Question

A solution is prepared with an unknown concentration of a theoretical compound whose \(\mathrm{K}_{\mathrm{a}}\) is exactly \(1.0\). What is the \(\mathrm{pH}\) of this solution? A. Higher than 7 B. Exactly 7 C. Lower than 7 D. Impossible to determine

Short answer

C. Lower than 7

Step-by-step solution

Understand the Compound's Nature

Determine if the compound is an acid or a base. Since \(\text{K}_\text{a} = 1.0\), it indicates the compound is an acid.

Analyze \(\text{K}_\text{a}\) Value

\(\text{K}_\text{a}\) reflects the strength of the acid. For \(\text{K}_\text{a} = 1.0\), it is a moderately strong acid, meaning it will partially dissociate in water.

Predict the \(\text{pH}\)

Since the compound is an acid, it will release \(\text{H}^+\) ions into the solution, decreasing the \(\text{pH}\). Therefore, the \(\text{pH}\) of the solution will be lower than 7.

Key concepts

pH determination

Determining the pH of a solution is crucial in understanding its acidity or alkalinity. pH is a measure of the hydrogen ion concentration in a solution. The formula to calculate pH is: \(\text{pH} = -\log[H^+]\). This means that if you know the concentration of hydrogen ions in your solution, you can easily find out the pH.

For instance, if the hydrogen ion concentration \(\left[H^+\right]\) is \(1 \times 10^{-3} \), the pH is \(\log(1 \times 10^{-3}) \) which equals 3.

Key points to remember when determining pH:

• A pH less than 7 indicates an acidic solution.
• A pH of exactly 7 indicates a neutral solution.
• A pH greater than 7 indicates a basic solution.

acid dissociation constant (Ka)

The acid dissociation constant, known as \(K_a\), helps to gauge the strength of an acid. It measures the extent to which an acid dissociates into its ions in water. The formula for \(K_a\) is: \[K_a = \frac{[H^+][A^-]}{[HA]} \]

where:

• \texttt{\[H^+\]} is the concentration of hydrogen ions.
• \texttt{\[A^-\]} is the concentration of the conjugate base.
• \texttt{\[HA\]} is the concentration of the undissociated acid.

In our example, \(K_a = 1.0\) indicates the compound is a moderately strong acid, meaning it partially dissociates in water.

strength of acids

The strength of acids is determined by their ability to donate hydrogen ions (\(H^+\)), which is quantified by the \(K_a\) value.

Here are some key insights:

• Strong acids have high \(K_a\) values indicating they dissociate completely in water.
• Weak acids have low \(K_a\) values and only partially dissociate in water.
• An acid with \(K_a = 1.0\) is considered moderately strong, meaning it's neither fully weak nor strong.

Understanding the \(K_a\) helps in predicting if a solution will be acidic (pH < 7), neutral (pH = 7), or basic (pH > 7). In our exercise, the moderately strong acid implies that the pH will be less than 7, making the solution acidic.