The concentration of hydronium ions in a cup of black coffee is `1.3 xx 10^(-5)` M. What will be the pH of the coffee?

Options

A. 4.89
B. 3.89
C. 2.2
D. None of these

Answer

To find the pH of the coffee given the concentration of hydronium ions \([H_3O^+]\) is \(1.3 \times 10^{-5}\) 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 in moles per liter.

### Step 2: Substitute the given concentration into the formula
We substitute the given concentration of hydronium ions 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:
\[ \text{pH} = -\log(1.3) - \log(10^{-5}) \]
Using the property of logarithms, \(\log(10^{-5}) = -5\):
\[ \text{pH} = -\log(1.3) + 5 \]

### Step 4: Find \(-\log(1.3)\)
Using a calculator or logarithm table, we find:
\[ \log(1.3) \approx 0.1139 \]
Thus,
\[ -\log(1.3) \approx -0.1139 \]

### Step 5: Combine the results
Now, we can substitute back into our pH equation:
\[ \text{pH} = -0.1139 + 5 \approx 4.8861 \]

### Step 6: Round the pH value
Rounding this to two decimal places, we get:
\[ \text{pH} \approx 4.89 \]

### Final Answer
The pH of the coffee is approximately **4.89**.

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