A solution has a pH=9. It is 1000 times more basic than the original solution. What was the pH of the original solution?

Options

A. 12
B. 6
C. 9
D. 10

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the given information
We are given that the pH of the current solution is 9, and it is stated to be 1000 times more basic than the original solution.

### Step 2: Calculate the pOH of the current solution
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
Substituting the given pH:
\[ 9 + \text{pOH} = 14 \]
From this, we can find pOH:
\[ \text{pOH} = 14 - 9 = 5 \]

### Step 3: Calculate the concentration of OH⁻ ions in the current solution
Using the formula for pOH:
\[ \text{pOH} = -\log[\text{OH}⁻] \]
Substituting the pOH value:
\[ 5 = -\log[\text{OH}⁻] \]
To find the concentration of OH⁻ ions, we can rearrange this equation:
\[ [\text{OH}⁻] = 10^{-5} \text{ M} \]

### Step 4: Determine the concentration of OH⁻ ions in the original solution
Since the current solution is 1000 times more basic than the original solution, the concentration of OH⁻ ions in the original solution will be:
\[ [\text{OH}⁻]_{\text{original}} = \frac{[\text{OH}⁻]_{\text{current}}}{1000} = \frac{10^{-5}}{1000} = 10^{-8} \text{ M} \]

### Step 5: Calculate the pOH of the original solution
Using the pOH formula again:
\[ \text{pOH} = -\log[\text{OH}⁻] \]
Substituting the concentration of OH⁻ ions:
\[ \text{pOH} = -\log(10^{-8}) = 8 \]

### Step 6: Calculate the pH of the original solution
Now we can find the pH of the original solution using the relationship:
\[ \text{pH} + \text{pOH} = 14 \]
Substituting the pOH we found:
\[ \text{pH} + 8 = 14 \]
Thus, we can find pH:
\[ \text{pH} = 14 - 8 = 6 \]

### Final Answer
The pH of the original solution is **6**.

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