At 20°C, the water autoionization constant, Kw, is 6.8 ´ 10–15. What is the H3O+ concentration in neutral water at this temperature?
A. 6.8 × 10–7 M
B. 3.4 × 10–15 M
C. 6.8 × 10–15 M
D. 8.2 × 10–8 M
E. 1.0 × 10–7 M
The Correct Answer and Explanation is:
The autoionization constant of water, ( K_w ), represents the product of the concentrations of hydrogen ions (( H_3O^+ )) and hydroxide ions (( OH^- )) in water. The equation for autoionization is:
[
H_2O \rightleftharpoons H_3O^+ + OH^-
]
At equilibrium, the concentrations of ( H_3O^+ ) and ( OH^- ) in pure water are equal. Therefore, we can express the concentration of ( H_3O^+ ) (or ( OH^- )) as:
[
[H_3O^+] = [OH^-]
]
The autoionization constant is given by:
[
K_w = [H_3O^+][OH^-]
]
At 20°C, ( K_w ) is provided as ( 6.8 \times 10^{-15} ). Since the concentrations of ( H_3O^+ ) and ( OH^- ) are equal in neutral water, we can rewrite the equation as:
[
K_w = [H_3O^+]^2
]
Substitute the value of ( K_w ) at 20°C:
[
6.8 \times 10^{-15} = [H_3O^+]^2
]
To find the concentration of ( H_3O^+ ), take the square root of both sides:
[
[H_3O^+] = \sqrt{6.8 \times 10^{-15}} = 8.2 \times 10^{-8} \, M
]
Therefore, the concentration of ( H_3O^+ ) in neutral water at 20°C is 8.2 × 10⁻⁸ M.
Answer: D. 8.2 × 10⁻⁸ M
Explanation:
The ( K_w ) value changes with temperature. At 20°C, the value of ( K_w ) is lower than at 25°C, where it is typically ( 1.0 \times 10^{-14} ). This lower ( K_w ) results in a lower concentration of ( H_3O^+ ) in neutral water at 20°C. The relationship between ( K_w ) and the concentration of ions is fundamental for understanding the pH of water and its variations with temperature. At 25°C, the concentration of ( H_3O^+ ) in neutral water would be ( 1.0 \times 10^{-7} \, M ), but at 20°C, due to the lower ( K_w ), the concentration is significantly lower, which is why the correct answer is ( 8.2 \times 10^{-8} \, M ).