Question

Find the \(\mathrm{pH}\) of solutions with the following \(\left[\mathrm{H}^{+}\right]\). Classify each as acidic or basic. (a) \(2.7 \times 10^{-3} \mathrm{M}\) (b) \(1.5 \mathrm{M}\) (c) \(1.45 \times 10^{-13} \mathrm{M}\) (d) \(6.4 \times 10^{-9} \mathrm{M}\)

Short answer

Solution: (a) Solution a has a \(\mathrm{pH}\) value of approximately 2.57 and is classified as acidic. (b) Solution b has a \(\mathrm{pH}\) value of approximately -0.18 and is classified as acidic. (c) Solution c has a \(\mathrm{pH}\) value of approximately 12.84 and is classified as basic. (d) Solution d has a \(\mathrm{pH}\) value of approximately 8.19 and is classified as basic.

Step-by-step solution

Find the pH of each solution

To find the pH of each solution, we'll use the formula for \(\mathrm{pH}\) as mentioned before: \(\mathrm{pH} = -\log_{10}\left[\mathrm{H}^{+}\right]\) (a) For the first solution, the concentration of hydrogen ions is \(2.7 \times 10^{-3} M\). Calculate its pH: \(\mathrm{pH}_a = -\log_{10}(2.7 \times 10^{-3})\) (b) For the second solution, the concentration of hydrogen ions is \(1.5M\). Calculate its pH: \(\mathrm{pH}_b = -\log_{10}(1.5)\) (c) For the third solution, the concentration of hydrogen ions is \(1.45 \times 10^{-13} M\). Calculate its pH: \(\mathrm{pH}_c = -\log_{10}(1.45 \times 10^{-13})\) (d) For the fourth solution, the concentration of hydrogen ions is \(6.4 \times 10^{-9} M\). Calculate its pH: \(\mathrm{pH}_d = -\log_{10}(6.4 \times 10^{-9})\)

Evaluate the pH values

Calculate the \(\mathrm{pH}\) values for each of the solutions: (a) \(\mathrm{pH}_a = -\log_{10}(2.7 \times 10^{-3}) \approx 2.57\) (b) \(\mathrm{pH}_b = -\log_{10}(1.5) \approx -0.18\) (c) \(\mathrm{pH}_c = -\log_{10}(1.45 \times 10^{-13}) \approx 12.84\) (d) \(\mathrm{pH}_d = -\log_{10}(6.4 \times 10^{-9}) \approx 8.19\)

Classify each solution as acidic, basic, or neutral

Now that we have our \(\mathrm{pH}\) values, we can classify the solutions as acidic, basic, or neutral based on their \(\mathrm{pH}\): (a) \(2.57 < 7\): The first solution is acidic. (b) \(-0.18 < 7\): The second solution is acidic. (c) \(12.84 > 7\): The third solution is basic. (d) \(8.19 > 7\): The fourth solution is basic.