Use Table B in your Student Guide to answer the questions about ion concentrations.
A solution with a [tex]$pH =13$[/tex] has approximately how many moles of [tex]$OH ^{-}$[/tex] ions per liter?
How many moles of [tex]$H ^{+}$[/tex] would this same solution have per liter?
(Use the decimal form of your answer.)
A different solution with an [tex]$H +$[/tex] concentration of [tex]$1.0 \times 10^{-4}$[/tex] would have a [tex]$pH =$[/tex]?
Answer (2)
Calculate the pO H using pO H = 14 − p H , which gives pO H = 14 − 13 = 1 .
Calculate the concentration of O H − ions using [ O H − ] = 1 0 − pO H , resulting in [ O H − ] = 1 0 − 1 = 0.1 moles/liter.
Calculate the concentration of H + ions using [ H + ] = 1 0 − p H , resulting in [ H + ] = 1 0 − 13 moles/liter.
Calculate the p H of the second solution using p H = − l o g 10 [ H + ] , resulting in p H = − l o g 10 ( 1.0 × 1 0 − 4 ) = 4 .
0.1 , 1 0 − 13 , 4
Explanation
Problem Analysis We are given a solution with a p H of 13 and asked to find the concentrations of O H − and H + ions in moles per liter. We are also given a different solution with a H + concentration of 1.0 × 1 0 − 4 and asked to find its p H .
Calculating O H − Concentration First, let's find the concentration of O H − ions for the solution with p H = 13 . We know that p H + pO H = 14 , so we can find the pO H of the solution: pO H = 14 − p H = 14 − 13 = 1
Now, we can find the concentration of O H − ions using the formula [ O H − ] = 1 0 − pO H : [ O H − ] = 1 0 − 1 = 0.1 moles/liter
Calculating H + Concentration Next, let's find the concentration of H + ions for the solution with p H = 13 . We can use the formula [ H + ] = 1 0 − p H : [ H + ] = 1 0 − 13 moles/liter
Calculating the p H Finally, let's find the p H of the solution with a H + concentration of 1.0 × 1 0 − 4 . We can use the formula p H = − l o g 10 [ H + ] : p H = − l o g 10 ( 1.0 × 1 0 − 4 ) = − ( − 4 ) = 4
Final Answer Therefore, for the solution with p H = 13 , the concentration of O H − ions is 0.1 moles/liter, the concentration of H + ions is 1 0 − 13 moles/liter, and the p H of the solution with a H + concentration of 1.0 × 1 0 − 4 is 4.
Examples
Understanding pH and ion concentrations is crucial in many real-world applications. For example, in agriculture, knowing the pH of the soil helps farmers choose the right crops and fertilizers. In medicine, maintaining the correct pH balance in the body is essential for various biological processes. In environmental science, monitoring the pH of water sources helps assess pollution levels and protect aquatic life. By mastering these concepts, you can make informed decisions and contribute to a healthier and more sustainable world.
A solution with a pH of 13 has approximately 0.1 moles/liter of [OH^-] ions and 10^{-13} moles/liter of [H^+] ions. A different solution with an [H^+] concentration of 1.0 × 10^{-4} has a pH of 4.
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