Question

At $60^{\circ} \text{C}$, the value of the ionic product of water ($K_{w}$) is $9.6 \times 10^{-14} \text{M}^{2}$. What is the value of [$\text{H}_{3}\text{O}^{+}$] for a neutral aqueous solution at $60^{\circ} \text{C}$, and what is the nature of the solution with $\text{pH} = 7.0$ at $60^{\circ} \text{C}$?

A: $3.1 \times 10^{-8}$, acidic
B: $3.1 \times 10^{-7}$, neutral
C: $3.1 \times 10^{-8}$, basic
D: $3.1 \times 10^{-7}$, basic

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Answer

To determine the correct answer, let's go through the solution step by step.

Step 1: Find [(\text{H}_3\text{O}^+)]

Given:

  • The ionic product of water at ( 60^\circ \text{C} ), ( K_w = 9.6 \times 10^{-14} \text{ M}^2 )

In a neutral aqueous solution at any temperature:

$$ [\text{H}_3\text{O}^+] = [\text{OH}^-] $$

So,

$$ [\text{H}_3\text{O}^+] \times [\text{OH}^-] = K_w $$

For a neutral solution:

$$ [\text{H}_3\text{O}^+] = [\text{OH}^-] $$

Thus,

$$ [\text{H}_3\text{O}^+]^2 = K_w $$

Hence,

$$ [\text{H}_3\text{O}^+] = \sqrt{K_w} = \sqrt{9.6 \times 10^{-14}} $$

Calculating the above equation:

$$ [\text{H}_3\text{O}^+] = \sqrt{9.6} \times 10^{-7} \approx 3.1 \times 10^{-7} \text{ M} $$

Step 2: Determine the nature of the solution

Given:

  • pH of the solution is 7.0

In a solution, the pH is defined as:

$$ \text{pH} = -\log[\text{H}_3\text{O}^+] $$

For a pH of 7.0:

$$ [\text{H}_3\text{O}^+] = 10^{-7} \text{ M} $$

Comparing this with the calculated $[\text{H}_3\text{O}^+]$ at ( 60^\circ \text{C} ):

  • Calculated $[\text{H}_3\text{O}^+] = 3.1 \times 10^{-7} \text{ M}$
  • Given $[\text{H}_3\text{O}^+] = 10^{-7} \text{ M}$

Since ( 3.1 \times 10^{-7} \text{ M} > 10^{-7} \text{ M} ), the solution with a pH of 7.0 at ( 60^\circ \text{C} ) will have a lower concentration of $[\text{H}_3\text{O}^+]$ compared to the neutral water at that temperature. This indicates that the solution is more basic or alkaline since it has a lower $[\text{H}_3\text{O}^+]$ than neutral water at the given temperature.

Final Answer:

  • $[\text{H}_3\text{O}^+] = 3.1 \times 10^{-7}$

  • Nature of the solution: क्षारीय (alkaline)

Therefore, the correct option is D.

Final Answer: D


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