Formulas For Acids And Bases

Overview of Acids and Bases

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In that location are 3 major classifications of substances known as acids or bases. The Arrhenius definition states that an acrid produces H⁺ in solution and a base produces OH^-. This theory was developed by Svante Arrhenius in 1883. Afterwards, two more sophisticated and general theories were proposed. These are the Brønsted-Lowry and the Lewis definitions of acids and bases. The Lewis theory is discussed elsewhere.

The Arrhenius Theory of Acids and Bases

In 1884, the Swedish chemist Svante Arrhenius proposed two specific classifications of compounds; acids and bases. When dissolved in an aqueous solution, certain ions were released into the solution. An Arrhenius acid is a chemical compound that increases the concentration of H⁺ ions that are nowadays when added to water. These H⁺ ions class the hydronium ion (H_iiiO⁺) when they combine with water molecules. This process is represented in a chemical equation by calculation H_iiO to the reactants side.

\[ HCl_{(aq)} \rightarrow H^+_{(aq)} + Cl^-_{(aq)} \]

In this reaction, hydrochloric acid (\(HCl\)) dissociates completely into hydrogen (H⁺) and chlorine (Cl^-) ions when dissolved in water, thereby releasing H⁺ ions into solution. Formation of the hydronium ion equation:

\[ HCl_{(aq)} + H_2O_{(l)} \rightarrow H_3O^+_{(aq)} + Cl^-_{(aq)} \]

The Arrhenius theory, which is the simplest and least general description of acids and bases, includes acids such as HClO₄ and HBr and bases such as \(NaOH\) or \(Mg(OH)_2\). For example the complete dissociation of \(HBr\) gas into h2o results generates free \(H_3O^+\) ions.

\[HBr_{(g)} + H_2O_{(l)} \rightarrow H_3O^+_{(aq)} + Br^-_{(aq)}\]

This theory successfully describes how acids and bases react with each other to make water and salts. However, it does not explain why some substances that do not comprise hydroxide ions, such as \(F^-\) and \(NO_2^-\), tin can make basic solutions in water. The Brønsted-Lowry definition of acids and bases addresses this trouble.

An Arrhenius base is a compound that increases the concentration of OH^- ions that are nowadays when added to water. The dissociation is represented by the following equation:

\[ NaOH \; (aq) \rightarrow Na^+ \; (aq) + OH^- \; (aq) \]

In this reaction, sodium hydroxide (NaOH) disassociates into sodium (Na⁺) and hydroxide (OH^-) ions when dissolved in water, thereby releasing OH^- ions into solution.

Note

• Arrhenius acids are substances which produce hydrogen ions in solution.
• Arrhenius bases are substances which produce hydroxide ions in solution.

Costless Hydrogen Ions exercise not Exist in Water

Attributable to the overwhelming excess of \(H_2O\) molecules in aqueous solutions, a bare hydrogen ion has no chance of surviving in water. The hydrogen ion in aqueous solution is no more than than a proton, a bare nucleus. Although it carries only a single unit of measurement of positive accuse, this accuse is full-bodied into a volume of space that is only about a hundred-millionth equally large as the book occupied by the smallest atom. (Call up of a pebble sitting in the middle of a sports stadium!) The resulting extraordinarily high charge density of the proton strongly attracts it to whatever part of a nearby atom or molecule in which in that location is an excess of negative accuse. In the case of h2o, this will be the lone pair (unshared) electrons of the oxygen cantlet; the tiny proton will be buried within the lone pair and will class a shared-electron (coordinate) bond with it, creating a hydronium ion, \(H_3O^+\). In a sense, \(H_2O\) is interim every bit a base here, and the product \(H_3O^+\) is the conjugate acrid of water:

Although other kinds of dissolved ions accept water molecules bound to them more or less tightly, the interaction betwixt H⁺ and \(H_2O\) is so strong that writing "H⁺ _(aq) " inappreciably does it justice, although it is formally right. The formula \(H_3O^+\) more than adequately conveys the sense that it is both a molecule in its own right, and is too the conjugate acid of h2o.

The equation "HA → H⁺ + A^–" is and then much easier to write that chemists still use it to represent acrid-base of operations reactions in contexts in which the proton donor-acceptor mechanism does non need to be emphasized. Thus, it is permissible to talk about "hydrogen ions" and use the formula H⁺ in writing chemical equations as long as you retrieve that they are non to be taken literally in the context of aqueous solutions.

Limitations to the Arrhenius Theory

The Arrhenius theory has many more limitations than the other two theories. The theory suggests that in order for a substance to release either H⁺ or OH^- ions, information technology must contain that particular ion. All the same, this does not explain the weak base of operations ammonia (NH₃) which, in the presence of water, releases hydroxide ions into solution, but does not incorporate OH^- itself.

Hydrochloric acid is neutralized by both sodium hydroxide solution and ammonia solution. In both cases, yous get a colourless solution which yous can crystallize to get a white salt - either sodium chloride or ammonium chloride. These are clearly very similar reactions. The total equations are:

\[ NaOH \; (aq) + HCl \; (aq) \rightarrow NaCl \; (aq) + H_2O \; (50) \]

\[ NH_3 \; (aq) + HCl \; (aq) \rightarrow NH_4Cl \; (aq) \]

In the sodium hydroxide instance, hydrogen ions from the acid are reacting with hydroxide ions from the sodium hydroxide - in line with the Arrhenius theory. However, in the ammonia instance, at that place are no hydroxide ions!

You can get effectually this by saying that, when the ammonia reacts with the h2o, it is dissolved in to produce ammonium ions and hydroxide ions:

\[ NH_3 \; (aq) + H_2O \; (l) \rightleftharpoons NH_4^+ \; (aq) + OH^- \;(aq) \]

This is a reversible reaction, and in a typical dilute ammonia solution, virtually 99% of the ammonia remains as ammonia molecules. Nevertheless, at that place are hydroxide ions there, and we tin squeeze this into the Arrhenius theory. However, this aforementioned reaction also happens betwixt ammonia gas and hydrogen chloride gas.

\[ NH_3 \; (g) + HCl \; (g) \rightarrow NH_4Cl \;(s) \]

In this case, there are not any hydrogen ions or hydroxide ions in solution - because there isn't any solution. The Arrhenius theory wouldn't count this as an acrid-base reaction, despite the fact that information technology is producing the same product as when the ii substances were in solution. Because of this shortcoming, later theories sought to better explain the behavior of acids and bases in a new manner.

The Brønsted-Lowry Definition

In 1923, chemists Johannes Nicolaus Brønsted and Thomas Martin Lowry independently adult definitions of acids and bases based on the compounds' abilties to either donate or accept protons (H⁺ ions). In this theory, acids are defined every bit proton donors; whereas bases are defined as proton acceptors. A compound that acts every bit both a Brønsted-Lowry acrid and base together is called amphoteric.This took the Arrhenius definition one step further, as a substance no longer needed to exist composed of hydrogen (H⁺) or hydroxide (OH^-) ions in order to be classified as an acid or base. Consider the post-obit chemical equation:

\[ HCl \; (aq) + NH_3 \; (aq) \rightarrow NH_4^+ \; (aq) + Cl^- \; (aq) \]

Here, muriatic acid (HCl) "donates" a proton (H⁺) to ammonia (NH₃) which "accepts" information technology , forming a positively charged ammonium ion (NH₄ ⁺) and a negatively charged chloride ion (Cl^-). Therefore, HCl is a Brønsted-Lowry acid (donates a proton) while the ammonia is a Brønsted-Lowry base of operations (accepts a proton). Also, Cl^- is called the cohabit base of the acid HCl and NH₄ ⁺ is chosen the conjugate acid of the base NH₃.

The Brønsted-Lowry Theory of Acids and Bases

• A Brønsted-Lowry acid is a proton (hydrogen ion) donor.
• A Brønsted-Lowry base is a proton (hydrogen ion) acceptor.

In this theory, an acrid is a substance that tin can release a proton (like in the Arrhenius theory) and a base is a substance that can take a proton. A basic salt, such every bit Na⁺F^-, generates OH^- ions in water by taking protons from water itself (to make HF):

\[F^-_{(aq)} + H_2O_{(l)} \rightleftharpoons HF_{(aq)} + OH^-\]

When a Brønsted acrid dissociates, it increases the concentration of hydrogen ions in the solution, \([H^+]\); conversely, Brønsted bases dissociate by taking a proton from the solvent (water) to generate \([OH^-]\).

• Acid dissociation

\[HA_{(aq)} \rightleftharpoons A^-_{(aq)} + H^+_{(aq)}\]

• Acrid Ionization Constant:

\[K_a=\dfrac{[A^-][H^+]}{[HA]}\]

• Base dissociation:

\[B_{(aq)} + H_2O_{(l)} \rightleftharpoons HB^+_{(aq)} + OH^-_{(aq)}\]

• Base Ionization Constant

\[K_b = \dfrac{[HB^+][OH^-]}{[B]}\]

Conjugate Acids and Bases

One important consequence of these equilibria is that every acid (\(HA\)) has a cohabit base (\(A^-\)), and vice-versa. In the base of operations, dissociation equilibrium above the conjugate acrid of base of operations \(B\) is \(HB^+\). For a given acid or base, these equilibria are linked by the h2o dissociation equilibrium:

\[H_2O_{(l)} \rightleftharpoons H^+_{(aq)} + OH^-_{(aq)}\]

with

\[K_w = [H^+][OH^-]\]

for which the equilibrium constant One thousand_w is one.00 x ten^-fourteen at 25°C. It can exist easily shown that the product of the acid and base dissociation constants K_a and Grand_b is K_w.

Strong and Weak Acids and Bases

Strong acids are molecular compounds that essentially ionize to completion in aqueous solution, disassociating into H⁺ ions and the additional anion; at that place are very few common strong acids. All other acids are "weak acids" that incompletely ionized in aqueous solution. Acids and bases that dissociate completely are said to be potent acids, e.thou.:

• \(HClO_{four(aq)} \rightarrow H^+_{(aq)} + ClO^-_{4(aq)}\)
• \(HBr_{(aq)} \rightarrow H^+_{(aq)} + Br^-_{(aq)}\)
• \(CH_3O^-_{(aq)} + H_2O_{(l)} \rightarrow CH_3OH_{(aq)} + OH^-_{(aq)}\)
• \(NH^-_{2(aq)} + H_2O_{(fifty)} \rightarrow NH_{3(aq)} + OH^-_{(aq)}\)

Here the right-handed arrow (\(\rightarrow\)) implies that the reaction goes to completion. That is, a 1.0 M solution of HClO_four in water really contains 1.0 K H⁺(aq) and 1.0 M ClO_iv ^-(aq), and no undissociated HClO₄.

Conversely, weak acids such as acetic acid (CH_threeCOOH) and weak bases such as ammonia (NH₃) dissociate but slightly in water - typically a few percent, depending on their concentration and be mostly as the undissociated molecules.

• STRONG ACIDS: HCl, HNO_iii, H_twoSO₄, HBr, Hello, HClO₄
• WEAK ACIDS: All other acids, such every bit HCN, HF, H₂South, HCOOH

Strong acids such every bit \(HCl\) dissociate to produce spectator ions such as \(Cl^-\) as conjugate bases, whereas weak acids produce weak conjugate bases. This is illustrated below for acetic acid and its cohabit base of operations, the acetate anion. Acetic acid is a weak acid (M_a = ane.eight 10 10^-5) and acetate is a weak base (G_b = K_w/K_a = 5.6 10 10^-ten)

Like acids, strong and weak bases are classified by the extent of their ionization. Potent bases disassociate almost or entirely to completion in aqueous solution. Similar to strong acids, at that place are very few common strong bases. Weak bases are molecular compounds where the ionization is not consummate.

• STRONG BASES: The hydroxides of the Group I and Group Ii metals such as LiOH, NaOH, KOH, RbOH, CsOH
• WEAK BASES: All other bases, such every bit NH₃, CH₃NH_two, C_fiveH_vNorthward

Annotation

The strength of a cohabit acrid/base varies inversely with the strength or weakness of its parent acid or base. Any acid or base is technically a conjugate acrid or conjugate base likewise; these terms are merely used to identify species in solution (i.eastward acetic acrid is the conjugate acrid of the acetate anion, a base, while acetate is the conjugate base of operations of acetic acid, an acrid).

How does one ascertain acids and bases? In chemistry, acids and bases accept been defined differently by three sets of theories. I is the Arrhenius definition, which revolves effectually the thought that acids are substances that ionize (intermission off) in an aqueous solution to produce hydrogen (H⁺) ions while bases produce hydroxide (OH^-) ions in solution. On the other manus, the Brønsted-Lowry definition defines acids every bit substances that donate protons (H⁺) whereas bases are substances that accept protons. Besides, the Lewis theory of acids and bases states that acids are electron pair acceptors while bases are electron pair donors. Acids and bases can be defined past their concrete and chemical observations.

pH Scale

Since acids increment the amount of H⁺ ions present and bases increase the corporeality of OH^- ions, under the pH scale, the forcefulness of acidity and basicity can exist measured by its concentration of H⁺ ions. This calibration is shown by the post-obit formula:

pH = -log[H⁺]

with [H⁺] beingness the concentration of H⁺ ions.

To run into how these calculations are done, refer to Calculating the pH of the solution of a Polyprotic Base/Acid

The pH scale is oft measured on a i to fourteen range, but this is incorrect (see pH for more than details). Something with a pH less than seven indicates acidic properties and greater than 7 indicates basic backdrop. A pH at exactly 7 is neutral. The higher the [H⁺], the lower the pH.

Figure four. The pH calibration shows that substances with a pH greater than 7 are basic and a pH less than 7 are acidic.

Lewis Theory

The Lewis theory of acids and bases states that acids act as electron pair acceptors and bases act as electron pair doners. This definition doesn't mention anything about the hydrogen atom at all, different the other definitions. Information technology only talks about the transfer of electron pairs. To demonstrate this theory, consider the following case.

This is a reaction between ammonia (NH_iii) and boron trifluoride (BF₃). Since there is no transfer of hydrogen atoms here, it is clear that this is a Lewis acid-base reaction. In this reaction, NH_three has a lone pair of electrons and BF₃ has an incomplete octet, since boron doesn't have enough electrons around it to form an octet.

Effigy 2. The Lewis structures of ammonia and boron trifluoride.

Because boron only has 6 electrons effectually information technology, it tin agree 2 more. BF_iii can act as a Lewis acrid and have the pair of electrons from the nitrogen in NH_{three ,} which volition then form a bond between the nitrogen and the boron.

Figure iii. The Lewis structure of \(H_3NBF_3\), which resulted from the coordinate covalent bond betwixt nitrogen and boron.

This is considered an acid-base reaction where NH₃ (base) is donating the pair of electrons to BF₃. BF₃ (acrid) is accepting those electrons to course a new compound, H_iiiNBF₃.

Neutralization

A special belongings of acids and bases is their ability to neutralize the other's properties. In an acrid-base (or neutralization) reaction, the H⁺ ions from the acid and the OH^- ions from the base of operations react to create water (H₂O). Another product of a neutralization reaction is an ionic chemical compound called a salt. Therefore, the general form of an acid-base reaction is:

The following are examples of neutralization reactions:

1.

(NOTE: To see this reaction done experimentally, refer to the YouTube video link under the section "References".)

two.

Titrations

Titrations are performed with acids and bases to determine their concentrations. At the equivalence point, the number of moles of the acrid will equal the number of moles of the base. This indicates that the reaction has been neutralized.

Neutralization: moles of acid = moles of base of operations

Here'south how the calculations are washed:

For case, hydrochloric acid is titrated with sodium hydroxide:

For instance, 30 mL of one.00 Grand NaOH is needed to titrate 60 mL of an HCl solution. The concentration of HCl needs to be determined. At the eqivalence betoken:

moles of HCl = moles of NaOH

To solve for the molarity of HCl, plug in the given information into the equation to a higher place.

M_HCl(60 mL HCl) = (i.00 M NaOH)(30 mL NaOH)

M_HCl=0.v Thou

The concentration of HCl is 0.5 M.

Sample Problems

one. Which of the following compounds is a strong acid?

1. CaSO_iv
2. NaCl
3. HNO_iii
4. NH₃

Solution: There are six stiff acids and all other acids are considered weak. HNO₃ is 1 of those 6 strong acids, while NH₃ is actuallly a weak base of operations.

The answer is (iii) HNO_{3 .}

2. Which of the following compounds is a Brønsted-Lowry base?

1. HCl
2. HPO_iv ^{2 -}
3. H_iiiPO₄
4. NH_four ⁺
5. CH₃NH₃ ⁺

Solution: A Brønsted-Lowry Base is a proton acceptor, which means it volition have in an H⁺. This eliminates HCl, H₃PO_{iv ,}NH₄ ⁺ and CH_iiiNH₃ ⁺ because they are Brønsted-Lowry acids. They all give away protons. In the case of HPO₄ ^two-, consider the following equation:

Hither, it is clear that HPO_iv ^{2 -} is the acid since it donates a proton to water to make H₃O⁺ and PO_iv ^{three -}. Now consider the following equation:

In this instance, HPO_four ^{2 -} is the base since it accepts a proton from water to form H₂PO_four ^- and OH^-. Thus, HPO₄ ^{two -} is an acid and base together, making it amphoteric.

Since HPO₄ ^{2 -} is the only compound from the options that tin can act as a base, the reply is (2) HPO₄ ^2-.

3. A fifty ml solution of 0.v M NaOH is titrated until neutralized into a 25 ml sample of HCl. What was the concentration of the HCl?

Solution: Since the number of moles of acid equals the number of moles of base at neutralization, the following equation is used to solve for the molarity of HCl:

Now, plug into the equation all the information that is given:

M_HCl(25 mL HCl) = (0.five M_NaOH)(50 mL NaOH)

M_HCl = i

The correct answer is 1 M_HCl .

4. In the following acrid-base of operations neutralization, ii.79 m of the acrid HBr (fourscore.91g/mol) neutralized 22.72 mL of a basic aqueous solution past the reaction:

Calculate the molarity of the basic solution.

Solution:

Offset, the number of moles of the acid needs to be calculated. This is done by using the molar mass of HBr to convert 2.79 g of HBr to moles.

(2.79 1000 HBr)/(eighty.91 grand/mol HBr) = 0.0345 moles HBr

Since this is a neutralization reaction, the number of moles of the acid (HBr) equals the number of moles of the base (NaOH) at neutralization:

moles of acid = moles of base of operations

0.0345 moles HBr = 0.0345 moles NaOH

The molarity of NaOH can now exist adamant since the amount of moles are found and the volume is given. Catechumen 22.72 mL to Liters beginning since molarity is in units of moles/50.

Molarity = (0.0345 moles NaOH)/(0.02272 50 NaOH) = ane.52 One thousand_NaOH

The correct reply is 1.52 1000_NaOH .

v. Which of the following is a Brønsted-Lowry base but not an Arrhenius base of operations?

1. NH3
2. NaOH
3. Ca(OH)2
4. KOH

Solution: The Brønsted-Lowry definition says that a base accepts protons (H⁺ ions). NaOH, Ca(OH)₂, and KOH are all Arrhenius bases because they yield the hydroxide ion (OH^-) when they ionize. However, NH₃ does non dissociate in water similar the others. Instead, it takes a proton from water and becomes NH_iv while h2o becomes a hydroxide.

Therefore, the correct answer is (1) NH₃ .

References

1. Brent, Lynnette. Acids and Bases. New York, NY: Crabtree Pub., 2009. Print.

2. Hulanicki, Adam. Reactions of Acids and Bases in Belittling Chemistry. Ellis Horwood Limited: 1987.

3. Oxlade, Chris. Acids & Bases. Chicago, IL: Heinemann Library, 2002. Print.

4. Petrucci, Ralph H. Full general Chemical science: Principles and Modern Applications. Macmillian: 2007.
5. Vanderwerd, Calvin A. Acids, Bases, and the Chemical science of the Covalent Bond. Reinhold: 1961.

Contributors and Attributions

• Catherine Broderick (UCD), Marianne Moussa (UCD)

• Jim Clark (Chemguide.co.uk)

Formulas For Acids And Bases,

Source: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Acids_and_Bases/Acid/Overview_of_Acids_and_Bases

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