Answer :
To determine the characteristics of a substance with a high concentration of hydrogen ions ([tex]\(\left[ H^{+} \right]\)[/tex]), let's carefully analyze the relationships between [tex]\(\left[ H^{+} \right]\)[/tex], [tex]\(\left[ OH^{-} \right]\)[/tex], pH, and pOH.
### Step-by-Step Analysis:
1. Understanding pH and [tex]\( \left[ H^{+} \right] \)[/tex]:
- pH is a measure of the acidity of a solution. It is defined as:
[tex]\[ \text{pH} = -\log \left( \left[ H^{+} \right] \right) \][/tex]
- A high [tex]\(\left[ H^{+} \right]\)[/tex] means a low pH value, indicating an acidic solution.
2. Understanding [tex]\( \left[ OH^{-} \right] \)[/tex] and pOH:
- pOH is a measure of the basicity of a solution. It is defined as:
[tex]\[ \text{pOH} = -\log \left( \left[ OH^{-} \right] \right) \][/tex]
- A high [tex]\(\left[ OH^{-} \right]\)[/tex] means a low pOH value, indicating a basic solution.
3. Relationship Between pH and pOH:
- pH and pOH are related by the equation:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
This means that if the pH is low (indicating high acidity and high [tex]\(\left[ H^{+} \right]\)[/tex]), the pOH must be high (indicating low basicity and low [tex]\(\left[ OH^{-} \right]\)[/tex]).
4. Determining [tex]\( \left[ OH^{-} \right] \)[/tex] from [tex]\( \left[ H^{+} \right] \)[/tex]:
- A high [tex]\(\left[ H^{+} \right]\)[/tex] leads to a low [tex]\(\left[ OH^{-} \right]\)[/tex] because of the inverse relationship in an aqueous solution where:
[tex]\[ \left[ H^{+} \right] \times \left[ OH^{-} \right] = 10^{-14} \][/tex]
- Thus, if [tex]\(\left[ H^{+} \right]\)[/tex] is high, [tex]\(\left[ OH^{-} \right]\)[/tex] has to be low.
### Conclusion:
Based on the relationships and definitions above, if a substance has a high [tex]\(\left[ H^{+} \right]\)[/tex] concentration:
- It will have a low pH.
- Consequently, it will have a high pOH, since [tex]\(\text{pH} + \text{pOH} = 14\)[/tex].
- It will have a low concentration of hydroxide ions, [tex]\(\left[ OH^{-} \right]\)[/tex].
### Answer:
A substance with a high [tex]\(\left[ H^{+} \right]\)[/tex] would likely have:
- A low [tex]\(\left[ OH^{-} \right]\)[/tex] and a high pOH.
Thus, the correct answer is:
[tex]\[ \boxed{\text{a low } \left[ OH^{-} \right] \text{ and a high pOH}} \][/tex]
### Step-by-Step Analysis:
1. Understanding pH and [tex]\( \left[ H^{+} \right] \)[/tex]:
- pH is a measure of the acidity of a solution. It is defined as:
[tex]\[ \text{pH} = -\log \left( \left[ H^{+} \right] \right) \][/tex]
- A high [tex]\(\left[ H^{+} \right]\)[/tex] means a low pH value, indicating an acidic solution.
2. Understanding [tex]\( \left[ OH^{-} \right] \)[/tex] and pOH:
- pOH is a measure of the basicity of a solution. It is defined as:
[tex]\[ \text{pOH} = -\log \left( \left[ OH^{-} \right] \right) \][/tex]
- A high [tex]\(\left[ OH^{-} \right]\)[/tex] means a low pOH value, indicating a basic solution.
3. Relationship Between pH and pOH:
- pH and pOH are related by the equation:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
This means that if the pH is low (indicating high acidity and high [tex]\(\left[ H^{+} \right]\)[/tex]), the pOH must be high (indicating low basicity and low [tex]\(\left[ OH^{-} \right]\)[/tex]).
4. Determining [tex]\( \left[ OH^{-} \right] \)[/tex] from [tex]\( \left[ H^{+} \right] \)[/tex]:
- A high [tex]\(\left[ H^{+} \right]\)[/tex] leads to a low [tex]\(\left[ OH^{-} \right]\)[/tex] because of the inverse relationship in an aqueous solution where:
[tex]\[ \left[ H^{+} \right] \times \left[ OH^{-} \right] = 10^{-14} \][/tex]
- Thus, if [tex]\(\left[ H^{+} \right]\)[/tex] is high, [tex]\(\left[ OH^{-} \right]\)[/tex] has to be low.
### Conclusion:
Based on the relationships and definitions above, if a substance has a high [tex]\(\left[ H^{+} \right]\)[/tex] concentration:
- It will have a low pH.
- Consequently, it will have a high pOH, since [tex]\(\text{pH} + \text{pOH} = 14\)[/tex].
- It will have a low concentration of hydroxide ions, [tex]\(\left[ OH^{-} \right]\)[/tex].
### Answer:
A substance with a high [tex]\(\left[ H^{+} \right]\)[/tex] would likely have:
- A low [tex]\(\left[ OH^{-} \right]\)[/tex] and a high pOH.
Thus, the correct answer is:
[tex]\[ \boxed{\text{a low } \left[ OH^{-} \right] \text{ and a high pOH}} \][/tex]
