Calculate the concentration of ions in the following saturated solutions: Note: Reference the Solubility product constants table for additional information. Part 1 of 2 Be sure your answer has the correct number of significant digits. $$ \left[\mathrm{I}^{-} ight] $$in AgI solution with $$ \left[\mathrm{Ag}^{+} ight]=7.1 imes 10^{-9} \mathrm{M}: $$ Part 2 of 2 $$ \mathrm{Be} \mathrm{sure} \mathrm{your} \mathrm{answer} \mathrm{has} \mathrm{the} \mathrm{correct} \mathrm{number} \mathrm{of} \mathrm{significant} \mathrm{digits.}_{\left[\mathrm{Al}^{3+} ight] ext { in } \mathrm{Al}(\mathrm{OH})_{3} ext { solutions with }\left[\mathrm{OH}^{-} ight]=6.1 imes 10^{-9} \mathrm{M}:}^{ ext {: }} $$ :

Question

Calculate the concentration of ions in the following saturated solutions: Note: Reference the Solubility product constants table for additional information. Part 1 of 2 Be sure your answer has the correct number of significant digits. $$ \left[\mathrm{I}^{-}ight] $$in AgI solution with $$ \left[\mathrm{Ag}^{+}ight]=7.1 	imes 10^{-9} \mathrm{M}: $$ Part 2 of 2 $$ \mathrm{Be} \mathrm{sure} \mathrm{your} \mathrm{answer} \mathrm{has} \mathrm{the} \mathrm{correct} \mathrm{number} \mathrm{of} \mathrm{significant} \mathrm{digits.}_{\left[\mathrm{Al}^{3+}ight] 	ext { in } \mathrm{Al}(\mathrm{OH})_{3} 	ext { solutions with }\left[\mathrm{OH}^{-}ight]=6.1 	imes 10^{-9} \mathrm{M}:}^{	ext {: }} $$ :

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**Part 1**

For the dissolution of silver iodide, the equilibrium is

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

with the solubility product expression

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

Using the solubility product for AgI, $$K_{sp}=8.3\times10^{-17}$$, and the given concentration

$$
\left[\mathrm{Ag}^+\right]=7.1\times10^{-9}\,M,
$$

we solve for $$\left[\mathrm{I}^-\right]$$:

$$
\left[\mathrm{I}^{-}\right]=\frac{K_{sp}}{\left[\mathrm{Ag}^{+}\right]}=\frac{8.3\times10^{-17}}{7.1\times10^{-9}}.
$$

Performing the calculation:

$$
\frac{8.3}{7.1}\approx1.17,\quad \text{and}\quad 10^{-17}\div10^{-9}=10^{-8},
$$

so

$$
\left[\mathrm{I}^{-}\right]\approx1.17\times10^{-8}\,M.
$$

Rounding to two significant figures (consistent with $$7.1\times10^{-9}\,M$$) gives

$$
\left[\mathrm{I}^{-}\right]\approx1.2\times10^{-8}\,M.
$$

---

**Part 2**

For the dissolution of aluminum hydroxide, the equilibrium is

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

with the solubility product expression

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

Using the solubility product for $$\mathrm{Al(OH)_3}$$, $$K_{sp}=3.0\times10^{-34}$$, and the given concentration

$$
\left[\mathrm{OH}^{-}\right]=6.1\times10^{-9}\,M,
$$

we solve for $$\left[\mathrm{Al}^{3+}\right]$$:

$$
\left[\mathrm{Al}^{3+}\right]=\frac{K_{sp}}{\left[\mathrm{OH}^{-}\right]^3}=\frac{3.0\times10^{-34}}{(6.1\times10^{-9})^3}.
$$

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

$$
(6.1\times10^{-9})^3=6.1^3\times10^{-27}\approx227\times10^{-27}=2.27\times10^{-25}.
$$

Now, compute

$$
\left[\mathrm{Al}^{3+}\right]=\frac{3.0\times10^{-34}}{2.27\times10^{-25}}.
$$

Dividing the numerical factors,

$$
\frac{3.0}{2.27}\approx1.32,
$$

and handling the powers of ten,

$$
10^{-34}\div10^{-25}=10^{-9},
$$

thus

$$
\left[\mathrm{Al}^{3+}\right]\approx1.32\times10^{-9}\,M.
$$

Rounding to two significant figures gives

$$
\left[\mathrm{Al}^{3+}\right]\approx1.3\times10^{-9}\,M.
$$

---

$$\boxed{\begin{aligned}
\left[\mathrm{I}^{-}\right]&\approx1.2\times10^{-8}\,M,$$6pt]
\left[\mathrm{Al}^{3+}\right]&\approx1.3\times10^{-9}\,M.
\end{aligned}}$$
\[ \left[\mathrm{I}^{-}\right] \approx 1.2 \times 10^{-8}\,M $$ $$ \left[\mathrm{Al}^{3+}\right] \approx 1.3 \times 10^{-9}\,M $$

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

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