16 Acids, Bases, and pH Problem Set
ACIDS, BASES, AND PH | PRACTICE PROBLEMS Complete the following to reinforce your understanding of the concept covered in this module.
PROBLEM 1: Given an acidic solution with a pH of 2.12, the molar concentration of hydrogen ions in the acidic solution is most close to: A. 6.3 × 10−3 B. 7.6 × 10−3 C. 9.2 × 10−3 D. 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒
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SOLUTION 1: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The PH of a solution REPRESENTS the CONCENTRATION of HYDROGEN [𝐻 + ] or HYDROXIDE IONS [𝑂𝐻 − ] in 1 LITER of SOLUTION. The abbreviation “pH” stands for POWER OF HYDROGEN, which DEFINES the NUMERICAL VALUE for PH as the NEGATIVE BASE 10 LOGARITHM of the MOLAR CONCENTRATION of HYDROGEN IONS. The FORMULA for PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The RELATIONSHIP between PH and MOLAR CONCENTRATION of HYDROGEN IONS is represented by the expression:
𝑝𝐻 = log10 (
1 ) [𝐻 + ]
Where: • pH is the measurement of the molar concentration of hydrogen ions • [𝐻 + ] Made with
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Looking at this formula, we may be INTIMIDATED by the use of a LOGARITHMIC FUNCTION. However, we can REARRANGE the equation, so that we can ELIMINATE the LOG BASE 10 term.
𝑝𝐻 = log10 (
1 ) = log10 ([𝐻 + ]−1 ) + [𝐻 ]
Let’s jump back to the RULES of LOGARITHMS that we learned in MATHEMATICS, so that we can re-write the formula, isolating the TERM [𝐻 + ] that represents the MOLAR CONCENTRATION of HYDROGEN IONS. The PROPERTIES AND IDENTITIES OF LOGARITHMS can be referenced under the topic of LOGARITHMS on page 23 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The logarithm of “𝑥” to the base “𝑏” is defined by: log 𝑏 (𝑥) = 𝑐, 𝑤ℎ𝑒𝑟𝑒 𝑏 𝑐 = 𝑥 Using this FORMULA for LOGARITHMS, we can re-write the expression representing the RELATIONSHIP between PH and the MOLAR CONCENTRATION of HYDROGEN IONS as: log10 ([𝐻 + ]−1 ) = 𝑝𝐻, 𝑤ℎ𝑒𝑟𝑒 10 𝑝𝐻 = [𝐻 + ]−1
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Let’s go ahead and RE-WRITE this expression one more time, so we have it in a FORM where we can plug and chug to calculate the MOLAR CONCENTRATION of HYDROGEN IONS in the SOLUTION:
10 𝑝𝐻 =
1 [𝐻 + ]
Isolating the TERM for the MOLAR CONCENTRATION of HYDROGEN IONS, we find: [𝐻 + ] = 10−𝑝𝐻 As we are told the pH of the SOLUTION, we plug in the value of 2.12 and SOLVE for the MOLAR CONCENTRATION of the HYDROGEN IONS as: [𝐻 + ] = 10−𝑝𝐻 = 10−2.12 = 7.58 × 10−3 𝑀 𝐻 +
Therefore, the correct answer choice is B. 𝟕. 𝟔 × 𝟏𝟎−𝟑
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PROBLEM 2: Given the concentration of hydroxide ions in a household cleaning chemical is 0.0022 M, the concentration of hydrogen ions is most close to: A. 4.54 × 10−10 B. 3.58 × 10−12 C. 4.54 × 10−12 D. 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒
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SOLUTION 2: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In this problem we are given the concentration of the HYDROXIDE IONS [𝑂𝐻 − ] and asked to CALCULATE the concentration of HYDROGEN IONS [𝐻 + ]. In pure water or any AQUEOUS SOLUTION, at a TEMPERATURE of 25°𝐶, the CONCETRATIONS of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] are equal and found to be: 𝐴𝑐𝑖𝑑: [𝐻 + ] = 1 × 10−7 𝑀 𝐵𝑎𝑠𝑒: [𝑂𝐻 − ] = 1 × 10−7 𝑀 The VALUE for the AUTOIONIZATION CONSTANT OF WATER can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We can then MULTIPLY these two values together to calculate the AUTOIONIZATION CONSTANT or ION-PRODUCT of WATER "𝐾𝑤 " , which represents the EQUILIBRIUM CONSTANT for WATER in any ACID-BASE REACTION.
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The RELATIONSHIP between the CONCENTRATION of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] in water or an aqueous solution is given by the IONPRODUCT of water, 𝐾𝑤 : 𝐾𝑤 = [𝐻 + ][𝑂𝐻 − ] = (1 × 10−7 𝑀)(1 × 10−7 𝑀) = 1 × 10−14 Plugging in the GIVEN concentration of HYDROXIDE IONS [𝑂𝐻 − ], we calculate the concentration of HYDROGEN IONS [𝐻 + ] as:
[𝐻 + ]
𝐾𝑤 1.0 × 10−14 = = = 4.54 × 10−12 𝑀 [𝑂𝐻 − ] 0.0022
Therefore, the correct answer choice is C. 𝟒. 𝟓𝟒 × 𝟏𝟎−𝟏𝟐
PROBLEM 3:
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The pH of rainwater collected in Flint, Michigan on a particular day was 4.82. Given the pH of the rainwater, the concentration of hydrogen ions in the rainwater is most close to: A. 6.3 × 10−3 B. 7.6 × 10−3 C. 9.2 × 10−3 D. 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒
SOLUTION 3: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. Made with
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In this problem we are given the PH of a SOLUTION, and asked to calculate the corresponding CONCENTRATION of HYDROGEN IONS [𝐻 + ] The PH of a solution REPRESENTS the CONCENTRATION of HYDROGEN [𝐻 + ] or HYDROXIDE IONS [𝑂𝐻 − ] in 1 LITER of SOLUTION. The abbreviation “pH” stands for POWER OF HYDROGEN, which DEFINES the NUMERICAL VALUE for PH as the NEGATIVE BASE 10 LOGARITHM of the MOLAR CONCENTRATION of HYDROGEN IONS. The FORMULA for PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The RELATIONSHIP between PH and MOLAR CONCENTRATION of HYDROGEN IONS is represented by the expression:
𝑝𝐻 = log10 (
1 ) [𝐻 + ]
Where: • pH is the measurement of the molar concentration of hydrogen ions • [𝐻 + ]
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Looking at this formula, we may be INTIMIDATED by the use of a LOGARITHMIC FUNCTION. However, we can REARRANGE the equation, so that we can ELIMINATE the LOG BASE 10 term.
𝑝𝐻 = log10 (
1 ) = log10 ([𝐻 + ]−1 ) + [𝐻 ]
Let’s jump back to the RULES of LOGARITHMS that we learned in MATHEMATICS, so that we can re-write the formula, isolating the TERM [𝐻 + ] that represents the MOLAR CONCENTRATION of HYDROGEN IONS. The PROPERTIES AND IDENTITIES OF LOGARITHMS can be referenced under the topic of LOGARITHMS on page 23 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The logarithm of “𝑥” to the base “𝑏” is defined by: log 𝑏 (𝑥) = 𝑐, 𝑤ℎ𝑒𝑟𝑒 𝑏 𝑐 = 𝑥 Using this FORMULA for LOGARITHMS, we can re-write the expression representing the RELATIONSHIP between PH and the MOLAR CONCENTRATION of HYDROGEN IONS as: log10 ([𝐻 + ]−1 ) = 𝑝𝐻, 𝑤ℎ𝑒𝑟𝑒 10 𝑝𝐻 = [𝐻 + ]−1
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Let’s go ahead and RE-WRITE this expression one more time, so we have it in a FORM where we can plug and chug to calculate the MOLAR CONCENTRATION of HYDROGEN IONS in the SOLUTION:
10 𝑝𝐻 =
1 [𝐻 + ]
Isolating the TERM for the MOLAR CONCENTRATION of HYDROGEN IONS, we find: [𝐻 + ] = 10−𝑝𝐻 As we are told the pH of the SOLUTION, we plug in the value of 4.82 and SOLVE for the MOLAR CONCENTRATION of the HYDROGEN IONS as: [𝐻 + ] = 10−𝑝𝐻 = 10−4.82 = 1.5 × 10−5 𝑀
Therefore, the correct answer choice is B. 𝟕. 𝟔 × 𝟏𝟎−𝟑
PROBLEM 4: Made with
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In the University of Florida chemistry lab, a sodium hydroxide [𝑁𝑎𝑂𝐻] solution is measured to have a hydroxide concentration of 2.9 × 10−4 𝑀. Given this hydroxide concentration, the pH of the solution is most close to: A. 5.61 B. 6.94 C. 9.82 D. 10.46
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SOLUTION 4: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In this problem we are given the concentration of HYDROXIDE IONS [𝑂𝐻 − ], and need to CALCULATE the PH of the SOLUTION. In order to CALCULATE the PH, we need to SOLVE for the concentration of HYDROGEN IONS [𝐻 + ] by using the ION-CONSTANT of WATER to related the concentrations of HYDROXIDE IONS [𝑂𝐻 − ] and HYDROGEN IONS [𝐻 + ]. In pure water or any AQUEOUS SOLUTION, at a TEMPERATURE of 25°𝐶, the CONCETRATIONS of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] are equal and found to be: 𝐴𝑐𝑖𝑑: [𝐻 + ] = 1 × 10−7 𝑀 𝐵𝑎𝑠𝑒: [𝑂𝐻 − ] = 1 × 10−7 𝑀 The VALUE for the AUTOIONIZATION CONSTANT OF WATER can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
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We can then MULTIPLY these two values together to calculate the AUTOIONIZATION CONSTANT or ION-PRODUCT of WATER "𝐾𝑤 " , which represents the EQUILIBRIUM CONSTANT for WATER in any ACID-BASE REACTION. The RELATIONSHIP between the CONCENTRATION of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] in water or an aqueous solution is given by the IONPRODUCT of water, 𝐾𝑤 : 𝐾𝑤 = [𝐻 + ][𝑂𝐻 − ] = (1 × 10−7 𝑀)(1 × 10−7 𝑀) = 1 × 10−14 Plugging in the GIVEN concentration of HYDROXIDE IONS [𝑂𝐻 − ], we calculate the concentration of HYDROGEN IONS [𝐻 + ] as:
[𝐻 + ]
𝐾𝑤 1.0 × 10−14 = = = 3.44 × 10−11 𝑀 [𝑂𝐻 − ] 2.9 × 10−4
Now that we have the concentration of HYDROGEN IONS [𝐻 + ], we can plug this into FORMULA for PH and solve for the PH of the SOLUTION. The PH of a solution REPRESENTS the CONCENTRATION of HYDROGEN [𝐻 + ] or HYDROXIDE IONS [𝑂𝐻 − ] in 1 LITER of SOLUTION. The abbreviation “pH” stands for POWER OF HYDROGEN, which DEFINES the NUMERICAL VALUE for PH as the NEGATIVE BASE 10 LOGARITHM of the MOLAR CONCENTRATION of HYDROGEN IONS.
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The FORMULA for PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The RELATIONSHIP between PH and MOLAR CONCENTRATION of HYDROGEN IONS is represented by the expression:
𝑝𝐻 = log10 (
1 ) [𝐻 + ]
Where: • pH is the measurement of the molar concentration of hydrogen ions • [𝐻 + ] Plugging in the CALCULATED value for the concentration of HYDROGEN IONS [𝐻 + ], we solve for the PH of the SOLUTION as:
𝑝𝐻 = log10 (
1 ) = 10.46 [3.44 × 10−11 𝑀]
Therefore, the correct answer choice is D. 10.46
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PROBLEM 1: Given an acidic solution with a pH of 2.12, the molar concentration of hydrogen ions in the acidic solution is most close to: A. 6.3 × 10−3 B. 7.6 × 10−3 C. 9.2 × 10−3 D. 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒
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SOLUTION 1: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The PH of a solution REPRESENTS the CONCENTRATION of HYDROGEN [𝐻 + ] or HYDROXIDE IONS [𝑂𝐻 − ] in 1 LITER of SOLUTION. The abbreviation “pH” stands for POWER OF HYDROGEN, which DEFINES the NUMERICAL VALUE for PH as the NEGATIVE BASE 10 LOGARITHM of the MOLAR CONCENTRATION of HYDROGEN IONS. The FORMULA for PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The RELATIONSHIP between PH and MOLAR CONCENTRATION of HYDROGEN IONS is represented by the expression:
𝑝𝐻 = log10 (
1 ) [𝐻 + ]
Where: • pH is the measurement of the molar concentration of hydrogen ions • [𝐻 + ] Made with
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Looking at this formula, we may be INTIMIDATED by the use of a LOGARITHMIC FUNCTION. However, we can REARRANGE the equation, so that we can ELIMINATE the LOG BASE 10 term.
𝑝𝐻 = log10 (
1 ) = log10 ([𝐻 + ]−1 ) + [𝐻 ]
Let’s jump back to the RULES of LOGARITHMS that we learned in MATHEMATICS, so that we can re-write the formula, isolating the TERM [𝐻 + ] that represents the MOLAR CONCENTRATION of HYDROGEN IONS. The PROPERTIES AND IDENTITIES OF LOGARITHMS can be referenced under the topic of LOGARITHMS on page 23 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The logarithm of “𝑥” to the base “𝑏” is defined by: log 𝑏 (𝑥) = 𝑐, 𝑤ℎ𝑒𝑟𝑒 𝑏 𝑐 = 𝑥 Using this FORMULA for LOGARITHMS, we can re-write the expression representing the RELATIONSHIP between PH and the MOLAR CONCENTRATION of HYDROGEN IONS as: log10 ([𝐻 + ]−1 ) = 𝑝𝐻, 𝑤ℎ𝑒𝑟𝑒 10 𝑝𝐻 = [𝐻 + ]−1
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Let’s go ahead and RE-WRITE this expression one more time, so we have it in a FORM where we can plug and chug to calculate the MOLAR CONCENTRATION of HYDROGEN IONS in the SOLUTION:
10 𝑝𝐻 =
1 [𝐻 + ]
Isolating the TERM for the MOLAR CONCENTRATION of HYDROGEN IONS, we find: [𝐻 + ] = 10−𝑝𝐻 As we are told the pH of the SOLUTION, we plug in the value of 2.12 and SOLVE for the MOLAR CONCENTRATION of the HYDROGEN IONS as: [𝐻 + ] = 10−𝑝𝐻 = 10−2.12 = 7.58 × 10−3 𝑀 𝐻 +
Therefore, the correct answer choice is B. 𝟕. 𝟔 × 𝟏𝟎−𝟑
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PROBLEM 2: Given the concentration of hydroxide ions in a household cleaning chemical is 0.0022 M, the concentration of hydrogen ions is most close to: A. 4.54 × 10−10 B. 3.58 × 10−12 C. 4.54 × 10−12 D. 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒
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SOLUTION 2: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In this problem we are given the concentration of the HYDROXIDE IONS [𝑂𝐻 − ] and asked to CALCULATE the concentration of HYDROGEN IONS [𝐻 + ]. In pure water or any AQUEOUS SOLUTION, at a TEMPERATURE of 25°𝐶, the CONCETRATIONS of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] are equal and found to be: 𝐴𝑐𝑖𝑑: [𝐻 + ] = 1 × 10−7 𝑀 𝐵𝑎𝑠𝑒: [𝑂𝐻 − ] = 1 × 10−7 𝑀 The VALUE for the AUTOIONIZATION CONSTANT OF WATER can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. We can then MULTIPLY these two values together to calculate the AUTOIONIZATION CONSTANT or ION-PRODUCT of WATER "𝐾𝑤 " , which represents the EQUILIBRIUM CONSTANT for WATER in any ACID-BASE REACTION.
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The RELATIONSHIP between the CONCENTRATION of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] in water or an aqueous solution is given by the IONPRODUCT of water, 𝐾𝑤 : 𝐾𝑤 = [𝐻 + ][𝑂𝐻 − ] = (1 × 10−7 𝑀)(1 × 10−7 𝑀) = 1 × 10−14 Plugging in the GIVEN concentration of HYDROXIDE IONS [𝑂𝐻 − ], we calculate the concentration of HYDROGEN IONS [𝐻 + ] as:
[𝐻 + ]
𝐾𝑤 1.0 × 10−14 = = = 4.54 × 10−12 𝑀 [𝑂𝐻 − ] 0.0022
Therefore, the correct answer choice is C. 𝟒. 𝟓𝟒 × 𝟏𝟎−𝟏𝟐
PROBLEM 3:
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The pH of rainwater collected in Flint, Michigan on a particular day was 4.82. Given the pH of the rainwater, the concentration of hydrogen ions in the rainwater is most close to: A. 6.3 × 10−3 B. 7.6 × 10−3 C. 9.2 × 10−3 D. 𝑁𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒
SOLUTION 3: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. Made with
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In this problem we are given the PH of a SOLUTION, and asked to calculate the corresponding CONCENTRATION of HYDROGEN IONS [𝐻 + ] The PH of a solution REPRESENTS the CONCENTRATION of HYDROGEN [𝐻 + ] or HYDROXIDE IONS [𝑂𝐻 − ] in 1 LITER of SOLUTION. The abbreviation “pH” stands for POWER OF HYDROGEN, which DEFINES the NUMERICAL VALUE for PH as the NEGATIVE BASE 10 LOGARITHM of the MOLAR CONCENTRATION of HYDROGEN IONS. The FORMULA for PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The RELATIONSHIP between PH and MOLAR CONCENTRATION of HYDROGEN IONS is represented by the expression:
𝑝𝐻 = log10 (
1 ) [𝐻 + ]
Where: • pH is the measurement of the molar concentration of hydrogen ions • [𝐻 + ]
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Looking at this formula, we may be INTIMIDATED by the use of a LOGARITHMIC FUNCTION. However, we can REARRANGE the equation, so that we can ELIMINATE the LOG BASE 10 term.
𝑝𝐻 = log10 (
1 ) = log10 ([𝐻 + ]−1 ) + [𝐻 ]
Let’s jump back to the RULES of LOGARITHMS that we learned in MATHEMATICS, so that we can re-write the formula, isolating the TERM [𝐻 + ] that represents the MOLAR CONCENTRATION of HYDROGEN IONS. The PROPERTIES AND IDENTITIES OF LOGARITHMS can be referenced under the topic of LOGARITHMS on page 23 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The logarithm of “𝑥” to the base “𝑏” is defined by: log 𝑏 (𝑥) = 𝑐, 𝑤ℎ𝑒𝑟𝑒 𝑏 𝑐 = 𝑥 Using this FORMULA for LOGARITHMS, we can re-write the expression representing the RELATIONSHIP between PH and the MOLAR CONCENTRATION of HYDROGEN IONS as: log10 ([𝐻 + ]−1 ) = 𝑝𝐻, 𝑤ℎ𝑒𝑟𝑒 10 𝑝𝐻 = [𝐻 + ]−1
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Let’s go ahead and RE-WRITE this expression one more time, so we have it in a FORM where we can plug and chug to calculate the MOLAR CONCENTRATION of HYDROGEN IONS in the SOLUTION:
10 𝑝𝐻 =
1 [𝐻 + ]
Isolating the TERM for the MOLAR CONCENTRATION of HYDROGEN IONS, we find: [𝐻 + ] = 10−𝑝𝐻 As we are told the pH of the SOLUTION, we plug in the value of 4.82 and SOLVE for the MOLAR CONCENTRATION of the HYDROGEN IONS as: [𝐻 + ] = 10−𝑝𝐻 = 10−4.82 = 1.5 × 10−5 𝑀
Therefore, the correct answer choice is B. 𝟕. 𝟔 × 𝟏𝟎−𝟑
PROBLEM 4: Made with
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In the University of Florida chemistry lab, a sodium hydroxide [𝑁𝑎𝑂𝐻] solution is measured to have a hydroxide concentration of 2.9 × 10−4 𝑀. Given this hydroxide concentration, the pH of the solution is most close to: A. 5.61 B. 6.94 C. 9.82 D. 10.46
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SOLUTION 4: The TOPIC of ACIDS, BASES, AND PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. In this problem we are given the concentration of HYDROXIDE IONS [𝑂𝐻 − ], and need to CALCULATE the PH of the SOLUTION. In order to CALCULATE the PH, we need to SOLVE for the concentration of HYDROGEN IONS [𝐻 + ] by using the ION-CONSTANT of WATER to related the concentrations of HYDROXIDE IONS [𝑂𝐻 − ] and HYDROGEN IONS [𝐻 + ]. In pure water or any AQUEOUS SOLUTION, at a TEMPERATURE of 25°𝐶, the CONCETRATIONS of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] are equal and found to be: 𝐴𝑐𝑖𝑑: [𝐻 + ] = 1 × 10−7 𝑀 𝐵𝑎𝑠𝑒: [𝑂𝐻 − ] = 1 × 10−7 𝑀 The VALUE for the AUTOIONIZATION CONSTANT OF WATER can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing.
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We can then MULTIPLY these two values together to calculate the AUTOIONIZATION CONSTANT or ION-PRODUCT of WATER "𝐾𝑤 " , which represents the EQUILIBRIUM CONSTANT for WATER in any ACID-BASE REACTION. The RELATIONSHIP between the CONCENTRATION of HYDROGEN IONS [𝐻 + ] and HYDROXIDE IONS [𝑂𝐻 − ] in water or an aqueous solution is given by the IONPRODUCT of water, 𝐾𝑤 : 𝐾𝑤 = [𝐻 + ][𝑂𝐻 − ] = (1 × 10−7 𝑀)(1 × 10−7 𝑀) = 1 × 10−14 Plugging in the GIVEN concentration of HYDROXIDE IONS [𝑂𝐻 − ], we calculate the concentration of HYDROGEN IONS [𝐻 + ] as:
[𝐻 + ]
𝐾𝑤 1.0 × 10−14 = = = 3.44 × 10−11 𝑀 [𝑂𝐻 − ] 2.9 × 10−4
Now that we have the concentration of HYDROGEN IONS [𝐻 + ], we can plug this into FORMULA for PH and solve for the PH of the SOLUTION. The PH of a solution REPRESENTS the CONCENTRATION of HYDROGEN [𝐻 + ] or HYDROXIDE IONS [𝑂𝐻 − ] in 1 LITER of SOLUTION. The abbreviation “pH” stands for POWER OF HYDROGEN, which DEFINES the NUMERICAL VALUE for PH as the NEGATIVE BASE 10 LOGARITHM of the MOLAR CONCENTRATION of HYDROGEN IONS.
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The FORMULA for PH can be referenced under the SUBJECT of CHEMISTRY on page 54 of the NCEES Supplied Reference Handbook, Version 9.4 for Computer Based Testing. The RELATIONSHIP between PH and MOLAR CONCENTRATION of HYDROGEN IONS is represented by the expression:
𝑝𝐻 = log10 (
1 ) [𝐻 + ]
Where: • pH is the measurement of the molar concentration of hydrogen ions • [𝐻 + ] Plugging in the CALCULATED value for the concentration of HYDROGEN IONS [𝐻 + ], we solve for the PH of the SOLUTION as:
𝑝𝐻 = log10 (
1 ) = 10.46 [3.44 × 10−11 𝑀]
Therefore, the correct answer choice is D. 10.46
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