Let's address the given statement about the ion product constant of water at [tex]$25^{\circ} C$[/tex].
### Important Background Information:
The ion product constant of water (denoted as [tex]\( K_w \)[/tex]) at [tex]$25^{\circ} C$[/tex] is a well-known property and is crucial in understanding the self-ionization of water. The formula for [tex]\( K_w \)[/tex] is:
[tex]\[
K_w = [H_3O^+][OH^-]
\][/tex]
### Recognized Value:
For pure water at [tex]$25^{\circ} C$[/tex], the product of the molar concentrations of hydronium ions ([tex]\([H_3O^+]\)[/tex]) and hydroxide ions ([tex]\([OH^-]\)[/tex]) is always:
[tex]\[
K_w = 1 \times 10^{-14}
\][/tex]
This value holds true regardless of whether the solution is acidic, neutral, or basic as long as it is at [tex]$25^{\circ} C$[/tex].
### Given Statement:
The given statement claims:
[tex]\[
K_w = [H_3O^+][OH^-] = 1 \times 10^{-7}
\][/tex]
### Verification:
- To verify whether this statement is true, compare the given value for [tex]\( K_w \)[/tex] with the well-established value of [tex]\( K_w \)[/tex] at [tex]$25^{\circ} C$[/tex].
- The correct value of [tex]\( K_w \)[/tex] is [tex]\( 1 \times 10^{-14} \)[/tex], which is substantially different from [tex]\( 1 \times 10^{-7} \)[/tex].
### Conclusion:
Since the given statement suggests that [tex]\( K_w = 1 \times 10^{-7} \)[/tex], which is incorrect (the correct value being [tex]\( 1 \times 10^{-14} \)[/tex]), we conclude that the given statement is false.
Thus, the answer to the given question is:
(B) False.
