Question

question 4

the ph of a solution is 5.00. which of the following is true about the solution?

its \\(\text{h}_3\text{o}^+\\) is \\(1.0 \times 10^{-9}\text{ m}\\)
it is more acidic than a solution whose ph is 4.00.
its \\(\text{h}_3\text{o}^+\\) is \\(1.0 \times 10^{-5}\text{ m}\\)
its \\(\text{h}_3\text{o}^+\\) is \\(1.0 \times 10^5\text{ m}\\)
none of these

Explanation:

🆕 New Concept Discovered: pH and Hydronium Ion Concentration
Measuring acidity using logarithmic scales

Step 1: Understand the relationship between pH and hydronium concentration

The pH of a solution is a logarithmic scale used to specify the acidity of an aqueous solution. It is mathematically defined as the negative logarithm (base 10) of the hydronium ion concentration \([\text{H}_3\text{O}^+]\):

$$\text{pH} = -\log[\text{H}_3\text{O}^+]$$

To find the hydronium ion concentration \([\text{H}_3\text{O}^+]\) from a given pH, we can rearrange this formula by taking the inverse logarithm:

$$[\text{H}_3\text{O}^+] = 10^{-\text{pH}}$$

What this means is that each unit change in pH represents a tenfold change in the concentration of hydronium ions.

Step 2: Calculate the hydronium ion concentration

Given that the pH of the solution is \(5.00\), we substitute this value into our rearranged formula:

$$[\text{H}_3\text{O}^+] = 10^{-5.00}\text{ M}$$

In scientific notation, this is written as:

$$[\text{H}_3\text{O}^+] = 1.0 \times 10^{-5}\text{ M}$$

Step 3: Evaluate the given options

Let's check each statement to find the true one:

• Its \([\text{H}_3\text{O}^+]\) is \(1.0 \times 10^{-9}\text{ M}\): This is incorrect because our calculated concentration is \(1.0 \times 10^{-5}\text{ M}\).
• It is more acidic than a solution whose pH is 4.00: This is incorrect. A lower pH value means a higher concentration of hydronium ions, making a solution with \(\text{pH} = 4.00\) more acidic than one with \(\text{pH} = 5.00\).
• Its \([\text{H}_3\text{O}^+]\) is \(1.0 \times 10^{-5}\text{ M}\): This matches our calculated concentration exactly, so this statement is true.
• Its \([\text{H}_3\text{O}^+]\) is \(1.0 \times 10^{5}\text{ M}\): This is incorrect because the exponent must be negative for a dilute acidic solution.

Answer:

Its \([\text{H}_3\text{O}^+]\) is \(1.0 \times 10^{-5}\text{ M}\)