Problem 40 - Chemistry: Principles and Reactions

Question

Rank the following solutions in order of increasing \(\left[\mathrm{H}^{+}\right]\). \(\begin{array}{llll}0.1 & M \mathrm{HBr}, & 0.1 \mathrm{M} \mathrm{HF}, & 0.1 \mathrm{MHCHO}_{2} & 0.1 \mathrm{MHCN}\end{array}\)

Step-by-Step Solution

Answer

Question: Arrange the following solutions in order of increasing proton concentration: 0.1 M HBr, 0.1 M HF, 0.1 M HCHO2, and 0.1 M HCN. Answer: HCN, HCHO2, HF, HBr

Step 1: Identify the Acids and their Dissociation Constants

The given solutions contain the following acids: 1. Hydrobromic Acid (HBr) 2. Hydrofluoric Acid (HF) 3. Formic Acid (HCHO2) 4. Hydrocyanic Acid (HCN) The acids dissociation constants ( \(K_a\) ) are: 1. HBr: \(K_a = 10^{9}\) 2. HF: \(K_a = 6.76 × 10^{-4}\) 3. HCHO2: \(K_a = 1.8 × 10^{-4}\) 4. HCN: \(K_a = 6.2 × 10^{-10}\)

Step 2: Determine the Concentration of protons (\(\left[\mathrm{H}^{+}\right]\)) for each acid

The concentration of protons for a given acid can be approximated using the following formula: \(\left[\mathrm{H}^{+}\right] \approx \sqrt{K_a × M}\) For the given acids: 1. HBr: \(\left[\mathrm{H}^{+}\right] \approx \sqrt{10^{9} × 0.1} = 10^{4}\) 2. HF: \(\left[\mathrm{H}^{+}\right] \approx \sqrt{6.76 × 10^{-4} × 0.1} = 8.21× 10^{-3}\) 3. HCHO2: \(\left[\mathrm{H}^{+}\right] \approx \sqrt{1.8 × 10^{-4} × 0.1} = 4.24× 10^{-3}\) 4. HCN: \(\left[\mathrm{H}^{+}\right] \approx \sqrt{6.2 × 10^{-10} × 0.1} = 7.87 × 10^{-6}\)

Step 3: Rank the Acids in Order of Increasing Proton Concentration

Now, arrange the acids based on increasing \(\left[\mathrm{H}^{+}\right]\): 1. Hydrocyanic Acid (HCN): \(\left[\mathrm{H}^{+}\right] = 7.87 × 10^{-6}\) 2. Formic Acid (HCHO2): \(\left[\mathrm{H}^{+}\right] = 4.24 × 10^{-3}\) 3. Hydrofluoric Acid (HF): \(\left[\mathrm{H}^{+}\right] = 8.21 × 10^{-3}\) 4. Hydrobromic Acid (HBr): \(\left[\mathrm{H}^{+}\right] = 10^{4}\) The correct order in terms of increasing proton concentration is HCN, HCHO2, HF, and HBr.

Key Concepts

Proton Concentration

Proton concentration is an important concept in chemistry, especially when discussing acids. When an acid dissolves in water, it dissociates, releasing hydrogen ions or protons ([\text{H}^{+}]). These protons are responsible for the acidic properties of the solution. The higher the concentration of protons, the stronger the acidity of a solution.

In the given problem, the goals are to calculate and compare the proton concentrations of different acidic solutions. In general, strong acids, which completely dissociate in water, produce higher proton concentrations than weak acids, which only partially dissociate.

• Strong acids like hydrobromic acid (HBr) dissociate completely, leading to a high concentration of protons.
• Weak acids, such as hydrofluoric acid (HF), formic acid (\text{HCHO}_2), and hydrocyanic acid (HCN), dissociate to a lesser extent, which results in a lower proton concentration.

To calculate the proton concentration for each acid, we use the approximate formula: \(\left[\text{H}^{+}\right] \approx \sqrt{K_a \times M}\), where \(M\) is molarity and \(K_a\) is the acid dissociation constant.

Acid Strength

The strength of an acid is determined by its ability to donate protons in a solution. Acid strength is generally characterized by its dissociation in water. A strong acid will dissociate completely, producing a large number of protons, whereas a weak acid will only partly dissociate.

Recognizing acid strength is vital for understanding how acidic a solution is. When you encounter different acids, it's important to remember:

• Strong acids like HBr dissociate fully, leading to a high concentration of protons, indicating a very strong acid.
• Weak acids like HF, \text{HCHO}_2, and HCN don't fully dissociate, providing a lower proton concentration compared to strong acids.

The ability of an acid to dissociate and the resulting proton concentration are intricately linked. It's why in neutralizing reactions or in determining pH, knowing the acid strength becomes pivotal.

For useful practice, try predicting the relative strength when given different acids by looking at their \(K_a\) values and resulting proton concentrations at the same molarity.

Ka Values

The \(K_a\) value, or acid dissociation constant, is a numerical representation of an acid's ability to donate protons. Higher \(K_a\) values mean stronger acids as they ionize more completely in a solution, producing more protons.

To better understand \(K_a\) values:

• A strong acid, such as HBr in our example, has a very high \(K_a\) value, usually on the order of 10⁹ or higher.
• Weak acids like HF and \text{HCHO}_2 have moderate \(K_a\) values, indicating partial dissociation.
• Very weak acids like HCN have low \(K_a\) values, meaning they dissociate only very slightly.

Knowing the \(K_a\) value helps us not only compare the strength of acids but also to calculate the concentration of protons using the equation: \(\left[\text{H}^{+}\right] \approx \sqrt{K_a \times M}\). This makes it clear how critical and impactful the \(K_a\) values are when evaluating acids.