Understanding pH for 10^-10 M NaOH: A Comprehensive Guide
The pH of a 10-10 M NaOH solution is often a challenging question due to the complexities of water's autoionization. Let's break down the process step-by-step and explore the underlying principles.
Step-by-Step Calculation of pH for 10-10 M NaOH
To determine the pH of a 10-10 M NaOH solution, we need to consider several steps involving the dissociation of NaOH and the impact of autoionization of water.
Step 1: Calculate [OH-]
NaOH is a strong base and dissociates completely in water:
NaOH → Na OH-
At a concentration of 10-10 M, the concentration of hydroxide ions, [OH-], is also 10-10 M.
Step 2: Calculate the pOH
The pOH can be calculated using the formula:
pOH -log[OH-]
Substituting the concentration of OH- into the formula:
pOH -log(10-10) 10
Step 3: Calculate the pH
To find the pH, we can use the relationship between pH and pOH:
pH pOH 14
Substituting the pOH value:
pH 14 - 10 4
Conclusion
Therefore, the pH of a 10-10 M NaOH solution is 4. This result highlights that even at very low concentrations, the contribution of water's autoionization, which produces 10-7 M of [H ], becomes significant and impacts the pH value.
Understanding the pH Range and Its Limitations
The pH of a 10-10 M NaOH solution is expected to be just slightly above 7, in the range of 7.0001-7.0003. This outcome is a result of water's autoionization, which produces hydrogen ions (H ), contributing to a more neutral pH.
Stoichiometric Problem and Its Misconceptions
Many students may incorrectly conclude that a 0.0000000001 N (10-10 M) NaOH solution with a [OH-] concentration of 10-10 M and a [H ] concentration of 10-4 M would have a pH of 4. However, this is incorrect because a solution of NaOH cannot be acidic; it must remain basic.
The correct approach involves solving for the concentration of [H ] using the relationship:
[OH-][H ] 10-14
By substituting the known values:
10-10 [H ] 10-14
[H ] 10-4
Therefore, the pH is given by:
pH -log[OH-] -log(10-10) 10 - 4 7.000217147
This value is consistent with our expected range.
The Importance of Autoionization
The equilibrium constant for pure water at room temperature is 10-14. The product of the concentrations of acid and base equals that value:
[OH-][H ] 10-14
Given [OH-] 10-10 M:
10-10 [H ] 10-14
[H ] 10-4 M
Therefore, the pH is:
pH -log[H ] -log(10-4) 4
The pH can range from 0 to 14, and the relationship between pH and pOH is well-established:
pH pOH 14
Given pOH 10, the pH must be 4.
Conclusion
Understanding the pH of a 10-10 M NaOH solution involves recognizing the effects of water's autoionization. By correctly applying the principles of acid-base chemistry, we can accurately determine the pH and ensure that our conclusions are sound.