Arrhenius Acid and Base theory and pH,pOH and the pH scale

• An Arrhenius acid is any species that increases the concentration of $\text{H}^+$H, start superscript, plus, end superscript in aqueous solution.
• An Arrhenius base is any species that increases the concentration of $\text{OH}^-$O, H, start superscript, minus, end superscriptin aqueous solution.
• In aqueous solution, $\text{H}^+$H, start superscript, plus, end superscript ions immediately react with water molecules to form hydronium ions, $\text{H}_3\text{O}^+$H, start subscript, 3, end subscript, O, start superscript, plus, end superscript.
• In an acid-base or neutralization reaction, an Arrhenius acid and base usually react to form water and a salt.

Arrhenius acid:-

An Arrhenius acid is any species that increases the concentration of H

$\greenD{\text{H}^+}$Hstart color greenD, H, start superscript, plus, end superscript, end color greenD ions—or protons—in aqueous solution. For example, let's consider the dissociation reaction for hydrochloric acid, $\text{HCl}$H, C, l, in water:

$\greenD{\text{H}}\text {Cl}(aq)\rightarrow \greenD{\text{H}^+}(aq)+\text{Cl}^-(aq)$start color greenD, H, end color greenD, C, l, left parenthesis, a, q, right parenthesis, right arrow, start color greenD, H, start superscript, plus, end superscript, end color greenD, left parenthesis, a, q, right parenthesis, plus, C, l, start superscript, minus, end superscript, left parenthesis, a, q, right parenthesis

When we make an aqueous solution of hydrochloric acid, $\greenD{\text{H}}\text{Cl}$start color greenD, H, end color greenD, C, l dissociates into $\greenD{\text{H}^+}$start color greenD, H, start superscript, plus, end superscript, end color greenD ions and $\text{Cl}^-$C, l, start superscript, minus, end superscript ions. Since this results in an increase in the concentration of $\greenD{\text{H}^+}$start color greenD, H, start superscript, plus, end superscript, end color greenD ions in solution, hydrochloric acid is an Arrhenius acid.

Hydrogen or hydronium ions?

Let's say we made a 2 M aqueous solution of hydrobromic acid, $\text{HBr}$H, B, r, which is an Arrhenius acid. Does that mean we have 2 M of $\text H^+$H, start superscript, plus, end superscript ions in our solution?

Actually, no. In practice, the positively charged protons react with the surrounding water molecules to form hydronium ions, $\text{H}_3\text{O}^+$H, start subscript, 3, end subscript, O, start superscript, plus, end superscript. This reaction can be written as follows:

$\text{H}^+(aq)+\text{H}_2\text{O}(l)\rightarrow\text{H}_3\text{O}^+(aq)$H, start superscript, plus, end superscript, left parenthesis, a, q, right parenthesis, plus, H, start subscript, 2, end subscript, O, left parenthesis, l, right parenthesis, right arrow, H, start subscript, 3, end subscript, O, start superscript, plus, end superscript, left parenthesis, a, q, right parenthesis

Even though we often write acid dissociation reactions showing the formation of $\text H^+(aq)$H, start superscript, plus, end superscript, left parenthesis, a, q, right parenthesis, there are no free $\text{H}^+$H, start superscript, plus, end superscript ions floating around in an aqueous solution. Instead, there are primarily $\text{H}_3\text{O}^+$H, start subscript, 3, end subscript, O, start superscript, plus, end superscript ions, which form immediately when an acid dissociates in water. 

Arrhenius bases

An Arrhenius base is defined as any species that increases the concentration of hydroxide ions, $\redD{\text{OH}^-}$start color redD, O, H, start superscript, minus, end superscript, end color redD, in aqueous solution. An example of an Arrhenius base is the highly soluble sodium hydroxide, $\text{NaOH}$N, a, O, H. Sodium hydroxide dissociates in water as follows:

$\text{Na} \redD{\text{OH}}(aq)\rightarrow\text{Na}^+(aq)+\redD{\text{OH}^-}(aq)$N, a, start color redD, O, H, end color redD, left parenthesis, a, q, right parenthesis, right arrow, N, a, start superscript, plus, end superscript, left parenthesis, a, q, right parenthesis, plus, start color redD, O, H, start superscript, minus, end superscript, end color redD, left parenthesis, a, q, right parenthesis

In water, sodium hydroxide fully dissociates to form $\redD{\text{OH}^-}$start color redD, O, H, start superscript, minus, end superscript, end color redD and $\text{Na}^+$N, a, start superscript, plus, end superscript ions, resulting in an increase in the concentration of hydroxide ions. Therefore, $\text{NaOH}$N, a, O, H is an Arrhenius base. Common Arrhenius bases include other Group 1 and Group 2 hydroxides such as $\text{LiOH}$L, i, O, H and $\text{Ba(OH)}_2$B, a, left parenthesis, O, H, right parenthesis, start subscript, 2, end subscript.

Acid-base reactions: Arrhenius acid + Arrhenius base = water + salt

When an Arrhenius acid reacts with an Arrhenius base, the products are usually water plus a salt. These reactions are also sometimes called neutralization reactions. For example, what happens when we combine aqueous solutions of hydrofluoric acid, $\text{HF}$H, F, and lithium hydroxide, $\text{LiOH}$L, i, O, H?

If we think about the acid solution and base solution separately, we know the following:

• An Arrhenius acid increases the concentration of $\greenD{\text H^+}(aq)$start color greenD, H, start superscript, plus, end superscript, end color greenD, left parenthesis, a, q, right parenthesis:

$\greenD{\text{H}}\text{F}(aq) \leftrightharpoons \greenD{\text{H}^+}(aq)+\text{F}^-(aq)$

• An Arrhenius base increases the concentration of $\redD{\text{OH}^-}(aq)$start color redD, O, H, start superscript, minus, end superscript, end color redD, left parenthesis, a, q, right parenthesis:

$\text{Li}\redD{\text{OH}}(aq) \rightarrow \text{Li}^+(aq)+\redD{\text{OH}^-}(aq)$L, i, start color redD, O, H, end color redD, left parenthesis, a, q, right parenthesis, right arrow, L, i, start superscript, plus, end superscript, left parenthesis, a, q, right parenthesis, plus, start color redD, O, H, start superscript, minus, end superscript, end color redD, left parenthesis, a, q, right parenthesis

When the acid and base combine in solution, $\text H_2 \text O$H, start subscript, 2, end subscript, O is produced from the reaction between hydrogen ions and hydroxide ions, while the other ions form the salt $\text{LiF}(aq)$L, i, F, left parenthesis, a, q, right parenthesis:

$\greenD{\text H^+}(aq)+\redD{\text{OH}^-}(aq) \rightarrow \text{H}_2 \text O(l)~~~~~~~~~~~~~\text{Formation of water}$start color greenD, H, start superscript, plus, end superscript, end color greenD, left parenthesis, a, q, right parenthesis, plus, start color redD, O, H, start superscript, minus, end superscript, end color redD, left parenthesis, a, q, right parenthesis, right arrow, H, start subscript, 2, end subscript, O, left parenthesis, l, right parenthesis, space, space, space, space, space, space, space, space, space, space, space, space, space, F, o, r, m, a, t, i, o, n, space, o, f, space, w, a, t, e, r

$\text{Li}^+(aq)+\text{F}^-(aq) \rightarrow\text{LiF}(aq)~~~~~~~~~~~~~~~~\text{Formation of salt}$L, i, start superscript, plus, end superscript, left parenthesis, a, q, right parenthesis, plus, F, start superscript, minus, end superscript, left parenthesis, a, q, right parenthesis, right arrow, L, i, F, left parenthesis, a, q, right parenthesis, space, space, space, space, space, space, space, space, space, space, space, space, space, space, space, space, F, o, r, m, a, t, i, o, n, space, o, f, space, s, a, l, t

If we add the reactions for the formation of water and the formation of salt, we get our overall neutralization reaction between hydrofluoric acid and lithium hydroxide:

$\greenD{\text{H}}\text{F}(aq) + \text{Li}\redD{\text{OH}}(aq) \rightarrow \text{H}_2 \text O(l)+\text{LiF}(aq)$start color greenD, H, end color greenD, F, left parenthesis, a, q, right parenthesis, plus, L, i, start color redD, O, H, end color redD, left parenthesis, a, q, right parenthesis, right arrow, H, start subscript, 2, end subscript, O, left parenthesis, l, right parenthesis, plus, L, i, F, left parenthesis, a, q, right parenthesis

Summary

• An Arrhenius acid is any species that increases the concentration of $\text{H}^+$H, start superscript, plus, end superscript in aqueous solution.
• An Arrhenius base is any species that increases the concentration of $\text{OH}^-$O, H, start superscript, minus, end superscriptin aqueous solution.
• In aqueous solution, $\text{H}^+$H, start superscript, plus, end superscript ions immediately react with water molecules to form hydronium ions, $\text{H}_3\text{O}^+$H, start subscript, 3, end subscript, O, start superscript, plus, end superscript.
• In an acid-base or neutralization reaction, an Arrhenius acid and base usually react to form water and a salt.

pH,pOH and the pH scale:-

• We can convert between $[\text{H}^+]$open bracket, H, start superscript, plus, end superscript, close bracket and $\text{pH}$p, H using the following equations:

$\begin{aligned}\text{pH}&=-\log[\text{H}^+]\\ \\ [\text H^+]&=10^{-\text{pH}}\end{aligned}$

• We can convert between $[\text{OH}^-]$open bracket, O, H, start superscript, minus, end superscript, close bracket and $\text{pOH}$p, O, H using the following equations:

$\begin{aligned}\text{pOH}&=-\log[\text{OH}^-]\\ \\ [\text {OH}^-]&=10^{-\text{pOH}}\end{aligned}$

• For any aqueous solution at $25\,^\circ\text{C}$25, space, degree, C:

$\text{pH}+\text{pOH}=14$p, H, plus, p, O, H, equals, 14.

• For every factor of $10$10 increase in concentration of $[\text{H}^+]$open bracket, H, start superscript, plus, end superscript, close bracket, $\text{pH}$p, H will decreaseby $1$1 unit, and vice versa.
• Both acid strength and concentration determine $[\text{H}^+]$open bracket, H, start superscript, plus, end superscript, close bracket and $\text{pH}$p, H.

Introduction

In aqueous solution, an acid is defined as any species that increases the concentration of $\text{H}^+(aq)$H, start superscript, plus, end superscript, left parenthesis, a, q, right parenthesis, while a base increases the concentration of $\text{OH}^-(aq)$O, H, start superscript, minus, end superscript, left parenthesis, a, q, right parenthesis. 

Definitions of $\text{pH}$p, H and $\text{pOH}$p, O, H

Relating $[\text H^+]$open bracket, H, start superscript, plus, end superscript, close bracket and $\text{pH}$p, H

The $\text{pH}$p, H for an aqueous solution is calculated from $[\text{H}^+]$open bracket, H, start superscript, plus, end superscript, close bracket using the following equation:

$\text{pH}=-\log[\text{H}^+]\quad\quad\quad\quad\;\;\;\text{(Eq. 1a)}$p, H, equals, minus, log, open bracket, H, start superscript, plus, end superscript, close bracket, space, space, space, space, space, space, space, left parenthesis, E, q, point, space, 1, a, right parenthesis

The lowercase $\text{p}$p indicates $``-\text{log}_{10}"$. You will often see people leave off the base $10$10 part as an abbreviation.

Relating $[\text {OH}^-]$open bracket, O, H, start superscript, minus, end superscript, close bracket and $\text{pOH}$p, O, H

The $\text{pOH}$p, O, H for an aqueous solution is defined in the same way for $[\text{OH}^-]$open bracket, O, H, start superscript, minus, end superscript, close bracket:

$\text{pOH}=-\log[\text{OH}^-]~\quad\quad\quad\;\;\text{(Eq. 2a)}$

Relating $\text{pH}$p, H and $\text{pOH}$p, O, HBased on equilibrium concentrations of 

$\text{H}^+$H, start superscript, plus, end superscript and $\text{OH}^-$O, H, start superscript, minus, end superscript in water, the following relationship is true for any aqueous solution at $25\,^\circ\text{C}$25, space, degree, C:

$\text{pH}+\text{pOH}=14~~\quad\quad\quad\quad\quad\quad\quad\quad\text{(Eq. 3)}$p, H, plus, p, O, H, equals, 14, space, space, space, space, space, space, space, space, space, space, left parenthesis, E, q, point, space, 3, right parenthesis

This relationship can be used to convert between $\text{pH}$p, H and $\text{pOH}$p, O, H. In combination with Eq. 1a/b and Eq. 2a/b,

Some important terminology to remember for aqueous solutions at $25\,^\circ\text{C}$25, space, degree, C:

• For a neutral solution, $\text{pH}=7$p, H, equals, 7.
• Acidic solutions have $\text{pH}<7$p, H, is less than, 7.
• Basic solutions have $\text{pH}>7$p, H, is greater than, 7.

The lower the $\text{pH}$p, H value, the more acidic the solution and the higher the concentration of $\text H^+$H, start superscript, plus, end superscript. The higher the $\text{pH}$p, H value, the more basic the solution and the lower the concentration of $\text H^+$H, start superscript, plus, end superscript. While we could also describe the acidity or basicity of a solution in terms of $\text{pOH}$p, O, H, it is a little more common to use $\text{pH}$p, H. Luckily, we can easily convert between $\text{pH}$p, H and $\text{pOH}$p, O, H values.

Relationship between $\text{pH}$p, H and acid strength

Based on the equation for $\text{pH}$p, H, we know that $\text{pH}$p, H is related to $[\text{H}^+]$open bracket, H, start superscript, plus, end superscript, close bracket. However, it is important to remember that $\text{pH}$p, H is not always directly related to acid strength.

The strength of an acid depends on the amount that the acid dissociates in solution: the stronger the acid, the higher $[\text{H}^+]$open bracket, H, start superscript, plus, end superscript, close bracket at a given acid concentration. For example, a $1.0\,\text M$1, point, 0, space, M solution of strong acid $\text{HCl}$H, C, l will have a higher concentration of $\text{H}^+$H, start superscript, plus, end superscript than a $1.0\,\text M$1, point, 0, space, M solution of weak acid $\text{HF}$H, F. Thus, for two solutions of monoprotic acid at the same concentration, $\text{pH}$p, H will be proportional to acid strength.

More generally though, both acid strength and concentration determine $[\text{H}^+]$open bracket, H, start superscript, plus, end superscript, close bracket. Therefore, we can't always assume that the $\text{pH}$p, H of a strong acid solution will be lower than the $\text{pH}$p, H of a weak acid solution.