Question

A 0.50 m solution of an acid ha has ph = 2.24. what is the value of ka for the acid?

Answer 1

The value of ${{\text{K}}_{\text{a}}}$ for the given acid is $\boxed{{\text{0}}{\text{.000067}}}$

Further Explanation:

An acid is a substance that has the ability to donate ${{\mathbf{H}}^{\mathbf{+}}}$ions or can accept electrons from the electron-rich species.

The acidic strength of an acid can be determined by pH value. The negative logarithm of hydronium ion concentration is defined as pH of the solution. Lower the pH value of an acid, the stronger will be the acid. Acidic solutions are likely to have pH less than 7. Basic or alkaline solutions have pH more than 7. Neutral solutions have pH equal to 7.

The formula to calculate pH of an acid is as follows:

${\text{pH}}=-{\text{log}}\left[{{{\text{H}}^+}}\right]$                       …… (1)

Here,

$\left[{{{\text{H}}^+}}\right]$ is hydrogen ion concentration.

Rearrange equation (1), we get:

$\left[{{{\text{H}}^+}}\right]={10^{-{\text{pH}}}}$                            …… (2)

The pH of acid is 2.24.

Substitute the value in equation (2).

$\begin{gathered}\left[{{{\text{H}}^+}}\right]={10^{-2.24}}\\=0.0057543\\\approx0.00574\;{\text{M}}\\\end{gathered}$

The general dissociation reaction of acid is as follows:

${\text{HA}}\left({aq}\right)\rightleftharpoons{{\text{H}}^+}\left({aq}\right)+{{\text{A}}^-}\left({aq}\right)$

Here, HA is a weak acid.

${{\text{A}}^-}$ is the conjugate base of a weak acid.

The formula to calculate the equilibrium constant of HA is as follows:

${{\text{K}}_{\text{a}}}=\frac{{\left[{{{\text{H}}^+}}\right]\left[{{{\text{A}}^-}}\right]}}{{\left[{{\text{HA}}}\right]}}$                              ……. (3)

Here,

${{\text{K}}_{\text{a}}}$ is the dissociation constant of HA.

$\left[{{\text{HA}}}\right]$is the concentration of weak acid.

$\left[{{{\text{H}}^+}}\right]$ is hydrogen ion concentration.

$\left[{{{\text{A}}^-}}\right]$ is the concentration of conjugate base of HA.

Since HA has pH of 2.24 so it is a weak base and cannot dissociate completely into its respective ions. So the concentration of hydrogen ion and that of conjugate base is the same. The concentration of acid decreases as it dissociates into ions.

The concentration of HA can be calculated as follows:

$\left[{{\text{HA}}}\right]={\left[{{\text{HA}}}\right]_{{\text{initial}}}}-\left[{{{\text{H}}^+}}\right]$             …… (4)

The value of ${\left[{{\text{HA}}}\right]_{{\text{initial}}}}$ is 0.50 M.

The value of $\left[{{{\text{H}}^+}}\right]$ is 0.00574 M.

Substitute these values in equation (4).

$\begin{gathered}\left[{{\text{HA}}}\right]={\text{0}}{\text{.50 M}}-{\text{0}}{\text{.00574 M}}\\={\text{0}}{\text{.49426 M}}\\\end{gathered}$

The value of $\left[{{\text{HA}}}\right]$ is 0.49426 M.

The value of $\left[{{{\text{H}}^+}}\right]$ is 0.00574 M.

The value of $\left[{{{\text{A}}^-}}\right]$ is 0.00574 M.

Substitute these values in equation (3).

$\begin{gathered}{{\text{K}}_{\text{a}}}=\frac{{\left({{\text{0}}{\text{.00574 M}}}\right)\left({{\text{0}}{\text{.00574 M}}}\right)}}{{\left({{\text{0}}{\text{.49426 M}}}\right)}}\\=0.0000666605\\\approx0.000067\\\end{gathered}$

So the value of ${{\mathbf{K}}_{\mathbf{a}}}$ for the given acid is 0.000067.

Learn more:

1. The reason for the acidity of water https://brainly.com/question/1550328

2. Reason for the acidic and basic nature of amino acid. https://brainly.com/question/5050077

Answer details:

Grade: High School

Subject: Chemistry

Chapter: Acid, base and salts.

Keywords: pH, 2.24, H+, A-, HA, weak acid, conjugate base, hydrogen ion concentration, dissociation constant, Ka, 0.49426 M, 0.00574 M, 0.000067.