Chemistry: pH and pOH Calculations Organizer for 9th - Higher Ed ... - Free Printable
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Step-by-step solution for: Chemistry: pH and pOH Calculations Organizer for 9th - Higher Ed ...
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Show Answer Key & Explanations
Step-by-step solution for: Chemistry: pH and pOH Calculations Organizer for 9th - Higher Ed ...
To solve this problem, we need to fill in the missing values in the table using the relationships between pH, pOH, $[H^+]$, and $[OH^-]$.
Here are the key formulas you need:
1. $pH + pOH = 14$ (at $25^\circ C$)
2. $[H^+] = 10^{-pH}$
3. $[OH^-] = 10^{-pOH}$
4. $[H^+] \times [OH^-] = 1.0 \times 10^{-14}$
We will go row by row to calculate the missing numbers. I will round pH/pOH to two decimal places and concentrations to two significant figures, which is standard for these problems.
* Given: $pH = 5.70$
* Find pOH: $14 - 5.70 = 8.30$
* Find $[H^+]$: $10^{-5.70} \approx 2.0 \times 10^{-6} \text{ M}$
* Find $[OH^-]$: $10^{-8.30} \approx 5.0 \times 10^{-9} \text{ M}$
* Given: $[H^+] = 1.80 \times 10^{-5} \text{ M}$
* Find pH: $-\log(1.80 \times 10^{-5}) \approx 4.74$
* Find pOH: $14 - 4.74 = 9.26$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{1.80 \times 10^{-5}} \approx 5.6 \times 10^{-10} \text{ M}$
* Given: $pOH = 9.18$
* Find pH: $14 - 9.18 = 4.82$
* Find $[H^+]$: $10^{-4.82} \approx 1.5 \times 10^{-5} \text{ M}$
* Find $[OH^-]$: $10^{-9.18} \approx 6.6 \times 10^{-10} \text{ M}$
* Given: $[OH^-] = 4.80 \times 10^{-10} \text{ M}$
* Find pOH: $-\log(4.80 \times 10^{-10}) \approx 9.32$
* Find pH: $14 - 9.32 = 4.68$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{4.80 \times 10^{-10}} \approx 2.1 \times 10^{-5} \text{ M}$
* Given: $pH = 6.80$
* Find pOH: $14 - 6.80 = 7.20$
* Find $[H^+]$: $10^{-6.80} \approx 1.6 \times 10^{-7} \text{ M}$
* Find $[OH^-]$: $10^{-7.20} \approx 6.3 \times 10^{-8} \text{ M}$
* Given: $[H^+] = 8.40 \times 10^{-10} \text{ M}$
* Find pH: $-\log(8.40 \times 10^{-10}) \approx 9.08$
* Find pOH: $14 - 9.08 = 4.92$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{8.40 \times 10^{-10}} \approx 1.2 \times 10^{-5} \text{ M}$
* Given: $pOH = 2.14$
* Find pH: $14 - 2.14 = 11.86$
* Find $[H^+]$: $10^{-11.86} \approx 1.4 \times 10^{-12} \text{ M}$
* Find $[OH^-]$: $10^{-2.14} \approx 7.2 \times 10^{-3} \text{ M}$
* Given: $[OH^-] = 5.10 \times 10^{-4} \text{ M}$
* Find pOH: $-\log(5.10 \times 10^{-4}) \approx 3.29$
* Find pH: $14 - 3.29 = 10.71$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{5.10 \times 10^{-4}} \approx 2.0 \times 10^{-11} \text{ M}$
* Given: $pH = 10.81$
* Find pOH: $14 - 10.81 = 3.19$
* Find $[H^+]$: $10^{-10.81} \approx 1.5 \times 10^{-11} \text{ M}$
* Find $[OH^-]$: $10^{-3.19} \approx 6.5 \times 10^{-4} \text{ M}$
* Given: $[H^+] = 3.20 \times 10^{-12} \text{ M}$
* Find pH: $-\log(3.20 \times 10^{-12}) \approx 11.49$
* Find pOH: $14 - 11.49 = 2.51$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{3.20 \times 10^{-12}} \approx 3.1 \times 10^{-3} \text{ M}$
* Given: $pOH = 8.64$
* Find pH: $14 - 8.64 = 5.36$
* Find $[H^+]$: $10^{-5.36} \approx 4.4 \times 10^{-6} \text{ M}$
* Find $[OH^-]$: $10^{-8.64} \approx 2.3 \times 10^{-9} \text{ M}$
* Given: $[OH^-] = 1.00 \times 10^{-7} \text{ M}$
* Find pOH: $-\log(1.00 \times 10^{-7}) = 7.00$
* Find pH: $14 - 7.00 = 7.00$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{1.00 \times 10^{-7}} = 1.0 \times 10^{-7} \text{ M}$
* Given: $pH = 1.00$
* Find pOH: $14 - 1.00 = 13.00$
* Find $[H^+]$: $10^{-1.00} = 1.0 \times 10^{-1} \text{ M}$ (or 0.10 M)
* Find $[OH^-]$: $10^{-13.00} = 1.0 \times 10^{-13} \text{ M}$
* Given: $[H^+] = 4.70 \times 10^{-13} \text{ M}$
* Find pH: $-\log(4.70 \times 10^{-13}) \approx 12.33$
* Find pOH: $14 - 12.33 = 1.67$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{4.70 \times 10^{-13}} \approx 2.1 \times 10^{-2} \text{ M}$
* Given: $pOH = 11.20$
* Find pH: $14 - 11.20 = 2.80$
* Find $[H^+]$: $10^{-2.80} \approx 1.6 \times 10^{-3} \text{ M}$
* Find $[OH^-]$: $10^{-11.20} \approx 6.3 \times 10^{-12} \text{ M}$
* Given: $[OH^-] = 1.10 \times 10^{-11} \text{ M}$
* Find pOH: $-\log(1.10 \times 10^{-11}) \approx 10.96$
* Find pH: $14 - 10.96 = 3.04$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{1.10 \times 10^{-11}} \approx 9.1 \times 10^{-4} \text{ M}$
* Given: $pH = 11.46$
* Find pOH: $14 - 11.46 = 2.54$
* Find $[H^+]$: $10^{-11.46} \approx 3.5 \times 10^{-12} \text{ M}$
* Find $[OH^-]$: $10^{-2.54} \approx 2.9 \times 10^{-3} \text{ M}$
* Given: $[H^+] = 8.50 \times 10^{-3} \text{ M}$
* Find pH: $-\log(8.50 \times 10^{-3}) \approx 2.07$
* Find pOH: $14 - 2.07 = 11.93$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{8.50 \times 10^{-3}} \approx 1.2 \times 10^{-12} \text{ M}$
* Given: $pOH = 12.26$
* Find pH: $14 - 12.26 = 1.74$
* Find $[H^+]$: $10^{-1.74} \approx 1.8 \times 10^{-2} \text{ M}$
* Find $[OH^-]$: $10^{-12.26} \approx 5.5 \times 10^{-13} \text{ M}$
* Given: $[OH^-] = 5.90 \times 10^{-2} \text{ M}$
* Find pOH: $-\log(5.90 \times 10^{-2}) \approx 1.23$
* Find pH: $14 - 1.23 = 12.77$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{5.90 \times 10^{-2}} \approx 1.7 \times 10^{-13} \text{ M}$
Final Answer:
Here are the completed values for the table rows:
1. pH=5.70 | pOH=8.30 | $[H^+]=2.0 \times 10^{-6}$ | $[OH^-]=5.0 \times 10^{-9}$
2. pH=4.74 | pOH=9.26 | $[H^+]=1.80 \times 10^{-5}$ | $[OH^-]=5.6 \times 10^{-10}$
3. pH=4.82 | pOH=9.18 | $[H^+]=1.5 \times 10^{-5}$ | $[OH^-]=6.6 \times 10^{-10}$
4. pH=4.68 | pOH=9.32 | $[H^+]=2.1 \times 10^{-5}$ | $[OH^-]=4.80 \times 10^{-10}$
5. pH=6.80 | pOH=7.20 | $[H^+]=1.6 \times 10^{-7}$ | $[OH^-]=6.3 \times 10^{-8}$
6. pH=9.08 | pOH=4.92 | $[H^+]=8.40 \times 10^{-10}$ | $[OH^-]=1.2 \times 10^{-5}$
7. pH=11.86 | pOH=2.14 | $[H^+]=1.4 \times 10^{-12}$ | $[OH^-]=7.2 \times 10^{-3}$
8. pH=10.71 | pOH=3.29 | $[H^+]=2.0 \times 10^{-11}$ | $[OH^-]=5.10 \times 10^{-4}$
9. pH=10.81 | pOH=3.19 | $[H^+]=1.5 \times 10^{-11}$ | $[OH^-]=6.5 \times 10^{-4}$
10. pH=11.49 | pOH=2.51 | $[H^+]=3.20 \times 10^{-12}$ | $[OH^-]=3.1 \times 10^{-3}$
11. pH=5.36 | pOH=8.64 | $[H^+]=4.4 \times 10^{-6}$ | $[OH^-]=2.3 \times 10^{-9}$
12. pH=7.00 | pOH=7.00 | $[H^+]=1.0 \times 10^{-7}$ | $[OH^-]=1.00 \times 10^{-7}$
13. pH=1.00 | pOH=13.00 | $[H^+]=1.0 \times 10^{-1}$ | $[OH^-]=1.0 \times 10^{-13}$
14. pH=12.33 | pOH=1.67 | $[H^+]=4.70 \times 10^{-13}$ | $[OH^-]=2.1 \times 10^{-2}$
15. pH=2.80 | pOH=11.20 | $[H^+]=1.6 \times 10^{-3}$ | $[OH^-]=6.3 \times 10^{-12}$
16. pH=3.04 | pOH=10.96 | $[H^+]=9.1 \times 10^{-4}$ | $[OH^-]=1.10 \times 10^{-11}$
17. pH=11.46 | pOH=2.54 | $[H^+]=3.5 \times 10^{-12}$ | $[OH^-]=2.9 \times 10^{-3}$
18. pH=2.07 | pOH=11.93 | $[H^+]=8.50 \times 10^{-3}$ | $[OH^-]=1.2 \times 10^{-12}$
19. pH=1.74 | pOH=12.26 | $[H^+]=1.8 \times 10^{-2}$ | $[OH^-]=5.5 \times 10^{-13}$
20. pH=12.77 | pOH=1.23 | $[H^+]=1.7 \times 10^{-13}$ | $[OH^-]=5.90 \times 10^{-2}$
Here are the key formulas you need:
1. $pH + pOH = 14$ (at $25^\circ C$)
2. $[H^+] = 10^{-pH}$
3. $[OH^-] = 10^{-pOH}$
4. $[H^+] \times [OH^-] = 1.0 \times 10^{-14}$
We will go row by row to calculate the missing numbers. I will round pH/pOH to two decimal places and concentrations to two significant figures, which is standard for these problems.
Row 1
* Given: $pH = 5.70$
* Find pOH: $14 - 5.70 = 8.30$
* Find $[H^+]$: $10^{-5.70} \approx 2.0 \times 10^{-6} \text{ M}$
* Find $[OH^-]$: $10^{-8.30} \approx 5.0 \times 10^{-9} \text{ M}$
Row 2
* Given: $[H^+] = 1.80 \times 10^{-5} \text{ M}$
* Find pH: $-\log(1.80 \times 10^{-5}) \approx 4.74$
* Find pOH: $14 - 4.74 = 9.26$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{1.80 \times 10^{-5}} \approx 5.6 \times 10^{-10} \text{ M}$
Row 3
* Given: $pOH = 9.18$
* Find pH: $14 - 9.18 = 4.82$
* Find $[H^+]$: $10^{-4.82} \approx 1.5 \times 10^{-5} \text{ M}$
* Find $[OH^-]$: $10^{-9.18} \approx 6.6 \times 10^{-10} \text{ M}$
Row 4
* Given: $[OH^-] = 4.80 \times 10^{-10} \text{ M}$
* Find pOH: $-\log(4.80 \times 10^{-10}) \approx 9.32$
* Find pH: $14 - 9.32 = 4.68$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{4.80 \times 10^{-10}} \approx 2.1 \times 10^{-5} \text{ M}$
Row 5
* Given: $pH = 6.80$
* Find pOH: $14 - 6.80 = 7.20$
* Find $[H^+]$: $10^{-6.80} \approx 1.6 \times 10^{-7} \text{ M}$
* Find $[OH^-]$: $10^{-7.20} \approx 6.3 \times 10^{-8} \text{ M}$
Row 6
* Given: $[H^+] = 8.40 \times 10^{-10} \text{ M}$
* Find pH: $-\log(8.40 \times 10^{-10}) \approx 9.08$
* Find pOH: $14 - 9.08 = 4.92$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{8.40 \times 10^{-10}} \approx 1.2 \times 10^{-5} \text{ M}$
Row 7
* Given: $pOH = 2.14$
* Find pH: $14 - 2.14 = 11.86$
* Find $[H^+]$: $10^{-11.86} \approx 1.4 \times 10^{-12} \text{ M}$
* Find $[OH^-]$: $10^{-2.14} \approx 7.2 \times 10^{-3} \text{ M}$
Row 8
* Given: $[OH^-] = 5.10 \times 10^{-4} \text{ M}$
* Find pOH: $-\log(5.10 \times 10^{-4}) \approx 3.29$
* Find pH: $14 - 3.29 = 10.71$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{5.10 \times 10^{-4}} \approx 2.0 \times 10^{-11} \text{ M}$
Row 9
* Given: $pH = 10.81$
* Find pOH: $14 - 10.81 = 3.19$
* Find $[H^+]$: $10^{-10.81} \approx 1.5 \times 10^{-11} \text{ M}$
* Find $[OH^-]$: $10^{-3.19} \approx 6.5 \times 10^{-4} \text{ M}$
Row 10
* Given: $[H^+] = 3.20 \times 10^{-12} \text{ M}$
* Find pH: $-\log(3.20 \times 10^{-12}) \approx 11.49$
* Find pOH: $14 - 11.49 = 2.51$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{3.20 \times 10^{-12}} \approx 3.1 \times 10^{-3} \text{ M}$
Row 11
* Given: $pOH = 8.64$
* Find pH: $14 - 8.64 = 5.36$
* Find $[H^+]$: $10^{-5.36} \approx 4.4 \times 10^{-6} \text{ M}$
* Find $[OH^-]$: $10^{-8.64} \approx 2.3 \times 10^{-9} \text{ M}$
Row 12
* Given: $[OH^-] = 1.00 \times 10^{-7} \text{ M}$
* Find pOH: $-\log(1.00 \times 10^{-7}) = 7.00$
* Find pH: $14 - 7.00 = 7.00$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{1.00 \times 10^{-7}} = 1.0 \times 10^{-7} \text{ M}$
Row 13
* Given: $pH = 1.00$
* Find pOH: $14 - 1.00 = 13.00$
* Find $[H^+]$: $10^{-1.00} = 1.0 \times 10^{-1} \text{ M}$ (or 0.10 M)
* Find $[OH^-]$: $10^{-13.00} = 1.0 \times 10^{-13} \text{ M}$
Row 14
* Given: $[H^+] = 4.70 \times 10^{-13} \text{ M}$
* Find pH: $-\log(4.70 \times 10^{-13}) \approx 12.33$
* Find pOH: $14 - 12.33 = 1.67$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{4.70 \times 10^{-13}} \approx 2.1 \times 10^{-2} \text{ M}$
Row 15
* Given: $pOH = 11.20$
* Find pH: $14 - 11.20 = 2.80$
* Find $[H^+]$: $10^{-2.80} \approx 1.6 \times 10^{-3} \text{ M}$
* Find $[OH^-]$: $10^{-11.20} \approx 6.3 \times 10^{-12} \text{ M}$
Row 16
* Given: $[OH^-] = 1.10 \times 10^{-11} \text{ M}$
* Find pOH: $-\log(1.10 \times 10^{-11}) \approx 10.96$
* Find pH: $14 - 10.96 = 3.04$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{1.10 \times 10^{-11}} \approx 9.1 \times 10^{-4} \text{ M}$
Row 17
* Given: $pH = 11.46$
* Find pOH: $14 - 11.46 = 2.54$
* Find $[H^+]$: $10^{-11.46} \approx 3.5 \times 10^{-12} \text{ M}$
* Find $[OH^-]$: $10^{-2.54} \approx 2.9 \times 10^{-3} \text{ M}$
Row 18
* Given: $[H^+] = 8.50 \times 10^{-3} \text{ M}$
* Find pH: $-\log(8.50 \times 10^{-3}) \approx 2.07$
* Find pOH: $14 - 2.07 = 11.93$
* Find $[OH^-]$: $\frac{1.0 \times 10^{-14}}{8.50 \times 10^{-3}} \approx 1.2 \times 10^{-12} \text{ M}$
Row 19
* Given: $pOH = 12.26$
* Find pH: $14 - 12.26 = 1.74$
* Find $[H^+]$: $10^{-1.74} \approx 1.8 \times 10^{-2} \text{ M}$
* Find $[OH^-]$: $10^{-12.26} \approx 5.5 \times 10^{-13} \text{ M}$
Row 20
* Given: $[OH^-] = 5.90 \times 10^{-2} \text{ M}$
* Find pOH: $-\log(5.90 \times 10^{-2}) \approx 1.23$
* Find pH: $14 - 1.23 = 12.77$
* Find $[H^+]$: $\frac{1.0 \times 10^{-14}}{5.90 \times 10^{-2}} \approx 1.7 \times 10^{-13} \text{ M}$
Final Answer:
Here are the completed values for the table rows:
1. pH=5.70 | pOH=8.30 | $[H^+]=2.0 \times 10^{-6}$ | $[OH^-]=5.0 \times 10^{-9}$
2. pH=4.74 | pOH=9.26 | $[H^+]=1.80 \times 10^{-5}$ | $[OH^-]=5.6 \times 10^{-10}$
3. pH=4.82 | pOH=9.18 | $[H^+]=1.5 \times 10^{-5}$ | $[OH^-]=6.6 \times 10^{-10}$
4. pH=4.68 | pOH=9.32 | $[H^+]=2.1 \times 10^{-5}$ | $[OH^-]=4.80 \times 10^{-10}$
5. pH=6.80 | pOH=7.20 | $[H^+]=1.6 \times 10^{-7}$ | $[OH^-]=6.3 \times 10^{-8}$
6. pH=9.08 | pOH=4.92 | $[H^+]=8.40 \times 10^{-10}$ | $[OH^-]=1.2 \times 10^{-5}$
7. pH=11.86 | pOH=2.14 | $[H^+]=1.4 \times 10^{-12}$ | $[OH^-]=7.2 \times 10^{-3}$
8. pH=10.71 | pOH=3.29 | $[H^+]=2.0 \times 10^{-11}$ | $[OH^-]=5.10 \times 10^{-4}$
9. pH=10.81 | pOH=3.19 | $[H^+]=1.5 \times 10^{-11}$ | $[OH^-]=6.5 \times 10^{-4}$
10. pH=11.49 | pOH=2.51 | $[H^+]=3.20 \times 10^{-12}$ | $[OH^-]=3.1 \times 10^{-3}$
11. pH=5.36 | pOH=8.64 | $[H^+]=4.4 \times 10^{-6}$ | $[OH^-]=2.3 \times 10^{-9}$
12. pH=7.00 | pOH=7.00 | $[H^+]=1.0 \times 10^{-7}$ | $[OH^-]=1.00 \times 10^{-7}$
13. pH=1.00 | pOH=13.00 | $[H^+]=1.0 \times 10^{-1}$ | $[OH^-]=1.0 \times 10^{-13}$
14. pH=12.33 | pOH=1.67 | $[H^+]=4.70 \times 10^{-13}$ | $[OH^-]=2.1 \times 10^{-2}$
15. pH=2.80 | pOH=11.20 | $[H^+]=1.6 \times 10^{-3}$ | $[OH^-]=6.3 \times 10^{-12}$
16. pH=3.04 | pOH=10.96 | $[H^+]=9.1 \times 10^{-4}$ | $[OH^-]=1.10 \times 10^{-11}$
17. pH=11.46 | pOH=2.54 | $[H^+]=3.5 \times 10^{-12}$ | $[OH^-]=2.9 \times 10^{-3}$
18. pH=2.07 | pOH=11.93 | $[H^+]=8.50 \times 10^{-3}$ | $[OH^-]=1.2 \times 10^{-12}$
19. pH=1.74 | pOH=12.26 | $[H^+]=1.8 \times 10^{-2}$ | $[OH^-]=5.5 \times 10^{-13}$
20. pH=12.77 | pOH=1.23 | $[H^+]=1.7 \times 10^{-13}$ | $[OH^-]=5.90 \times 10^{-2}$
Parent Tip: Review the logic above to help your child master the concept of chemistry ph worksheet.
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