Math Snap

STEP 1

1. The solution is of a weak monoprotic acid.
2. The concentration of the acid is $6.81 \times 10^{-2} \mathrm{M}$.
3. The pH of the solution is 5.28.
4. We need to calculate the percent dissociation of the acid to 3 significant figures.

STEP 2

1. Calculate the concentration of hydrogen ions $[\mathrm{H}^+]$ using the pH.
2. Determine the initial concentration of the acid.
3. Calculate the percent dissociation of the acid.

STEP 3

Calculate the concentration of hydrogen ions $[\mathrm{H}^+]$ using the pH.
The formula to find the concentration of hydrogen ions from pH is:
$$\mathrm{pH} = -\log_{10}[\mathrm{H}^+]$$ Rearrange to find $[\mathrm{H}^+]$:
$$[\mathrm{H}^+] = 10^{-\mathrm{pH}}$$ Substitute the given pH value:
$$[\mathrm{H}^+] = 10^{-5.28}$$ Calculate $[\mathrm{H}^+]$:
$$[\mathrm{H}^+] \approx 5.25 \times 10^{-6} \mathrm{M}$$

STEP 4

Determine the initial concentration of the acid, which is given as:
$$[\text{Acid}]_0 = 6.81 \times 10^{-2} \mathrm{M}$$

Calculate the percent dissociation of the acid.
Percent dissociation is given by the formula:
$$\text{Percent Dissociation} = \left( \frac{[\mathrm{H}^+]}{[\text{Acid}]_0} \right) \times 100\%$$ Substitute the values:
$$\text{Percent Dissociation} = \left( \frac{5.25 \times 10^{-6}}{6.81 \times 10^{-2}} \right) \times 100\%$$ Calculate the percent dissociation:
$$\text{Percent Dissociation} \approx 0.00771\%$$ Round to 3 significant figures:
$$\text{Percent Dissociation} \approx 0.00771\%$$