The concentration of hydronium ions in a cup of black coffee is `1.3xx10^(-5)` M. Find the pH of the coffee. Is this coffee acidic or alkaline ?

Answer

To find the pH of the coffee given the concentration of hydronium ions \([H_3O^+]\) as \(1.3 \times 10^{-5}\) M, we can follow these steps:

### Step 1: Understand the pH Formula
The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log[H_3O^+] \]
where \([H_3O^+]\) is the concentration of hydronium ions.

### Step 2: Substitute the Given Concentration
We have the concentration of hydronium ions:
\[ [H_3O^+] = 1.3 \times 10^{-5} \, \text{M} \]
Now, we substitute this value into the pH formula:
\[ \text{pH} = -\log(1.3 \times 10^{-5}) \]

### Step 3: Calculate the Logarithm
To calculate \(-\log(1.3 \times 10^{-5})\), we can break it down:
\[ \text{pH} = -\log(1.3) - \log(10^{-5}) \]
We know that \(-\log(10^{-5}) = 5\).

Now, we need to find \(-\log(1.3)\). Using a calculator, we find:
\[ -\log(1.3) \approx -0.113 \]

### Step 4: Combine the Results
Now we combine the results:
\[ \text{pH} = -0.113 + 5 \approx 4.887 \]
Rounding this gives us:
\[ \text{pH} \approx 4.89 \]

### Step 5: Determine if the Coffee is Acidic or Alkaline
The pH scale ranges from 0 to 14, where:
- A pH less than 7 indicates an acidic solution.
- A pH equal to 7 indicates a neutral solution.
- A pH greater than 7 indicates an alkaline (basic) solution.

Since the calculated pH of the coffee is approximately 4.89, which is less than 7, we conclude that:
- The coffee is acidic.

### Final Answer
The pH of the coffee is approximately **4.89**, and it is **acidic**.

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