Question

ph = -logh+
aeen is drinking a beverage that has a ph of 3.3. marien is drinking a beverage that has a ph of 2.7.
about how many times the hydrogen ion concentration of aeen’s drink is the hydrogen ion concentration of marien’s drink? round to the nearest whole number.

Explanation:

Step1: Recall pH formula

The formula for pH is \( \text{pH} = -\log[H^+] \), where \( [H^+] \) is the hydrogen ion concentration. We need to find \( [H^+] \) for both Aeen's and Marien's drinks and then find the ratio.

Step2: Find \( [H^+] \) for Aeen's drink

For Aeen, \( \text{pH} = 3.3 \). Using the formula \( 3.3 = -\log[H^+]_{Aeen} \), we can rewrite it as \( \log[H^+]_{Aeen} = -3.3 \). Converting from logarithmic to exponential form (base 10), we get \( [H^+]_{Aeen} = 10^{-3.3} \).

Step3: Find \( [H^+] \) for Marien's drink

For Marien, \( \text{pH} = 2.7 \). Using the formula \( 2.7 = -\log[H^+]_{Marien} \), we rewrite it as \( \log[H^+]_{Marien} = -2.7 \). Converting to exponential form, \( [H^+]_{Marien} = 10^{-2.7} \).

Step4: Find the ratio of \( [H^+]_{Aeen} \) to \( [H^+]_{Marien} \)

The ratio \( \frac{[H^+]_{Aeen}}{[H^+]_{Marien}} = \frac{10^{-3.3}}{10^{-2.7}} \). Using the property of exponents \( \frac{a^m}{a^n} = a^{m - n} \), this becomes \( 10^{-3.3 + 2.7} = 10^{-0.6} \).

Step5: Calculate \( 10^{-0.6} \)

We know that \( 10^{-0.6} \approx \frac{1}{10^{0.6}} \). Calculating \( 10^{0.6} \approx 3.981 \), so \( \frac{1}{3.981} \approx 0.251 \). Wait, no, wait. Wait, the question is "how many times the hydrogen ion concentration of Aeen’s drink is the hydrogen ion concentration of Marien’s drink", so it's \( \frac{[H^+]_{Marien}}{[H^+]_{Aeen}} \). Oh, I made a mistake earlier. Let's correct that.

So \( \frac{[H^+]_{Marien}}{[H^+]_{Aeen}} = \frac{10^{-2.7}}{10^{-3.3}} = 10^{-2.7 + 3.3} = 10^{0.6} \). Now, \( 10^{0.6} \approx 3.981 \), which rounds to 4.

Answer:

4