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Which of these solutions is the most acidic?

A. [tex]\(\left[ OH^{-} \right] = 2 \times 10^{-12} \, M\)[/tex]

B. [tex]\(\left[ OH^{-} \right] = 3 \times 10^{-3} \, M\)[/tex]

C. [tex]\(\left[ H_{3}O^{+} \right] = 4 \times 10^{-4} \, M\)[/tex]

D. [tex]\(\left[ H_{3}O^{+} \right] = 6 \times 10^{-6} \, M\)[/tex]

Sagot :

GinnyAnswer
To determine which of the given solutions is the most acidic, we need to calculate the pH for each solution. The pH is a measure of the hydrogen ion concentration, and solutions with lower pH values are more acidic.

### Step 1: Calculate the pOH from the given [tex]\( \left[ OH ^{-} \right] \)[/tex] concentrations.

1. For [tex]\( \left[ OH ^{-} \right] = 0.2 \times 10^{-12} \)[/tex] M:
[tex]\[ \text{pOH} = -\log_{10}(0.2 \times 10^{-12}) \approx 12.698970004336019 \][/tex]

2. For [tex]\( \left[ OH ^{-} \right] = 3 \times 10^{-3} \)[/tex] M:
[tex]\[ \text{pOH} = -\log_{10}(3 \times 10^{-3}) \approx 2.5228787452803374 \][/tex]

### Step 2: Calculate the pH from the pOH values.

Using the relationship [tex]\( \text{pH} + \text{pOH} = 14 \)[/tex]:

1. For [tex]\( \text{pOH} = 12.698970004336019 \)[/tex]:
[tex]\[ \text{pH} = 14 - 12.698970004336019 \approx 1.3010299956639813 \][/tex]

2. For [tex]\( \text{pOH} = 2.5228787452803374 \)[/tex]:
[tex]\[ \text{pH} = 14 - 2.5228787452803374 \approx 11.477121254719663 \][/tex]

### Step 3: Calculate the pH from the given [tex]\( \left[ H _3 O ^{+} \right] \)[/tex] concentrations.

1. For [tex]\( \left[ H _3 O ^{+} \right] = 4 \times 10^{-4} \)[/tex] M:
[tex]\[ \text{pH} = -\log_{10}(4 \times 10^{-4}) \approx 3.3979400086720375 \][/tex]

2. For [tex]\( \left[ H _3 O ^{+} \right] = 6 \times 10^{-6} \)[/tex] M:
[tex]\[ \text{pH} = -\log_{10}(6 \times 10^{-6}) \approx 5.221848749616356 \][/tex]

### Step 4: Compare the pH values to determine the most acidic solution.

The pH values we've calculated are:
1. From [tex]\( \left[ OH ^{-} \right] = 0.2 \times 10^{-12} \)[/tex] M: [tex]\( \text{pH} \approx 1.3010299956639813 \)[/tex]
2. From [tex]\( \left[ OH ^{-} \right] = 3 \times 10^{-3} \)[/tex] M: [tex]\( \text{pH} \approx 11.477121254719663 \)[/tex]
3. From [tex]\( \left[ H _3 O ^{+} \right] = 4 \times 10^{-4} \)[/tex] M: [tex]\( \text{pH} \approx 3.3979400086720375 \)[/tex]
4. From [tex]\( \left[ H _3 O ^{+} \right] = 6 \times 10^{-6} \)[/tex] M: [tex]\( \text{pH} \approx 5.221848749616356 \)[/tex]

The most acidic solution is the one with the lowest pH value. Comparing the pH values:

- 1.3010299956639813
- 11.477121254719663
- 3.3979400086720375
- 5.221848749616356

The lowest pH value is [tex]\( 1.3010299956639813 \)[/tex].

### Conclusion

The most acidic solution is the one with [tex]\( \left[ OH ^{-} \right] = 0.2 \times 10^{-12} \)[/tex] M, corresponding to the pH value of approximately [tex]\( 1.3010299956639813 \)[/tex].
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