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The acidity of a solution is measured by its pH . If \( \left[\mathrm{H}^{+}\right] \)represents the concentration of hydrogen ions (in moles/liter) in the solution, the pH is defined by \( \mathrm{pH}=-\log \left[\mathrm{H}^{+}\right] \) Based on careful measurements and calculations, a chemist examines two solutions and asserts: "The hydrogen ion concentration of Solution A is 6.22 times greater than the hydrogen ion concentration of Solution B." If the pH of solution B is 3.3 , determine the pH of Solution A. Report your answer to one decimal place. Solution A has pH equal to Number

Ask by Fitzgerald Lawson. in the United States
Mar 20,2025

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The pH of Solution A is 2.5.

Solution

Given that the pH of Solution B is 3.3, we can use the formula \( \mathrm{pH} = -\log \left[\mathrm{H}^{+}\right] \) to find the concentration of hydrogen ions in Solution B. Let's denote the concentration of hydrogen ions in Solution B as \( \left[\mathrm{H}^{+}\right]_{B} \). We have: \[ \mathrm{pH}_{B} = -\log \left[\mathrm{H}^{+}\right]_{B} \] \[ 3.3 = -\log \left[\mathrm{H}^{+}\right]_{B} \] To find the concentration of hydrogen ions in Solution B, we can rearrange the equation: \[ \left[\mathrm{H}^{+}\right]_{B} = 10^{-3.3} \] Now, we are given that the hydrogen ion concentration of Solution A is 6.22 times greater than the hydrogen ion concentration of Solution B. Let's denote the concentration of hydrogen ions in Solution A as \( \left[\mathrm{H}^{+}\right]_{A} \). We have: \[ \left[\mathrm{H}^{+}\right]_{A} = 6.22 \times \left[\mathrm{H}^{+}\right]_{B} \] Substitute the value of \( \left[\mathrm{H}^{+}\right]_{B} \) into the equation: \[ \left[\mathrm{H}^{+}\right]_{A} = 6.22 \times 10^{-3.3} \] Now, we can find the pH of Solution A using the formula \( \mathrm{pH} = -\log \left[\mathrm{H}^{+}\right] \): \[ \mathrm{pH}_{A} = -\log \left(6.22 \times 10^{-3.3}\right) \] Let's calculate the pH of Solution A. The pH of Solution A is approximately 2.5.

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To find the pH of Solution A, we start by determining the hydrogen ion concentration of Solution B. The formula for pH is given by: \[ \text{pH} = -\log \left[\mathrm{H}^{+}\right] \] Given that the pH of Solution B is 3.3, we can calculate \(\left[\mathrm{H}^{+}\right]_B\): \[ \left[\mathrm{H}^{+}\right]_B = 10^{-\text{pH}} = 10^{-3.3} \approx 0.0005012 \, \text{moles/liter} \] According to the chemist, the hydrogen ion concentration of Solution A is 6.22 times greater than that of Solution B: \[ \left[\mathrm{H}^{+}\right]_A = 6.22 \times \left[\mathrm{H}^{+}\right]_B = 6.22 \times 0.0005012 \approx 0.003123 \, \text{moles/liter} \] Now we can find the pH of Solution A: \[ \text{pH}_A = -\log \left[\mathrm{H}^{+}\right]_A = -\log(0.003123) \approx 2.5 \] So, the pH of Solution A is approximately **2.5**.

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Chemistry Singapore Mar 20, 2025

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