one brand of vinegar has a ph of 4.5. another brand has a ph of 5.0. the equation for the ph of a substance is $\text{ph} = -\log\text{h}^+$, where $\text{h}^+$ is the concentration of hydrogen ions. what is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

$2.2 \times 10^{-5}$
$3.2 \times 10^{-5}$
$3.2 \times 10^1$
$6.8 \times 10^4$

Question

one brand of vinegar has a ph of 4.5. another brand has a ph of 5.0. the equation for the ph of a substance is \$\text{ph} = -\log\text{h}^+\$, where \$\text{h}^+\$ is the concentration of hydrogen ions. what is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

\$2.2 \times 10^{-5}\$
\$3.2 \times 10^{-5}\$
\$3.2 \times 10^1\$
\$6.8 \times 10^4\$

$2.2 \times 10^{-5}$
$3.2 \times 10^{-5}$
$3.2 \times 10^1$
$6.8 \times 10^4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "pH Scale Calculations" ], "new_concepts": [], "current_concepts": [ "pH Scale Calculations", "Logarithmic Functions" ] } ## Calculate hydrogen ion concentrations Using the *pH Scale Calculations* knowledge point $$ \begin{aligned} \text{pH} &= -\log[\text{H}^+] \ [\text{H}^+] &= 10^{-\text{pH}} \ [\text{H}^+]_1 &= 10^{-4.5} \approx 3.162 \times 10^{-5} \ [\text{H}^+]_2 &= 10^{-5.0} = 1.000 \times 10^{-5} \end{aligned} $$ ## Find the difference in concentration Using the *pH Scale Calculations* knowledge point $$ \begin{aligned} \Delta [\text{H}^+] &= [\text{H}^+]_1 - [\text{H}^+]_2 \ \Delta [\text{H}^+] &= 3.162 \times 10^{-5} - 1.000 \times 10^{-5} \ \Delta [\text{H}^+] &= 2.162 \times 10^{-5} \approx 2.2 \times 10^{-5} \end{aligned} $$

(A) $2.2 \times 10^{-5}$

(B) $3.2 \times 10^{-5}$

(C) $3.2 \times 10^{1}$

(D) $6.8 \times 10^{4}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "pH Scale Calculations" ] }

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Question

Explanation:

Calculate hydrogen ion concentrations

Find the difference in concentration

Answer: