Chemistry The pH of a chemical solution is given by the formula $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right]$where $\left[{\mathrm{H}}^{+}\right]$is the concentration of hydrogen ions in moles per liter. Values of pH range from $0$(acidic) to $14$(alkaline).

(a) What is the pH of a solution for which role="math" localid="1647170062627" $\left[{\mathrm{H}}^{+}\right]$is $0.1$?

(b) What is the pH of a solution for which $\left[{\mathrm{H}}^{+}\right]$is $0.01$?

(c) What is the pH of a solution for which $\left[{\mathrm{H}}^{+}\right]$is $0.001$?

(d) What happens to pH as the hydrogen ion concentration decreases?

(e) Determine the hydrogen ion concentration of an orange$\left(\mathrm{pH}=3.5\right).$

(f) Determine the hydrogen ion concentration of human blood $\left(\mathrm{pH}=7.4\right).$

It is given that $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

We need to determine the pH of a solution for which$\left[{\mathrm{H}}^{+}\right]$is$0.1.$

Substitute $0.1$to data-custom-editor="chemistry" ${\mathrm{H}}^{+}$in role="math" localid="1647167906658" $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

So, role="math" localid="1647168310094" $\mathrm{pH}=-{\log }_{10}0.1.$

$=-{\log }_{10}\left({10}^{-1}\right).$

$=-\left(-1\right).$

$=1.$

It is given that $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

We need to determine the pH of a solution for which$\left[{\mathrm{H}}^{+}\right]$is$0.01.$

Substitute $0.01$to data-custom-editor="chemistry" ${\mathrm{H}}^{+}$in data-custom-editor="chemistry" $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

So, data-custom-editor="chemistry" $\mathrm{pH}=-{\log }_{10}\left(0.01\right).$

$=-{\log }_{10}\left({10}^{-2}\right).$

$=\left(-2\right){\log }_{10}\left(10\right).$

$=2.$

It is given that $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

We need to determine the pH of a solution for which $\left[{\mathrm{H}}^{+}\right]$is $0.001.$

Substitute $0.001$to data-custom-editor="chemistry" ${\mathrm{H}}^{+}$in data-custom-editor="chemistry" $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

So, data-custom-editor="chemistry" $\mathrm{pH}=-{\log }_{10}0.001.$

$=-{\log }_{10}\left({10}^{-3}\right).$

$=-\left(-3\right){\log }_{10}10.$

$=3.$

It is given that $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$We need to write what happens to pH as the hydrogen ion concentration decreases.

From parts (a), (b), and (c), we get,

when ${\mathrm{H}}^{+}=0.1,\mathrm{pH}=1,$

when ${\mathrm{H}}^{+}=0.01,\mathrm{pH}=2,$

when ${\mathrm{H}}^{+}=0.001,\mathrm{pH}=3.$

Hence, the hydrogen ion concentration$\left[{\mathrm{H}}^{+}\right]$decreases the pH increases.

It is given that $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

We need to determine the hydrogen ion concentration of an orange$\left(\mathrm{pH}=3.5\right).$

Substitute $3.5$to pH in data-custom-editor="chemistry" $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

data-custom-editor="chemistry" $3.5=-{\log }_{10}{\mathrm{H}}^{+}.$

data-custom-editor="chemistry" ${\log }_{10}{\mathrm{H}}^{+}=-3.5.$

role="math" ${\mathrm{H}}^{+}=-10-3.5.$

$\approx 0.000316.$

It is given that $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

We need to determine the hydrogen ion concentration of human blood$\left(\mathrm{pH}=7.4\right).$

Substitute $7.4$to pH in data-custom-editor="chemistry" $\mathrm{pH}=-{\log }_{10}\left[{\mathrm{H}}^{+}\right].$

data-custom-editor="chemistry" $7.4=-{\log }_{10}{\mathrm{H}}^{+}.$

data-custom-editor="chemistry" $7.4={\log }_{10}{\mathrm{H}}^{+}.$

data-custom-editor="chemistry" ${\mathrm{H}}^{+}=10-7.4.$

$=3.981071706\times {10}^{-10}.$

Thus,data-custom-editor="chemistry" ${\mathrm{H}}^{+}\approx 3.981\times {10}^{-8}.$