Problem 7 - Chemistry The Molecular Science

Question

Solution A has a pH of 8 and solution \(\mathrm{B}\) a p \(\mathrm{H}\) of 10 Which has the greater hydronium ion concentration? How many times greater is its concentration?

Step-by-Step Solution

Answer

Solution A has a 100 times greater hydronium ion concentration.

Step 1: Understanding pH and Hydronium Ion Concentration

The pH of a solution is the negative logarithm (base 10) of the hydronium ion concentration: \( \text{pH} = -\log[\text{H}_3\text{O}^+] \). To find which solution has a greater hydronium ion concentration, compare their pH values.

Step 2: Determine Hydronium Ion Concentration for Solution A

For Solution A with a pH of 8, use the formula: \( [\text{H}_3\text{O}^+] = 10^{-\text{pH}} = 10^{-8} \). This results in a hydronium ion concentration of \( 10^{-8} \) M.

Step 3: Determine Hydronium Ion Concentration for Solution B

For Solution B with a pH of 10, use the formula: \( [\text{H}_3\text{O}^+] = 10^{-\text{pH}} = 10^{-10} \). This results in a hydronium ion concentration of \( 10^{-10} \) M.

Step 4: Compare Hydronium Ion Concentrations

Since \( 10^{-8} \) M (Solution A) is greater than \( 10^{-10} \) M (Solution B), Solution A has a higher hydronium ion concentration.

Step 5: Calculate the Concentration Difference

To find how many times greater Solution A's concentration is compared to Solution B, divide their concentrations: \( \frac{10^{-8}}{10^{-10}} = 10^{2} = 100 \). So, Solution A's concentration is 100 times greater.

Key Concepts

Acid-Base Chemistry

In acid-base chemistry, the pH scale serves as a crucial tool to characterize the acidity or basicity of a solution. The pH scale ranges from 0 to 14. A pH value lower than 7 indicates an acidic solution, meaning it has a high concentration of hydronium ions (\([ ext{H}_3 ext{O}^+]\)). On the other hand, a pH greater than 7 points to a basic solution with a lower concentration of these ions.

Acids donate protons (\( ext{H}^+\) ions) that lead to the formation of hydronium ions when mixed with water. Bases, conversely, reduce the hydronium ion concentration by producing hydroxide ions (\( ext{OH}^-\)), which interact with the hydronium ions. Understanding how acids and bases interact aids in predicting how a solution's pH will change during chemical reactions. These concepts are crucial when working with or analyzing chemical reactions involving solutions.

When comparing solutions like Solution A and Solution B, the one with a lower pH—Solution A—has more available hydronium ions, thus is more acidic than Solution B. This essential knowledge is foundational in chemistry, aiding in everything from lab analysis to industrial applications.

Logarithmic Scale in Chemistry

Chemistry often involves vast ranges of values, especially when dealing with ion concentrations. The pH scale is logarithmic, a vital mathematical concept that helps chemists easily express very small or large numbers. Understanding logs is crucial because they translate multiplicative relationships of small numbers into additive scales.

The formula for pH reflects this: \( ext{pH} = - ext{log}_{10}{[ ext{H}_3 ext{O}^+]}\). Here, every one-unit change in pH corresponds to a tenfold change in hydronium ion concentration. For instance, a solution with a pH of 8 compared to one with a pH of 10 is 100 times more acidic because \(10^2 = 100\). This logarithmic aspect allows chemists to manage and compare values that differ widely in magnitude without cumbersome notation.

In real-world applications, it simplifies the comparison of acidic and basic substances, making it much simpler to convey valuable chemical information, such as the potency of various solutions, without dealing in tiny decimals or immense numbers.

Solutions and Concentration

Solutions are homogeneous mixtures of two or more substances, where a solute is dissolved in a solvent. Concentration describes the amount of solute in a given volume of solution, commonly expressed in molarity (M), which is moles of solute per liter of solution (mol/L).

When discussing hydronium ion concentration in the context of pH, it's an indication of how many \([ ext{H}_3 ext{O}^+]\) ions are dissolved in the solution. Solutions with higher concentrations of hydronium ions are more acidic. The concentration informs not only the chemical properties of the solution but also its behavior in reactions.

Understanding the concentration of solutions is essential when working in any chemical setting. Whether preparing medical drugs or analyzing environmental samples, the concentration dictates how reactive a solution will be and its potential effects. Solution A, with a concentration of \(10^{-8} \) M, illustrates a higher quantity of hydronium ions compared to Solution B's \(10^{-10}\) M, highlighting basic ideas of how concentration influences chemical dynamics.