[H3O+] when pOH=5.58
The correct answer and explanation is :
To determine the concentration of [H3O+][H_3O^+] (hydronium ions) when the pOH is 5.58, we can use the relationship between pOH and pH, as well as the equation that links [H3O+][H_3O^+] with pH. Here’s how to approach the problem:
Step 1: Understanding pOH and pH relationship
The pH and pOH are related by the equation: pH+pOH=14\text{pH} + \text{pOH} = 14
So, if the pOH is 5.58, we can calculate the pH: pH=14−pOH=14−5.58=8.42\text{pH} = 14 – \text{pOH} = 14 – 5.58 = 8.42
Step 2: Calculating the hydronium ion concentration [H3O+][H_3O^+]
The concentration of hydronium ions [H3O+][H_3O^+] is related to pH by the following equation: pH=−log[H3O+]\text{pH} = -\log[H_3O^+]
Rearranging the equation to solve for [H3O+][H_3O^+], we get: [H3O+]=10−pH[H_3O^+] = 10^{-\text{pH}}
Now, substituting the pH value of 8.42: [H3O+]=10−8.42[H_3O^+] = 10^{-8.42}
Using a calculator, this gives: [H3O+]≈3.98×10−9 M[H_3O^+] \approx 3.98 \times 10^{-9} \, \text{M}
Final Answer:
[H3O+]≈3.98×10−9 M[H_3O^+] \approx 3.98 \times 10^{-9} \, \text{M}
Explanation:
- pOH and pH: The pOH scale is similar to the pH scale but focuses on the concentration of hydroxide ions ([OH−][OH^-]) rather than hydronium ions ([H3O+][H_3O^+]). The sum of pH and pOH always equals 14 in aqueous solutions at 25°C, because they are inversely related.
- Logarithmic Relationship: Both pH and pOH are logarithmic scales, which means they reflect the powers of ten of the concentrations of hydronium and hydroxide ions, respectively. When you know the pH or pOH, you can use the logarithmic formula to find the concentration of hydronium or hydroxide ions.
- Hydronium Ion Concentration: In this case, since the pH is 8.42, the concentration of [H3O+][H_3O^+] is very low, indicating that the solution is basic (since a pH greater than 7 means a basic solution). The calculation of [H3O+][H_3O^+] reflects this basic nature.