Chapter 7: Problem 6
Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of the following strong acid solutions: (a) \(0.020 \mathrm{M}\) \(\mathrm{HClO}_{4}\) (b) \(1.3 \times 10^{-4} M \mathrm{HNO}_{3}\) (c) \(1.2 M \mathrm{HCl}\) (d) \(1.2 \times 10^{-9} M \mathrm{HCl}\) (e) \(2.4 \times 10^{-7} M \mathrm{HNO}_{3}\).
Short Answer
Step by step solution
Understand the Problem
Calculate pH for Part (a)
Calculate pOH for Part (a)
Calculate pH for Part (b)
Calculate pOH for Part (b)
Calculate pH for Part (c)
Calculate pOH for Part (c)
Calculate pH for Part (d) Applying Neutralization
Calculate pOH for Part (d)
Calculate pH for Part (e) Applying Neutralization
Calculate pOH for Part (e)
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Strong Acids
Examples include hydrochloric acid \(\text{HCl}\), nitric acid \(\text{HNO}_3\), and perchloric acid \(\text{HClO}_4\). The concentration of these acids directly reflects the concentration of hydronium ions \(\text{H}_3\text{O}^+\) in the solution.
- These ions are responsible for the solution's acidity.
- Knowing the original concentration of the acid provides the \(\text{H}^+\) concentration.
- One key characteristic is their pH, which is typically low due to the high concentration of hydrogen ions.
Water Ionization
This process is expressed in the water dissociation constant (Kw), where \[K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}\].
- This \(Kw\) value is significant because it represents the product of the concentrations of hydrogen and hydroxide ions.
- At a neutral pH of 7, both \(\text{H}^+\) and \(\text{OH}^-\) concentrations are \(1.0 \times 10^{-7}\) M.
- Changes in these values reveal whether a solution is acidic or basic.
Hydronium Ion Concentration
In solutions of strong acids, the concentration of hydronium ions is equivalent to the initial concentration of the acid due to complete dissociation. Calculating the \(\text{H}_3\text{O}^+\) concentration is straightforward:
- Directly equals the \(\text{H}^+\) concentration in strong acids.
- Direct measurement allows for precise pH calculations using \(\text{pH} = -\log[\text{H}_3\text{O}^+]\).
- When considering a mixture or balance with water ionization, adjust calculations to estimate the correct hydronium concentration.
pOH Calculation
The formula \(\text{pH} + \text{pOH} = 14\) is derived from the water ionization constant. Here’s why pOH is vital:
- It provides clarity on the concentration of hydroxide ions \(\text{OH}^-\) present.
- By knowing either pH or pOH, calculating the other becomes easy using their defined relationship.
- For dilute acidic solutions, pOH becomes crucial to account for water's contribution to the ion concentrations.