Calculate the solubility at $$ 25^{\circ} \mathrm{C} $$ of CuBr in pure water and in a 0.0110 MCoBr solution. You'll find $$ K_{s p} $$ data in the ALEKS Data tab. Round both of your answers to 2 significant digits. solubility in pure water:

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Let the solubility (in molarity) of $$\ce{CuBr}$$ be $$s$$. When $$\ce{CuBr}$$ dissolves it dissociates as

$$
\ce{CuBr(s)} \rightarrow \ce{Cu^+(aq)} + \ce{Br^-(aq)}.
$$

Thus, in pure water the ion concentrations are

$$
[\ce{Cu^+}] = s,\quad [\ce{Br^-}] = s.
$$

The solubility product is

$$
K_{sp} = [\ce{Cu^+}][\ce{Br^-}] = s^2.
$$

Assume the ALEKS Data tab provides

$$
K_{sp} = 7.7\times10^{-9}.
$$

### Solubility in Pure Water

Solve for $$s$$:

$$
s = \sqrt{K_{sp}} = \sqrt{7.7\times10^{-9}}.
$$

First, compute the square root of $$7.7$$:

$$
\sqrt{7.7}\approx 2.8.
$$

Also,

$$
\sqrt{10^{-9}} = 10^{-4.5}.
$$

Recalling that

$$
10^{-4.5} = 10^{-4}\times10^{-0.5}\approx (1.0\times10^{-4})\times(0.32)=3.2\times10^{-5},
$$

we have

$$
s\approx 2.8\times3.2\times10^{-5}\approx 8.96\times10^{-5}\, \text{M}.
$$

Rounded to 2 significant digits,

$$
s\approx 9.0\times10^{-5}\, \text{M}.
$$

### Solubility in a $$0.0110\,\text{M}$$ $$\ce{CoBr}$$ Solution

In the common-ion situation, the $$\ce{Br^-}$$ comes both from the dissolved $$\ce{CuBr}$$ and from the $$\ce{CoBr}$$ salt (which we assume dissociates completely to give $$\ce{Br^-}$$). Let the additional solubility of $$\ce{CuBr}$$ be $$s'$$. Then

$$
[\ce{Cu^+}] = s'
$$
$$
[\ce{Br^-}] = 0.0110 + s'.
$$

The solubility product becomes

$$
K_{sp}=s'(0.0110+s').
$$

Because $$s'$$ is very small compared to 0.0110, we approximate

$$
0.0110+s'\approx 0.0110.
$$

Thus,

$$
K_{sp}\approx s'\times0.0110.
$$

Now solve for $$s'$$:

$$
s'\approx\frac{K_{sp}}{0.0110}=\frac{7.7\times10^{-9}}{0.0110}.
$$

Divide:

$$
s'\approx7.0\times10^{-7}\, \text{M}.
$$

Rounded to 2 significant digits, we have

$$
s'\approx7.0\times10^{-7}\, \text{M}.
$$

### Final Answers

- Solubility in pure water: $$9.0\times10^{-5}\, \text{M}$$
- Solubility in $$0.0110\,\text{M}$$ $$\ce{CoBr}$$ solution: $$7.0\times10^{-7}\, \text{M}$$
The solubility of CuBr in pure water is $$9.0 \times 10^{-5}\, \text{M}$$, and in a $$0.0110\,\text{M}$$ CoBr solution, it is $$7.0 \times 10^{-7}\, \text{M}$$.

Calculate the solubility at of CuBr in pure water and in a 0.0110 MCoBr solution. You’ll find data in the ALEKS Data tab.
Round both of your answers to 2 significant digits.
solubility in pure water:

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Calculate the solubility at of CuBr in pure water and in a 0.0110 MCoBr solution. You’ll find data in the ALEKS Data tab. Round both of your answers to 2 significant digits. solubility in pure water: