Calculating PH For [H+] = 2.3 X 10^-9 A Step-by-Step Guide

by Omar Yusuf 59 views

Hey guys! Let's dive into the fascinating world of pH and tackle a common chemistry question. We're going to explore how to calculate the pH of a solution when we know the concentration of hydrogen ions ([H+]). This is a fundamental concept in chemistry, crucial for understanding acidity and basicity. So, grab your thinking caps, and let’s get started!

Understanding pH: More Than Just a Number

pH, the power of Hydrogen, is a measure of the acidity or basicity of an aqueous solution. It tells us the relative amount of hydrogen ([H+]) and hydroxide ([OH-]) ions present in a solution. The pH scale ranges from 0 to 14, with 7 being neutral. Values below 7 indicate acidity – the lower the number, the higher the acidity. Values above 7 indicate basicity (also called alkalinity) – the higher the number, the higher the basicity.

Think of it like a seesaw: on one side, you have hydrogen ions ([H+]), and on the other, you have hydroxide ions ([OH-]). A neutral solution has these ions perfectly balanced, like pure water. An acidic solution has more hydrogen ions, tipping the seesaw towards the acidic side. A basic solution has more hydroxide ions, tipping the seesaw towards the basic side.

But why is pH so important? Well, pH plays a vital role in many chemical and biological processes. In our bodies, pH affects enzyme activity, protein structure, and the transport of oxygen in the blood. In the environment, pH affects the solubility of nutrients in soil and the survival of aquatic life. In industries, pH is crucial for chemical reactions, manufacturing processes, and water treatment. Understanding pH is essential in diverse fields like medicine, agriculture, environmental science, and chemical engineering.

Now, how do we actually determine the pH of a solution? This is where the magic formula comes in!

The pH Formula: Your Key to Unlocking Acidity

The pH formula is a simple yet powerful equation:

pH = -log10[H+]

Where [H+] represents the molar concentration of hydrogen ions in the solution. The “log10” is the base-10 logarithm, a mathematical function that tells us the power to which 10 must be raised to equal a given number. Don’t worry if you’re not a math whiz – most calculators have a log function that does the work for you!

Let's break down the formula. The negative sign in front of the logarithm ensures that pH values are typically positive numbers. Since the concentration of hydrogen ions is usually a very small number (like 10^-7 for neutral water), the logarithm will be negative. Multiplying by -1 gives us a positive pH value.

The logarithm compresses the scale, making it easier to work with. For example, a solution with [H+] = 10^-3 M has a pH of 3, while a solution with [H+] = 10^-5 M has a pH of 5. Even though the concentration of hydrogen ions differs by a factor of 100 (10^-3 / 10^-5 = 10^2), the pH values only differ by 2. This logarithmic scale allows us to represent a wide range of acidities and basicities on a manageable scale from 0 to 14.

Now, let's put this formula into action and solve the problem at hand!

Solving the pH Puzzle: [H+] = 2.3 x 10^-9

In our question, we're given the concentration of hydrogen ions: [H+] = 2.3 x 10^-9 M. Our mission is to find the pH of this solution.

Let's follow these steps:

  1. Plug the [H+] value into the pH formula:

    pH = -log10(2.3 x 10^-9)

  2. Use a calculator to find the logarithm of 2.3 x 10^-9:

    Most calculators have a “log” button. Enter “2.3 x 10^-9” and press the “log” button. You should get a value close to -8.638.

  3. Multiply the result by -1:

    pH = -(-8.638)
pH = 8.638

  4. Round the answer to the appropriate number of significant figures:

    The given [H+] value has two significant figures (2.3). Therefore, we should round our pH value to two decimal places: pH ≈ 8.64.

So, the pH of the solution is approximately 8.64. Looking at the answer choices, option C (8.64) is the correct answer. Hooray! We've solved the puzzle!

But what does this pH value tell us about the solution? Is it acidic, basic, or neutral?

Interpreting the pH Value: Acidic, Basic, or Neutral?

We found that the pH of the solution is 8.64. Remember, a pH of 7 is neutral, values below 7 are acidic, and values above 7 are basic. Since 8.64 is greater than 7, this solution is basic, also known as alkaline.

Think of it this way: the concentration of hydroxide ions ([OH-]) is higher than the concentration of hydrogen ions ([H+]) in this solution. This excess of hydroxide ions gives the solution its basic character.

Solutions with a pH around 8.64 are commonly found in everyday life. For example, seawater has a pH around 8.2, and baking soda solutions are also slightly basic. Understanding the pH of different solutions helps us predict their behavior and how they will interact with other substances.

Now that we've mastered the pH calculation and interpretation, let's address some common questions and potential pitfalls.

Common pH Pitfalls and FAQs

Calculating pH can be tricky, and there are a few common mistakes that students often make. Let's clear up some confusion:

  • Forgetting the negative sign: The pH formula is pH = -log10[H+]. Don't forget to multiply the logarithm by -1! This is a crucial step to get the correct pH value.
  • Using the wrong concentration: Make sure you're using the molar concentration of hydrogen ions ([H+]), not any other concentration. Sometimes, problems might give you the concentration of hydroxide ions ([OH-]) instead. You'll need to use the relationship Kw = [H+][OH-] = 1.0 x 10^-14 to find [H+] before calculating the pH.
  • Misunderstanding the logarithmic scale: Remember that pH is a logarithmic scale. A change of one pH unit represents a tenfold change in the concentration of hydrogen ions. For example, a solution with pH 3 is ten times more acidic than a solution with pH 4.
  • Significant figures: Pay attention to significant figures! The number of decimal places in the pH value should match the number of significant figures in the [H+] concentration.

Here are some Frequently Asked Questions about pH:

Q: What is the pH of pure water? A: Pure water has a pH of 7, which is neutral.

Q: What is the difference between pH and pOH? A: pH measures the concentration of hydrogen ions ([H+]), while pOH measures the concentration of hydroxide ions ([OH-]). They are related by the equation pH + pOH = 14.

Q: How does temperature affect pH? A: Temperature can affect the pH of a solution. The dissociation of water (H2O ⇌ H+ + OH-) is an endothermic process, meaning it absorbs heat. As temperature increases, the concentration of both H+ and OH- ions increases, but the solution remains neutral (pH = 7) because the concentrations are equal. However, the pH of a neutral solution at a higher temperature is still 7, but the concentrations of H+ and OH- are higher than at room temperature.

Q: What are some practical applications of pH measurement? A: pH measurement is used in many fields, including:

*   **Medicine:** Monitoring blood pH and urine pH.
*   **Agriculture:** Testing soil pH for optimal plant growth.
*   **Environmental science:** Assessing water quality in lakes and rivers.
*   **Industry:** Controlling pH in chemical reactions and manufacturing processes.

Wrapping Up: pH Masters!

We've journeyed through the world of pH, from understanding its fundamental concept to solving a pH calculation problem. We've learned the pH formula, how to interpret pH values, and how to avoid common pitfalls. You guys are now well-equipped to tackle any pH challenge that comes your way!

Remember, pH is a powerful tool for understanding the acidity and basicity of solutions, and it has wide-ranging applications in science and everyday life. Keep exploring, keep learning, and keep those pH skills sharp!

If you have any more questions about pH or other chemistry topics, feel free to ask. Happy calculating!