what is the hydroxide ion concentration of an unknown acid with a ph of 1.9?

An acid is a substance that has the ability to donate [tex]{{\text{H}}^ + }[/tex] ions or can accept electrons from the electron-rich species. The general dissociation reaction of acid is as follows:

[tex]\text{HA}}\to{{\text{H}}^+}+{{\text{A}}^-}[/tex]

Here, HA is an acid.

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. At [tex]25\;^\circ {\text{C}}[/tex], pH value of an acid is less than 7.

The formula to calculate pH of acid is as follows:

[tex]{\text{pH}} = -\log\left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^+}}\right][/tex]

Here,

[tex]\left[ {{{\text{H}}_3}{{\text{O}}^ + }} \right][/tex] is the concentration of hydronium ion.

The relation between the concentration of hydronium ion and hydroxide ion is as follows:

[tex]\left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^+}}\right]\left[{{\text{O}}{{\text{H}}^ - }}\right] = {10^{ - 14}}[/tex]

Here,

[tex]\left[ {{{\text{H}}_3}{{\text{O}}^ + }} \right][/tex] is the concentration of hydronium ion.

[tex]\left[ {{\text{O}}{{\text{H}}^ - }} \right][/tex] is the concentration of hydroxide ion.

Given information:

The pH value of unknown acid is 1.9.

To calculate:

The hydroxide ion concentration of unknown acid.

Solution:

Step 1: Initially, we have to calculate the concentration of hydronium ion by using equation (1).

The formula to calculate pH of the unknown acid is as follows:[tex]{\text{pH}} = - \log \left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^ + }} \right][/tex]

...... (1)

Rearrange the equation (1) to calculate the concentration of hydronium ion.

[tex]\left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^ + }} \right] = {10^{ - {\text{pH}}}}[/tex]

...... (2)

Substitute 1.9 for pH in the equation (2).

[tex]\begin{gathered} \left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^ + }} \right] = {10^{ - 1.9}} \\ = 1.2589 \times {10^{ - 2}}\;{\text{M}} \\ \end{gathered}[/tex]

Step 2: The concentration of hydronium ion calculated in step (1) can be used to calculate the concentration of [tex]{\text{O}}{{\text{H}}^ - }[/tex] ions by using the relation (3).

The relation between the concentration of hydronium ion and hydroxide ion is as follows:

[tex]\left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^ + }} \right]\left[ {{\text{O}}{{\text{H}}^ - }} \right] = {10^{ - 14}}[/tex] ...... (3)

Rearrange the equation (3) to calculate the concentration of hydroxide ion.

[tex]\left[ {{\text{O}}{{\text{H}}^ - }} \right] = \frac{{{{10}^{ - 14}}}}{{\left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^ + }} \right]}}[/tex] ...... (4)

Substitute [tex]1.2589 \times {10^{ - 2}}[/tex] for \left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^ + }} \right] in the equation (4).

[tex]\begin{gathered} \left[ {{\text{O}}{{\text{H}}^ - }} \right] = \frac{{{{10}^{ - 14}}}}{{1.2589 \times {{10}^{ - 2}}}} \\ = 7.9434 \times {10^{ - 13}}\;{\text{M}} \\ \end{gathered}[/tex]

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: Senior School

Subject: Chemistry

Chapter: Acids, bases, and salts

Keywords: pH, acid, pOH, base, hydronium ion, hydrogen ion, hydroxide ion, acidic nature, and basic nature.