Problem 99 - A Complete Resource Book in Chemistry for JEE Main

Question

The dissociation constant of water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) is \(1.0 \times 10-{ }^{14}\) and that of heavy water \(\left(\mathrm{D}_{2} \mathrm{O}\right)\) is \(3.0 \times 10^{-15}\). This is because the extent of dissociation of \(\mathrm{H}_{2} \mathrm{O}\) is about (a) \(1 / 3\) times that of \(\mathrm{D}_{2} \mathrm{O}\) (b) 3 times that of \(\mathrm{D}_{2} \mathrm{O}\) (c) 3000 times that of \(\mathrm{D}_{2} \mathrm{O}\) (d) 30 times that of \(\mathrm{D}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The extent of dissociation of \(\text{H}_2\text{O}\) is about 3 times that of \(\text{D}_2\text{O}\); option (b).

Step 1: Understand the Given Values

We have the dissociation constant of water (H₂O) as K_w(H₂O) = \(1.0 \times 10^{-14}\), and for heavy water (D₂O), K_w(D₂O) = \(3.0 \times 10^{-15}\). These values tell us how much each type of water dissociates into ions.

Step 2: Calculate the Ratio of Dissociation Constants

To determine how the extent of dissociation of H₂O compares to D₂O, calculate the ratio of the dissociation constants: \[\text{Ratio} = \frac{K_w(\text{H}_2\text{O})}{K_w(\text{D}_2\text{O})} = \frac{1.0 \times 10^{-14}}{3.0 \times 10^{-15}}\]

Step 3: Simplify the Ratio

Perform the division: \[\frac{1.0 \times 10^{-14}}{3.0 \times 10^{-15}} = \frac{10^{-14}}{3 \times 10^{-15}}\]This simplifies to:\[\frac{10^{-14}}{3 \times 10^{-15}} = \frac{10}{3} = 3.33\]

Step 4: Interpret the Result

The result 3.33 indicates that the extent of dissociation of \(\text{H}_2\text{O}\) is approximately 3.33 times that of \(\text{D}_2\text{O}\). However, the closest offered option is (b) 3 times that of \(\text{D}_2\text{O}\).

Key Concepts

Dissociation Constant

The dissociation constant is a valuable measure that tells us how much a substance, like water, breaks apart into ions. When water dissociates, it splits into hydrogen ions (H⁺) and hydroxide ions (OH⁻). The dissociation constant, represented by the symbol \(K_w\), quantitatively shows the extent of this reaction. If a compound dissociates extensively and forms many ions, it will have a larger dissociation constant.

The value for the dissociation constant of regular water (H₂O) is \(1.0 \times 10^{-14}\). This number may seem small, but it is significant in the context of chemical reactions. A related concept is the dissociation constant of heavy water (D₂O), which has a lower value of \(3.0 \times 10^{-15}\). This indicates that heavy water dissociates less than regular water.

Understanding these values helps to predict how these substances will react in different chemical environments. Knowing the \(K_w\) allows chemists to make deductions about the acidity and basicity of a solution.

Heavy Water

Heavy water, chemically known as D₂O, is a form of water where the regular hydrogen atoms (H) are replaced with deuterium atoms (D). Deuterium is an isotope of hydrogen that contains one extra neutron, making it heavier than regular hydrogen. Because of the presence of deuterium, it behaves slightly differently at the molecular level.

In terms of chemical properties, heavy water differs from regular water in several aspects. Notably, its dissociation constant \(K_w\) is \(3.0 \times 10^{-15}\), showing that it dissociates into ions at a lower rate than H₂O. This makes it less reactive in some chemical processes.

Heavy water is significant in scientific fields such as nuclear chemistry and materials science. It serves as a neutron moderator in certain types of nuclear reactors, helping to control the nuclear reactions safely. Despite its benefits in these applications, heavy water is not suitable for consumption due to its different properties from regular water.

Extent of Dissociation

The extent of dissociation is a key concept in understanding the behavior of substances in solution. It describes how completely a substance separates into its ions in a particular situation. When the extent of dissociation is high, a substance is largely broken up into ions, making it more reactive.

In the example of water, we compare the extent of dissociation between regular water (H₂O) and heavy water (D₂O). By looking at their dissociation constants, we derived that H₂O has a dissociation constant of \(1.0 \times 10^{-14}\), while D₂O has \(3.0 \times 10^{-15}\).

Finding the ratio of these constants, \(\frac{K_w(\text{H}_2\text{O})}{K_w(\text{D}_2\text{O})} = 3.33\), shows that H₂O dissociates more extensively than D₂O. So, the extent of its dissociation is about 3.33 times that of heavy water. This is a crucial finding as it highlights the chemical differences between the two types of water in terms of their roles and reactions in different chemical settings.