Understanding Hydrogen and Hydroxide Ions in Water: Acids, Bases, and Logarithms | Study Guides, Projects, Research Elementary Mathematics

MATH 1010 PROJECT

ACIDS, BASES, AND LOGARITHMS

Water is a chemical compound formed by combination of two hydrogen (H) atoms and

one oxygen (O) atom. Thus water is often chemically designated as HO. In general, water is

regarded as a stable substance. However, individual water molecules are in constant motion,

and through collisions with one another they sometimes collide with so much force that they ionize

(break apart into electrically charged ions):

(–) (+)

W +

water hydroxide ion hydrogen ion

H O OH H

2–+

The double arrow indicates that the reaction proceeds in both directions. Thus, water molecules

constantly gain, lose, and swap hydrogen atoms: molecules dissociate to form ions; the ions

recombine to reform water molecules. At any given time about two of every billion water

molecules are ionized.

Pure water has equal concentrations of hydrogen ions (H ) and hydroxide ions (OH ), but in

+–

many solutions the concentrations of H and OH ions are not the same. If the concentration of H

+–+

ions exceeds the concentration of OH ions, the solution is acidic; if the concentration of OH ions

– –

is greater, the solution is basic. The exact amounts of hydrogen and hydroxide present are

controlled by the product:

K = [H ]*[OH ].

w+–

For pure water, the concentrations of H and OH must be equal (see reaction above).

+–

Experimentally, they have been determined to be 1 x 10 each. Therefore, K has a value of 1 x

–7 w

10 . This is a constant, so whenever one concentration is changed, the other must change in

–14

response to keep their product equal to 1 x 10 . Although pure water contains both hydrogen

–14

ions (acid) and hydroxide ions (base), it is considered to be neutral overall because these ions

are present in equal amounts.

Any substance which, when added to water, increases the concentration of hydrogen ions

is called an acid. For example, when hydrogen chloride (HCl) is added to water, virtually all the

HCl molecules separate into hydrogen (H ) and chloride (Cl ) ions.

+–

HCl 6 H + Cl

+–

The water now has an excess of hydrogen ions, and is considered to be acidic. This does not

mean that there are no hydroxide ions remaining, just that there are relatively few of them

remaining. Any such addition of hydrogen (H ) ions to water will always result in a corresponding

decline in hydroxide ions (OH ). For example, if [H ] were increased to 1 x 10 , then [OH ] must

–+–6 –

decrease to 1 x 10 so that their product remains constant at 1 x 10 .

–8 –14

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MATH 1010 PROJECT

ACIDS, BASES, AND LOGARITHMS

Water is a chemical compound formed by combination of two hydrogen (H) atoms and

one oxygen (O) atom. Thus water is often chemically designated as H O 2. In general, water is

regarded as a stable substance. However, individual water molecules are in constant motion,

and through collisions with one another they sometimes collide with so much force that they ionize

(break apart into electrically charged ions ):

W +

water hydroxide ion hydrogen ion

H O 2 OH^ –^ H +

The double arrow indicates that the reaction proceeds in both directions. Thus, water molecules

constantly gain, lose, and swap hydrogen atoms: molecules dissociate to form ions; the ions

recombine to reform water molecules. At any given time about two of every billion water

molecules are ionized.

Pure water has equal concentrations of hydrogen ions (H ) and hydroxide ions (OH ), but in +^ –

many solutions the concentrations of H and OH ions are not the same. If the concentration of H

+ – +

ions exceeds the concentration of OH –^ ions, the solution is acidic ; if the concentration of OH – ions

is greater, the solution is basic. The exact amounts of hydrogen and hydroxide present are

controlled by the product:

K w = [H ]*[OH ]. +^ –

For pure water, the concentrations of H +^ and OH – must be equal (see reaction above).

Experimentally, they have been determined to be 1 x 10 –7^ each. Therefore, K w has a value of 1 x

10 –14. This is a constant , so whenever one concentration is changed, the other must change in

response to keep their product equal to 1 x 10. Although pure water contains both hydrogen

ions (acid) and hydroxide ions (base), it is considered to be neutral overall because these ions

are present in equal amounts.

Any substance which, when added to water, increases the concentration of hydrogen ions

is called an acid. For example, when hydrogen chloride (HCl) is added to water, virtually all the

HCl molecules separate into hydrogen (H ) and chloride (Cl ) ions. +^ –

HCl 6 H +^ + Cl –

The water now has an excess of hydrogen ions, and is considered to be acidic. This does not

mean that there are no hydroxide ions remaining, just that there are relatively few of them

remaining. Any such addition of hydrogen (H ) ions to water will always result in a corresponding +

decline in hydroxide ions (OH ). For example, if [H ] were increased to 1 x 10 , then [OH ] must

- + –6 –

decrease to 1 x 10 –8^ so that their product remains constant at 1 x 10 –^14.

Any substance which, when added to water, increases the concentration of hydroxide ions

is called a base. For example, when potassium hydroxide (KOH) is dissolved in water, it

separates to form K and OH ions.

KOH 6 K +^ + OH –

The water now contains an excess of hydroxide ions, and is considered basic.

As shown above, the concentrations of H +^ and OH – in water are usually very small, and

therefore are often written in exponential notation. However, a more convenient method of

expressing the concentration of hydrogen ions is by pH. The pH of a solution is defined to be the

negative log of its hydrogen ion concentration. Concentrations of most acid or base

solutions are generally much less than one; therefore the concentration, when expressed

exponentially, carries a negative exponent (e.g. 1 x 10 ). The letter "p" is used as an

abbreviation for "–log", and is meant to express the concentration as a power of ten. Thus the pH

of pure water would be:

[H ] = 1 x 10+^ –

pH = –log[H ] = –log(1 x 10 )

pH = –(–7) Y pH = 7

As the concentration of H +^ increases, e.g. [H ] = 1 x 10+^ –2, the pH decreases.

pH = –log[H ]+^ Y pH = –log[1 x 10 –2]

pH = –(–2) Y pH = 2

The pH of an acidic solution will always be less than 7.

As the concentration of OH increases, e.g. [OH ] = 1 x 10 , the hydrogen ion concentration must

- – –

decrease. How much?

K w = [H ]*[OH ] +^ –

1 x 10 –14^ = [H ]*[1 x 10 +^ –3 ]

1 x 10 –11^ = [H ] +

pH = –log(1 x 10 –11 )

pH = –(–11) Y pH = 11

The pH of a basic solution will always be greater than 7.

A solution that has a pH between 7 and 9 is slightly basic, one with a pH between 9 and 11 is

moderately basic, and one with a pH between 12 and 14 is strongly basic.

1 x 10

- 3.

1 x 10

- 4.

= 1 x 10 0.9^ .. 7.

1 x 10 – 14

1 x 10 – 11.^

= 1 x 10

- 2.

EXAMPLES

Example 1: Calculate the concentration of H +ions in wine.

pH = 3.3 = –(–3.3) = –log(1 x 10 –3.3)^ | H +^ = 1 x 10–3.

Example 2: Which is more acidic, wine or seawater?

Wine is more acidic than seawater, since it is to the left of seawater on the pH table.

Seawater is more basic than wine, since it is to the right of wine on the pH table.

Example 3: How many times more acidic is wine than acid rain?

Concentration of H ions in wine = 1 x 10 and

– 3.

concentration of H +^ ions in acid rain = 1 x 10– 4.

times as acidic

Example 4: How many times more basic is pure water than vinegar?

Since the pH value increases by 4 units, the basicity increases by

1 x 10 = 10,000 times as basic.

Example 5: Calculate the concentration of OH – ions in household ammonia.

pH = 11.5 | concentration of H = 1 x 10

– 11.

Since K w = [H ] ( [OH ], where K w= 1 x 10 , and we know [H ] = 1 x 10 ,

– – 14 + – 11.

then 1 x 10 = 1 x 10 ( [OH ] | [OH ] =.

14 – 11.5 – –

In one of the exercises you will be asked to prove that 14 = pH + pOH, a commonly

used shortcut. Since the pH of household ammonia is given as 11.5, its pOH must

be 2.5, which implies that [OH ] = 1 x 10–^ – 2.5.

Example 6: Find the pH of a substance which has a hydrogen ion concentration of 4.1 x 10 – 2.

pH = – log[H ] = – log(4.1 x 10 ) = –(log 4.1 + log 10 ) .. 1.

– 2 – 2

PROJECT

1. Calculate the concentration of H +ions in stomach acid.

2. What is the concentration of H +ions in acid rain?

3. What is the concentration of H ions in oven cleaner?

4. If the pH of a substance is known to be n, what will be the concentration of H +ions in the

substance?

5. How many times more acidic is acid rain than normal rain?

6. How many times more acidic is battery acid than orange juice?

7. Which substance is 100 times as acidic as cola:

8. What would be the pH of a substance that is 1000 times less acidic than lemon juice?

9. Calculate the concentration of OH – ions in an egg.

10. Find the concentration of OH – ions in seawater.

11. How many times more basic is seawater than normal rain?

12. Which substance is 10,000 times as basic as baking soda?

13. What would be the pH of substance that is 10 times less basic than beer?

14. Use logarithms and the identity K w = [H ]*[OH ], where K +^ –^ w = 1x 10 –14 , to derive the expression

14 = pH + pOH.

15. Use the above shortcut to complete this table.

[ H +^ ] [ OH –^ ] [ H +^ ] [ OH – ]

milk oven cleaner

normal rain cola

blood stomach acid

16. A typical tomato has a hydrogen ion concentration of 3.2 x 10 – 4.

Is this acidic or basic?

What is its pH?

What is the concentration of hydroxide ions present?

Judy Ahrens/Jerry Burns Pellissippi State Technical Community College September 1997

Understanding Hydrogen and Hydroxide Ions in Water: Acids, Bases, and Logarithms, Study Guides, Projects, Research of Elementary Mathematics

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Partial preview of the text

Download Understanding Hydrogen and Hydroxide Ions in Water: Acids, Bases, and Logarithms and more Study Guides, Projects, Research Elementary Mathematics in PDF only on Docsity!

MATH 1010 PROJECT

ACIDS, BASES, AND LOGARITHMS

Water is a chemical compound formed by combination of two hydrogen (H) atoms and

one oxygen (O) atom. Thus water is often chemically designated as H O 2. In general, water is

regarded as a stable substance. However, individual water molecules are in constant motion,

and through collisions with one another they sometimes collide with so much force that they ionize

(break apart into electrically charged ions ):

W +

water hydroxide ion hydrogen ion

H O 2 OH^ –^ H +

The double arrow indicates that the reaction proceeds in both directions. Thus, water molecules

constantly gain, lose, and swap hydrogen atoms: molecules dissociate to form ions; the ions

recombine to reform water molecules. At any given time about two of every billion water

molecules are ionized.

Pure water has equal concentrations of hydrogen ions (H ) and hydroxide ions (OH ), but in +^ –

many solutions the concentrations of H and OH ions are not the same. If the concentration of H

ions exceeds the concentration of OH –^ ions, the solution is acidic ; if the concentration of OH – ions

is greater, the solution is basic. The exact amounts of hydrogen and hydroxide present are

controlled by the product:

K w = [H ]*[OH ]. +^ –

For pure water, the concentrations of H +^ and OH – must be equal (see reaction above).

Experimentally, they have been determined to be 1 x 10 –7^ each. Therefore, K w has a value of 1 x

10 –14. This is a constant , so whenever one concentration is changed, the other must change in

response to keep their product equal to 1 x 10. Although pure water contains both hydrogen

ions (acid) and hydroxide ions (base), it is considered to be neutral overall because these ions

are present in equal amounts.

Any substance which, when added to water, increases the concentration of hydrogen ions

is called an acid. For example, when hydrogen chloride (HCl) is added to water, virtually all the

HCl molecules separate into hydrogen (H ) and chloride (Cl ) ions. +^ –

HCl 6 H +^ + Cl –

The water now has an excess of hydrogen ions, and is considered to be acidic. This does not

mean that there are no hydroxide ions remaining, just that there are relatively few of them

remaining. Any such addition of hydrogen (H ) ions to water will always result in a corresponding +

decline in hydroxide ions (OH ). For example, if [H ] were increased to 1 x 10 , then [OH ] must

decrease to 1 x 10 –8^ so that their product remains constant at 1 x 10 –^14.

Any substance which, when added to water, increases the concentration of hydroxide ions

is called a base. For example, when potassium hydroxide (KOH) is dissolved in water, it

separates to form K and OH ions.

The water now contains an excess of hydroxide ions, and is considered basic.

As shown above, the concentrations of H +^ and OH – in water are usually very small, and

therefore are often written in exponential notation. However, a more convenient method of

expressing the concentration of hydrogen ions is by pH. The pH of a solution is defined to be the

negative log of its hydrogen ion concentration. Concentrations of most acid or base

solutions are generally much less than one; therefore the concentration, when expressed

exponentially, carries a negative exponent (e.g. 1 x 10 ). The letter "p" is used as an

abbreviation for "–log", and is meant to express the concentration as a power of ten. Thus the pH

of pure water would be:

[H ] = 1 x 10+^ –

pH = –log[H ] = –log(1 x 10 )

pH = –(–7) Y pH = 7

As the concentration of H +^ increases, e.g. [H ] = 1 x 10+^ –2, the pH decreases.

pH = –log[H ]+^ Y pH = –log[1 x 10 –2]

pH = –(–2) Y pH = 2

The pH of an acidic solution will always be less than 7.

As the concentration of OH increases, e.g. [OH ] = 1 x 10 , the hydrogen ion concentration must

decrease. How much?

K w = [H ]*[OH ] +^ –

1 x 10 –14^ = [H ]*[1 x 10 +^ –3 ]

1 x 10 –11^ = [H ] +

pH = –log(1 x 10 –11 )

pH = –(–11) Y pH = 11

The pH of a basic solution will always be greater than 7.

A solution that has a pH between 7 and 9 is slightly basic, one with a pH between 9 and 11 is

moderately basic, and one with a pH between 12 and 14 is strongly basic.

1 x 10

1 x 10

= 1 x 10 0.9^ .. 7.

1 x 10 – 14

1 x 10 – 11.^

= 1 x 10

EXAMPLES

Example 1: Calculate the concentration of H +ions in wine.

Example 2: Which is more acidic, wine or seawater?

Wine is more acidic than seawater, since it is to the left of seawater on the pH table.

Seawater is more basic than wine, since it is to the right of wine on the pH table.

Example 3: How many times more acidic is wine than acid rain?