Calculate the concentration of ions in the following saturated solutions: Note: Reference the Solubility product constants table for additional Part 1 of 2 Be sure your answer has the correct number of significant digits. $$ \left[\mathrm{I}^{-} ight] $$in AgI solution with $$ \left[\mathrm{Ag}^{+} ight]=9.1 imes 10^{-9} \mathrm{M}: $$ Part 2 of 2 $$ \mathrm{Be} \mathrm{sure} \mathrm{your} \mathrm{answer} \mathrm{has} \mathrm{the} \mathrm{correct} \mathrm{number} \mathrm{of} \mathrm{significant} \mathrm{digits.}_{\left[\mathrm{Al}^{3+} ight] ext { in } \mathrm{Al}(\mathrm{OH})_{3} ext { solutions with }\left[\mathrm{OH}^{-} ight]=3.1 imes 10^{-9} \mathrm{M}:}^{\mathrm{M}} $$

Question

Calculate the concentration of ions in the following saturated solutions: Note: Reference the Solubility product constants table for additional Part 1 of 2 Be sure your answer has the correct number of significant digits. $$ \left[\mathrm{I}^{-}ight] $$in AgI solution with $$ \left[\mathrm{Ag}^{+}ight]=9.1 	imes 10^{-9} \mathrm{M}: $$ Part 2 of 2 $$ \mathrm{Be} \mathrm{sure} \mathrm{your} \mathrm{answer} \mathrm{has} \mathrm{the} \mathrm{correct} \mathrm{number} \mathrm{of} \mathrm{significant} \mathrm{digits.}_{\left[\mathrm{Al}^{3+}ight] 	ext { in } \mathrm{Al}(\mathrm{OH})_{3} 	ext { solutions with }\left[\mathrm{OH}^{-}ight]=3.1 	imes 10^{-9} \mathrm{M}:}^{\mathrm{M}} $$

UpStudy AI · Accepted Answer

**Part 1**

For the dissolution of silver iodide, the equilibrium is

$$
\mathrm{AgI\ (s) \rightleftharpoons Ag^+ \ (aq) + I^- \ (aq)}
$$

The solubility product is given by

$$
K_{sp} = [\mathrm{Ag}^+][\mathrm{I}^-].
$$

We are given $$[\mathrm{Ag}^+]=9.1\times10^{-9}\ \mathrm{M}$$ and the standard value for $$K_{sp}$$ of AgI is

$$
K_{sp} = 8.3\times10^{-17}.
$$

Solve for $$[\mathrm{I}^{-}]$$:

$$
[\mathrm{I}^{-}] = \frac{K_{sp}}{[\mathrm{Ag}^+]} = \frac{8.3\times10^{-17}}{9.1\times10^{-9}}.
$$

Calculate the ratio:

$$
\frac{8.3}{9.1}\approx0.912.
$$

And combining the powers of 10:

$$
[\mathrm{I}^{-}] \approx 0.912\times10^{-8}\ \mathrm{M} = 9.1\times10^{-9}\ \mathrm{M}.
$$

Since the given concentration has two significant figures, the answer is

$$
[\mathrm{I}^{-}] = 9.1\times10^{-9}\ \mathrm{M}.
$$

---

**Part 2**

For the dissolution of aluminum hydroxide, the equilibrium is

$$
\mathrm{Al(OH)_3\ (s) \rightleftharpoons Al^{3+}\ (aq) + 3\ OH^-\ (aq)}.
$$

The solubility product expression is

$$
K_{sp} = [\mathrm{Al}^{3+}][\mathrm{OH}^{-}]^3.
$$

We are given $$[\mathrm{OH^{-}}]=3.1\times10^{-9}\ \mathrm{M}$$ and the standard value for $$K_{sp}$$ of $$\mathrm{Al(OH)_3}$$ is

$$
K_{sp} = 3.0\times10^{-34}.
$$

Solve for $$[\mathrm{Al}^{3+}]$$:

$$
[\mathrm{Al}^{3+}] = \frac{K_{sp}}{[\mathrm{OH}^{-}]^3} = \frac{3.0\times10^{-34}}{(3.1\times10^{-9})^3}.
$$

First, calculate the cube of $$[\mathrm{OH^-}]$$:

$$
(3.1\times10^{-9})^3 = 3.1^3\times(10^{-9})^3 \approx 29.8 \times 10^{-27} = 2.98\times10^{-26}.
$$

Then,

$$
[\mathrm{Al}^{3+}] \approx \frac{3.0\times10^{-34}}{2.98\times10^{-26}} \approx 1.01\times10^{-8}\ \mathrm{M}.
$$

Rounded to two significant figures (as $$3.1$$ has two significant figures), the concentration is

$$
[\mathrm{Al}^{3+}] = 1.0\times10^{-8}\ \mathrm{M}.
$$
**Part 1** $$ [\mathrm{I}^{-}] = 9.1 \times 10^{-9}\ \mathrm{M} $$ **Part 2** $$ [\mathrm{Al}^{3+}] = 1.0 \times 10^{-8}\ \mathrm{M} $$

Calculate the concentration of ions in the following saturated solutions:
Note: Reference the Solubility product constants table for additional
Part 1 of 2
Be sure your answer has the correct number of significant digits.
in AgI solution with
Part 2 of 2

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Chemistry Questions

Calculate the concentration of ions in the following saturated solutions: Note: Reference the Solubility product constants table for additional Part 1 of 2 Be sure your answer has the correct number of significant digits. in AgI solution with Part 2 of 2