What Is The PH Of Pure Water At $40.0^{\circ} C$ If The $K_{W}$ At This Temperature Is $2.92 \times 10^{-14}$?A. 6.767 B. 7.000 C. 0.465 D. 7.233

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Introduction

Pure water is a fundamental substance in chemistry, and its properties are essential to understand various chemical reactions and processes. The pH of pure water is a critical parameter that determines its acidity or basicity. At room temperature, the pH of pure water is neutral, with a value of 7. However, the pH of pure water can change with temperature. In this article, we will explore the pH of pure water at an elevated temperature of 40.0°C, given the ion product constant of water (Kw) at this temperature.

The Ion Product Constant of Water (Kw)

The ion product constant of water (Kw) is a measure of the concentration of hydrogen ions (H+) and hydroxide ions (OH-) in water. It is defined as the product of the concentrations of H+ and OH- ions:

Kw = [H+][OH-]

At 25°C, the Kw of pure water is 1.0 x 10^-14. However, the Kw of pure water changes with temperature. At 40.0°C, the Kw is given as 2.92 x 10^-14.

Calculating the pH of Pure Water at 40.0°C

To calculate the pH of pure water at 40.0°C, we can use the Kw expression:

Kw = [H+][OH-]

Since pure water is neutral, the concentration of H+ ions is equal to the concentration of OH- ions. Let's denote the concentration of H+ ions as [H+]. Then, the concentration of OH- ions is also [H+].

We can rewrite the Kw expression as:

Kw = [H+][H+]

Kw = [H+]^2

Now, we can substitute the given value of Kw at 40.0°C:

2.92 x 10^-14 = [H+]^2

To find the concentration of H+ ions, we can take the square root of both sides:

[H+] = √(2.92 x 10^-14)

[H+] = 1.71 x 10^-7

Calculating the pH of Pure Water

The pH of a solution is defined as the negative logarithm of the concentration of H+ ions:

pH = -log[H+]

Now, we can substitute the value of [H+]:

pH = -log(1.71 x 10^-7)

pH ≈ 6.767

Conclusion

In this article, we calculated the pH of pure water at an elevated temperature of 40.0°C, given the ion product constant of water (Kw) at this temperature. We used the Kw expression to find the concentration of H+ ions and then calculated the pH of pure water using the negative logarithm of the concentration of H+ ions. The calculated pH of pure water at 40.0°C is approximately 6.767.

Comparison with Other Options

Let's compare our calculated pH with the other options:

  • A. 6.767: This is our calculated pH.
  • B. 7.000: This is the pH of pure water at room temperature, not at 40.0°C.
  • C. 0.465: This is not a valid pH value.
  • D. 7.233: This is not the pH of pure water at 40.0°C.

Conclusion

In conclusion, the pH of pure water at 40.0°C is approximately 6.767, given the ion product constant of water (Kw) at this temperature. This value is different from the pH of pure water at room temperature, which is 7.