Question

The ionic product of water is defined as (1) The product of the concentration of proton and hydroxyl ion in pure water (2) The product of the concentration of acid and hydroxyl ion in aqueous solution (3) The ratio of the concentration of dissociated water to the undissociated water (4) All the above

Short answer

Option (1) is correct.

Step-by-step solution

Define Ionic Product of Water

The ionic product of water, commonly denoted as $K_w$, is defined for pure water as the product of the concentrations of the hydrogen ion (proton) $[H^{+}]$ and the hydroxyl ion $[O{H}^{-}]$.

Explore Given Options

Analyze each given option to check which one correctly corresponds to the definition of the ionic product of water.

Verify Option (1)

Option (1): 'The product of the concentration of proton and hydroxyl ion in pure water' matches the definition of the ionic product of water, $[H^{+}][O{H}^{-}]$.

Verify Option (2)

Option (2) talks about the product of the concentration of acid and hydroxyl ion in an aqueous solution. This doesn't correspond directly to the definition of $K_w$.

Verify Option (3)

Option (3) mentions the ratio of the concentration of dissociated water to undissociated water, which is not the same as the ionic product of water.

Verify Option (4)

Option (4) claims that all the given statements are correct. Since not all options correspond to the definition of the ionic product of water, this option is incorrect.

Conclusion

Based on the evaluation, the correct option is (1), which accurately describes the ionic product of water.

Key concepts

Proton Concentration

In chemistry, the term 'proton concentration' refers to the concentration of hydrogen ions, often denoted as $[H^{+}]$. Protons are positively charged atoms that are released when an acid dissociates in water. In pure water, the concentration of protons is extremely low because water is only very slightly ionized. This proton concentration is one of the two critical components when we talk about the ionic product of water, $[K_w]$. The formula representing proton concentration in water is:
$[H_{2}O]\leftrightharpoons H^{+}+O{H}^{-}$
Here, $[H^{+}]$ is the proton concentration.

To measure acid or base strength, we look at the $[H^{+}]$ concentration.

• Strong acids have high $[H^{+}]$ concentrations.
• Weak acids have relatively low $[H^{+}]$ concentrations.

Knowing $[H^{+}]$ is crucial to understanding the reactivity and characteristics of substances in aqueous solutions.

Hydroxyl Ion Concentration

Hydroxyl ion concentration refers to the concentration of $[O{H}^{-}]$ ions in a solution. Hydroxyl ions are negatively charged and typically arise from the dissociation of bases. In the context of water's autoionization, the equation is:
$[H_{2}O]\leftrightharpoons H^{+}+O{H}^{-}$
This shows that water dissociates into equal parts hydrogen ions and hydroxyl ions. The concentration of hydroxyl ions in pure water is quite low but equal to that of hydrogen ions, both being $${10}^{-7}$$ M at 25°C.

• Strong bases have high $[O{H}^{-}]$ concentrations.
• Weak bases have relatively lower $[O{H}^{-}]$ concentrations.

Understanding $[O{H}^{-}]$ concentration is essential when analyzing pH and pOH, as these values can tell us how acidic or basic a solution is.

Kw Constant

The ionic product of water, denoted as $$K_w$$, is a critical concept. For pure water at 25°C, $$K_w$$ is expressed as:
$$K_w=[H^{+}][O{H}^{-}]$$
The value of $[K_w]$ is $$1\times {10}^{-14}{M}^2$$. This means that the product of the concentrations of hydrogen ions and hydroxyl ions in pure water is constant at this temperature.

If we increase the temperature, the value of $[K_w]$ also increases, and vice versa. This constant forms the foundation for understanding the pH scale, where:

• pH = -log$[H^{+}]$
• pOH = -log$[O{H}^{-}]$

Additionally, in any aqueous solution, the product of $[H^{+}]$ and $[O{H}^{-}]$ must equal $[K_w]$. This constraint helps chemists predict and manipulate the acidity and basicity of solutions by adjusting ion concentrations.