario where the hydronium ion concentration is given as 5.2 x 10^-8 M. We'll break down the underlying principles, the mathematical formula involved, and offer a step-by-step approach to arriving at the correct pH value. By the end of this exploration, you'll not only be able to solve this particular problem but also gain a deeper understanding of pH calculations in chemistry. The correct answer to the question posed in the title is C. 7.28, and we will explore why this is the case in detail below.

The Fundamentals of pH

Before we dive into the calculations, it's important to establish a solid understanding of what pH actually represents. pH, which stands for "potential of hydrogen," is a logarithmic scale used to measure the acidity or basicity of an aqueous solution. The scale ranges from 0 to 14, with values below 7 indicating acidity, values above 7 indicating basicity (or alkalinity), and a value of 7 indicating neutrality. At the heart of pH is the concentration of hydronium ions (H3O+) in the solution. Hydronium ions are formed when a proton (H+) from an acid combines with a water molecule (H2O). The higher the concentration of hydronium ions, the more acidic the solution, and conversely, the lower the concentration, the more basic the solution. The pH scale is logarithmic, meaning that each whole number change in pH represents a tenfold change in the concentration of hydronium ions. For instance, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4, and one hundred times more acidic than a solution with a pH of 5. This logarithmic nature allows us to conveniently express a wide range of concentrations, from very acidic to very basic, on a manageable scale.

The pH Formula and Its Application

The mathematical formula that links pH and hydronium ion concentration is straightforward yet powerful. The pH is defined as the negative base-10 logarithm (log) of the hydronium ion concentration [H3O+]. Mathematically, this is expressed as: pH = -log[H3O+]. This formula is the key to calculating the pH of any solution if you know its hydronium ion concentration. To use the formula effectively, it's essential to understand logarithms. The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In the case of pH, we use the base-10 logarithm, often denoted as log10 or simply log. When you take the negative logarithm of the hydronium ion concentration, you're essentially finding the power of 10 that corresponds to the reciprocal of that concentration. This resulting value is the pH. Now, let's apply this formula to the problem at hand. We are given a hydronium ion concentration of 5.2 x 10^-8 M. To find the pH, we simply plug this value into the formula: pH = -log(5.2 x 10^-8). The next step involves using a calculator to evaluate the logarithm. The log(5.2 x 10^-8) is approximately -7.28. Finally, we take the negative of this value: pH = -(-7.28) = 7.28. Therefore, the pH of the solution is 7.28.

Step-by-Step Calculation

Let's break down the calculation process into a clear, step-by-step guide to ensure a thorough understanding:

  1. Identify the Hydronium Ion Concentration: The problem states that the concentration of H3O+ is 5.2 x 10^-8 M.
  2. Apply the pH Formula: Recall the formula: pH = -log[H3O+].
  3. Substitute the Concentration: Substitute the given concentration into the formula: pH = -log(5.2 x 10^-8).
  4. Calculate the Logarithm: Use a calculator to find the base-10 logarithm of 5.2 x 10^-8. This yields approximately -7.28.
  5. Take the Negative: Multiply the result by -1: pH = -(-7.28) = 7.28.
  6. State the Result: The pH of the solution is 7.28.

This step-by-step approach makes the calculation process straightforward and minimizes the chances of error. It's crucial to follow each step carefully and double-check your calculations to ensure accuracy.

Why the Answer is 7.28

Now that we've calculated the pH to be 7.28, it's essential to understand why this value makes sense in the context of the given hydronium ion concentration. The concentration of 5.2 x 10^-8 M H3O+ is quite low. Recall that pure water has a hydronium ion concentration of 1.0 x 10^-7 M, which corresponds to a pH of 7 (neutral). Our solution has a slightly lower hydronium ion concentration than pure water, indicating that it is slightly less acidic or, equivalently, slightly more basic. A pH of 7.28 is indeed slightly above 7, confirming our expectation. It's crucial to note that even though the concentration of hydronium ions is relatively low, it still influences the pH significantly. The logarithmic nature of the pH scale amplifies the effect of even small changes in concentration. This is why a concentration of 5.2 x 10^-8 M results in a pH that is noticeably different from 7. Furthermore, this example highlights an important consideration when dealing with very dilute solutions. In such cases, we must account for the autoionization of water, which contributes a certain amount of H3O+ and OH- ions even in the absence of any added acid or base. This autoionization maintains a constant ion product of water (Kw), which is approximately 1.0 x 10^-14 at 25°C. In extremely dilute solutions, the contribution of H3O+ from the autoionization of water can become significant and must be factored into the pH calculation.

Common Mistakes to Avoid

When calculating pH, several common mistakes can lead to incorrect answers. Being aware of these pitfalls can help you avoid them and ensure accurate results:

  • Forgetting the Negative Sign: The most common mistake is forgetting to multiply the logarithm by -1. The pH is defined as the negative logarithm of the hydronium ion concentration. Omitting the negative sign will result in an incorrect pH value.
  • Incorrectly Using the Calculator: Logarithms can be tricky to calculate without a calculator, and even with one, it's easy to make errors. Make sure you are using the correct function (log or log10 for base-10 logarithm) and entering the numbers correctly. Double-check your input and the result.
  • Misunderstanding Scientific Notation: Hydronium ion concentrations are often expressed in scientific notation (e.g., 5.2 x 10^-8). Ensure you understand how to enter these numbers into your calculator correctly. A mistake in the exponent can lead to a vastly different result.
  • Ignoring the Autoionization of Water: As mentioned earlier, in very dilute solutions, the contribution of H3O+ from the autoionization of water can be significant. Ignoring this contribution can lead to inaccuracies, especially when the concentration of the solute is close to or below 1.0 x 10^-7 M.
  • Confusing pH with pOH: pH measures acidity, while pOH measures basicity. pOH is defined as -log[OH-], where [OH-] is the hydroxide ion concentration. While pH and pOH are related (pH + pOH = 14 at 25°C), they are distinct concepts. Be sure to calculate pH when the question asks for pH and pOH when it asks for pOH.

By being mindful of these common mistakes and taking the time to double-check your work, you can significantly improve the accuracy of your pH calculations.

Real-World Applications of pH

Understanding pH is not just an academic exercise; it has numerous real-world applications across various fields. Here are a few examples:

  • Environmental Science: pH is a critical parameter in environmental monitoring. The pH of water bodies (rivers, lakes, oceans) affects the solubility and bioavailability of nutrients and pollutants, which in turn impacts aquatic life. Acid rain, caused by atmospheric pollution, can lower the pH of lakes and streams, harming fish and other organisms. Similarly, soil pH affects the availability of nutrients to plants, influencing agricultural productivity.
  • Medicine: pH plays a crucial role in human physiology. The pH of blood is tightly regulated at around 7.4, and deviations from this range can indicate various medical conditions. Gastric pH in the stomach is highly acidic (around 1.5 to 3.5) to aid in digestion and kill harmful bacteria. Urinary pH can provide clues about kidney function and metabolic disorders.
  • Chemistry and Biochemistry: pH is fundamental to many chemical and biochemical reactions. Enzyme activity, protein structure, and chemical equilibrium are all influenced by pH. Many laboratory procedures, such as titrations and buffer preparation, rely on precise pH control.
  • Food Science: pH affects the taste, texture, and preservation of food. For example, acidic foods like vinegar and citrus fruits have a sour taste and can inhibit the growth of spoilage microorganisms. The pH of dairy products influences their texture and stability. In brewing and winemaking, pH control is essential for fermentation and flavor development.
  • Agriculture: Soil pH is a key factor in determining plant health and crop yields. Different plants have different pH preferences, and maintaining the optimal pH range for a particular crop is crucial for maximizing growth and productivity. Soil pH can be adjusted through the addition of lime (to raise pH) or sulfur (to lower pH).

These are just a few examples of the many ways in which pH impacts our world. A solid understanding of pH and its calculation is essential for anyone working in these fields.

Conclusion

In summary, calculating the pH of a solution with a given hydronium ion concentration involves a straightforward application of the formula pH = -log[H3O+]. For a solution with a concentration of 5.2 x 10^-8 M H3O+, the pH is 7.28. This value indicates that the solution is slightly basic, which is consistent with the relatively low hydronium ion concentration. By understanding the fundamentals of pH, the pH formula, and the step-by-step calculation process, you can confidently tackle similar problems. Moreover, being aware of common mistakes and the real-world applications of pH will enhance your understanding of this crucial concept in chemistry and its relevance to various fields.