Question

13 multiple choice 7 points in chemistry, logarithms are key to calculating the ph of a solution. in the equation below, h+ is the hydrogen ion concentration. calculate the hydrogen ion concentration of a substance with a ph of 2.6. give the answer in scientific notation. (\text{ph} = -log(\text{h}^+)) (\text{h}^+ approx 2.5 \times 10^{-3}) (\text{h}^+ approx 2.5 \times 10^{-2}) (\text{h}^+ approx 2.5 \times 10^{3}) (\text{h}^+ approx 2.5 \times 10^{2})

Explanation:

Step1: Start with the pH formula

We know the formula for pH is \( \text{pH} = -\log(H^+) \). We are given that \( \text{pH} = 2.6 \), so we can substitute this value into the formula:
\( 2.6 = -\log(H^+) \)

Step2: Isolate the logarithm term

Multiply both sides of the equation by -1 to get:
\( -2.6 = \log(H^+) \)

Step3: Convert from logarithmic to exponential form

Recall that if \( \log_b(x) = y \), then \( x = b^y \). In the case of common logarithms (base 10), this means \( H^+ = 10^{-2.6} \)

Step4: Calculate \( 10^{-2.6} \)

We can rewrite \( -2.6 \) as \( -3 + 0.4 \), so \( 10^{-2.6} = 10^{-3 + 0.4} = 10^{0.4} \times 10^{-3} \)
We know that \( 10^{0.4} \approx 2.5 \) (since \( \log(2.5) \approx 0.4 \) because \( 10^{0.4} \approx 2.5 \))
So \( 10^{-2.6} \approx 2.5 \times 10^{-3} \)

Answer:

\( H^+ \approx 2.5 \times 10^{-3} \) (corresponding to the first option: \( H^+ \approx 2.5 \times 10^{-3} \))