Question

If acid \(\mathrm{C}\) has a smaller \(K_{a}\) value than acid \(\mathrm{D}\), which acid is stronger?

Short answer

Acid D is stronger than Acid C.

Step-by-step solution

Understanding the Relationship Between Acid Strength and \(Ka\)

The strength of an acid is determined by the extent to which it can donate protons, or H+ ions. A higher \(Ka\) means the acid dissociates more and donates more protons, thus it's stronger. So, if \(Ka\) of Acid C is smaller than that of Acid D, Acid D is stronger.

Comparing the \(Ka\) values

Since the \(Ka\) of Acid C is smaller than the \(Ka\) of Acid D, Acid D is the stronger acid.

Key concepts

Acid Dissociation Constant

The acid dissociation constant, often symbolized as Ka, is a quantitative measure of how readily an acid gives up its proton, or hydrogen ion, in solution. It's crucial to understand that these constants are specific to each acid and are determined through experimentation.

To grasp this concept, picture an acid in water. Some of the acid molecules will donate protons to the water, creating hydronium ions (H₃O⁺). The acid dissociation constant quantifies the ratio of dissociated (ionized) to undissociated acid molecules at equilibrium. A larger Ka value suggests more of the acid is ionized, signifying a strong tendency to lose its proton.

Ka Value

The Ka value is an important aspect to consider when studying acids. It provides insights into the strength of the acid. With a simple formula, we can calculate the Ka value: it's the concentration of the products (protons and conjugate base) over the concentration of the undissociated acid.

Thinking of it in terms of a high school relationship, a high Ka value is like a couple that's 'not so strong' and 'breaks up' frequently, representing a strong acid that readily donates its protons. Conversely, a low Ka value is akin to a couple that 'stays together,' mirroring a weak acid that keeps hold of its protons.

Proton Donation

The term 'proton donation' refers to an acid's ability to donate a proton, also known as a hydrogen ion (H⁺), to another substance. This is central to the Brønsted-Lowry definition of an acid. The ease with which an acid donates a proton is a key indicator of its strength.

Imagine a runner handing off a baton in a relay race. In this analogy, the baton is the proton, and the faster it's handed off, the stronger the acid. Some acids are like sprinters who release the baton quickly (strong acids), while others are like joggers who cling to it a bit longer (weak acids).

Comparing Acids

When comparing the strengths of different acids, look at their Ka values. The higher the Ka, the stronger the acid. Simply put, it's like comparing different light bulbs: a bulb with a higher wattage shines brighter just as an acid with a higher Ka value 'shines' with acidity, being more effective at donating protons.

Returning to acids C and D, since Acid D has a higher Ka value than Acid C, we infer that Acid D is the more formidable 'proton donor' and thus the stronger acid. It's important for students to remember this direct relationship when tackling homework problems involving acid strength.