Problem 97 - Chemistry: Principles and Reactions

Question

Which of the following is/are true about a \(0.10 \mathrm{M}\) solution of a strong acid, HY? (a) \(\left[\mathrm{Y}^{-}\right]=0.10 \mathrm{M}\) (b) \([\mathrm{HY}]=0.10 \mathrm{M}\) (c) \(\left[\mathrm{H}^{+}\right]=0.10 \mathrm{M}\) (d) \(\mathrm{pH}=1.0\) (c) \(\left[\mathrm{H}^{+}\right]+\left[\mathrm{Y}^{-}\right]=0.20 \mathrm{M}\)

Step-by-Step Solution

Answer

(a) [Y⁻] = 0.10 M (b) [HY] = 0.10 M (c) [H⁺] = 0.10 M (d) pH = 1.0 (e) [H⁺] + [Y⁻] = 0.20 M Answer: (a), (c), (d), and (e) are true.

Step 1: Understand the behavior of strong acids in solution

Strong acids, such as HY, are acids that completely dissociate in water. That means that for a strong acid, its hydrogen ion (H+) concentration is equal to its initial molarity, and its conjugate base ion (Y-) concentration is also equal to the initial molarity of the acid.

Step 2: Analyze statement (a)

(a) \([\mathrm{Y}^{-}]=0.10 \mathrm{M}\) Since HY is a strong acid, it dissociates completely, meaning the concentration of Y⁻ ions in the solution is equal to the initial concentration of HY. In this case, the statement is true.

Step 3: Analyze statement (b)

(b) \([\mathrm{HY}]=0.10 \mathrm{M}\) After dissociation, the concentration of the undissociated HY molecules should essentially be zero. The statement is false.

Step 4: Analyze statement (c)

(c) \([\mathrm{H}^{+}]=0.10 \mathrm{M}\) As HY is a strong acid, its hydrogen ion concentration, \([\mathrm{H}^{+}]\), is equal to its initial molarity (0.10 M). This statement is true.

Step 5: Analyze statement (d)

(d) \(\mathrm{pH}=1.0\) pH is calculated using the formula \(\mathrm{pH}=-\log_{10}\left([\mathrm{H}^{+}]\right)\). Since \([\mathrm{H}^{+}]=0.10 \mathrm{M}\): \(\mathrm{pH}=-\log_{10}(0.10)\) \(\mathrm{pH}=1.0\) The statement is true.

Step 6: Analyze statement (e)

(e) \([\mathrm{H}^{+}]+[\mathrm{Y}^{-}]=0.20 \mathrm{M}\) Since both the hydrogen ion and Y- ion concentrations are equal to the initial concentration of HY (0.10 M), their sum is: \(0.10 \mathrm{M} + 0.10 \mathrm{M} = 0.20 \mathrm{M}\) The statement is true.

Step 7: Conclusion

Based on our analysis, the following statements about the 0.10 M solution of the strong acid, HY, are true: (a) \([\mathrm{Y}^{-}]=0.10 \mathrm{M}\) (c) \([\mathrm{H}^{+}]=0.10 \mathrm{M}\) (d) \(\mathrm{pH}=1.0\) (e) \([\mathrm{H}^{+}]+[\mathrm{Y}^{-}]=0.20 \mathrm{M}\)

Key Concepts

Dissociation

Strong acids like HY have a unique property in water. When we say a strong acid dissociates, it means the acid molecules break apart completely into their ions. This dissociation leads to the formation of hydrogen ions (H⁺) and conjugate base ions (Y⁻) in the solution.

• In the case of a 0.10 M solution of HY, the dissociation means each molecule of HY breaks into one H⁺ ion and one Y⁻ ion.
• Because HY dissociates completely, the entire 0.10 M concentration of HY turns into 0.10 M of H⁺ ions and 0.10 M of Y⁻ ions.

This means that for every mole of HY dissolved, you will end up with exactly one mole of H⁺ and one mole of Y⁻. This total breakup ensures we have no undissociated HY left in the solution.

Conjugate Base

Every acid has a corresponding conjugate base, which is what remains after the acid donates a proton (H⁺). For the strong acid HY, when it loses its hydrogen ion, it turns into its conjugate base, Y⁻.

• In a strong acid solution, because of the complete dissociation, the concentration of the conjugate base Y⁻ matches the initial concentration of the acid.
• This means in our original 0.10 M solution of HY, the concentration of the conjugate base Y⁻ is also 0.10 M.
• The complete dissociation property of strong acids assures us that the conjugate base Y⁻ concentration is predictable and equal to the amount of dissolved strong acid.

Recognizing the relationship between an acid and its conjugate base helps in understanding how acids behave in a solution, especially those classified as strong acids.

pH Calculation

Understanding how to calculate pH is crucial when dealing with strong acids, as this numerical value tells us how acidic a solution is. For a strong acid like HY at 0.10 M concentration, the pH can be directly calculated using the concentration of H⁺ ions.

• The pH formula is given by \[ pH = -\log_{10}([H^+]) \]
• Applying this to our solution where \[ [H^+] = 0.10 \], we input \[ -\log_{10}(0.10) \]
• Mathematically, this gives us a pH of 1.0, indicating a very acidic solution.

The simple relation between strong acids' concentration and their pH arises due to their complete dissociation. The more H⁺ in the solution, the lower the pH. Hence, understanding and computing pH tells us about the H⁺ ion concentration readily available in the solution.