pH to concentration conversion: If a solution has pH = 7.00, what is the hydrogen ion concentration [H+] in moles per liter (mol/L)?

Introduction / Context:
Converting between pH and [H+] is a routine skill. At 25 °C for pure water, pH 7 corresponds to neutral conditions where [H+] equals [OH–].

Given Data / Assumptions:

• Definition: pH = −log10[H+].
• pH given as exactly 7.00.
• Assume standard temperature where Kw ≈ 1.0 x 10^-14.

Concept / Approach:
Rearrange pH definition: [H+] = 10^(-pH). Substitute pH = 7 to obtain [H+] = 10^-7 mol/L.

Step-by-Step Solution:
Start with pH = −log10[H+]. Take antilog: [H+] = 10^(-pH). Plug pH 7: [H+] = 10^-7 mol/L. Therefore, the correct numerical value is 1 x 10^-7 mol/L.

Verification / Alternative check:
Using Kw = [H+][OH–] = 1.0 x 10^-14 and [H+] = [OH–] at neutrality also yields [H+] = 1.0 x 10^-7 mol/L.

Why Other Options Are Wrong:
Options with 7 or 7 x 10^-7 are incorrect manipulations; 5 x 10^-7 is arbitrary; 1 x 10^-5 corresponds to pH 5, not 7.

Common Pitfalls:
Forgetting the negative sign in the definition, misplacing the exponent by one or two orders of magnitude.

Final Answer:
1 x 10^-7.