Question

pH of soft drink is 3.6. Calculate the concentration of hydrogen ions in it.

• A. $2.51 \times 10^{-4}\ \text{M}$
• B. $2.3 \times 10^{-3}\ \text{M}$
• C. $2.0 \times 10^{-3}\ \text{M}$
• D. $2.81 \times 10^{-4}\ \text{M}$

Hint:

When dealing with a fractional pH like $3.6$, round it up to the next highest integer to find your exponent power ($10^{-4}$). Since the value $3.6$ is past the halfway mark to 4, the prefix multiplier has to be a small value between 1 and 5, helping you instantly pick $2.51 \times 10^{-4}\ \text{M}$ over other choices!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem provides the pH value of a soft drink sample as 3.6. We are required to calculate the exact molar concentration of hydrogen ions ($[\text{H}^+]$) corresponding to this value.

Step 2: Key Formula or Approach:
By standard definition, pH is the negative logarithm to the base 10 of the hydrogen ion concentration:
$$\text{pH} = -\log_{10}[\text{H}^+] \implies [\text{H}^+] = 10^{-\text{pH}} = \text{Antilog}(-\text{pH})$$

Step 3: Detailed Explanation:
Given that $\text{pH} = 3.6$, we set up our concentration expression:
$$[\text{H}^+] = 10^{-3.6}$$ To evaluate a negative fractional exponent using standard antilog logarithm procedures, we split the negative value into an integer component and a positive decimal part by subtracting and adding 1:
$$-3.6 = -3 - 0.6 = (-3 - 1) + (1 - 0.6) = -4 + 0.4 = \bar{4}.4$$ Now, we find the antilogarithm of $\bar{4}.4$:
$$[\text{H}^+] = \text{Antilog}(\bar{4}.4) = \text{Antilog}(0.4) \times 10^{-4}$$ We know that $\log_{10}(2) \approx 0.301$ and $\log_{10}(3) \approx 0.477$. The antilog of $0.4$ must fall squarely between 2 and 3, calculating out precisely to $2.512$.
$$[\text{H}^+] = 2.51 \times 10^{-4}\ \text{M}$$ This matches option (A).

Step 4: Final Answer:
The concentration of hydrogen ions is $2.51 \times 10^{-4}\ \text{M}$, which corresponds to option (A).