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7.) Suppose you are brewing a batch of beer. You need to have a total of $101 \mathrm{ppm}^{2}$ of $\mathrm{Ca}^{2+}$ in 12.0 gallons of water for the mash. You must have equal parts of $\mathrm{CaCl}_{2}$ and $\mathrm{CaSO}_{4}$ in the water to accomplish this,
a) and b) How many grams of each should you add?
c), d) and e) What is the molarity of $\mathrm{Ca}^{2+}, \mathrm{CaCl}_{2}$, and $\mathrm{CaSO}_{4}$ in the resulting solution?
$\left(\mathrm{Ca}^{2+}=40.078 \mathrm{~g} / \mathrm{mol}, \mathrm{CaCl}_{2}=110.984 \mathrm{~g} / \mathrm{mol}, \mathrm{CaSO}_{4}=136.140 \mathrm{~g} / \mathrm{mol}, 1.000 \mathrm{gal} .=3.785 \mathrm{~L}\right)$
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Answer from Sia

Posted 4 months ago

Solution

1

$101 \mathrm{ppm} \times 12.0 \text{ gallons} \times 3.785 \text{ L/gallon} \times \frac{1 \text{ g}}{1000 \text{ mg}} = \text{mass of } \mathrm{Ca}^{2+} \text{ in grams}$

2

$\text{Mass of } \mathrm{Ca}^{2+} \text{ from each compound} = \frac{\text{Total mass of } \mathrm{Ca}^{2+}}{2}$

$\text{Mass of } \mathrm{CaCl}_{2} = \text{Mass of } \mathrm{Ca}^{2+} \text{ from } \mathrm{CaCl}_{2} \times \frac{\text{Molar mass of } \mathrm{CaCl}_{2}}{\text{Molar mass of } \mathrm{Ca}^{2+}}$

$\text{Mass of } \mathrm{CaSO}_{4} = \text{Mass of } \mathrm{Ca}^{2+} \text{ from } \mathrm{CaSO}_{4} \times \frac{\text{Molar mass of } \mathrm{CaSO}_{4}}{\text{Molar mass of } \mathrm{Ca}^{2+}}$

3

$\text{Molarity of } \mathrm{CaCl}_{2} = \frac{\text{Mass of } \mathrm{CaCl}_{2}}{\text{Molar mass of } \mathrm{CaCl}_{2} \times \text{Total volume in L}}$

$\text{Molarity of } \mathrm{CaSO}_{4} = \frac{\text{Mass of } \mathrm{CaSO}_{4}}{\text{Molar mass of } \mathrm{CaSO}_{4} \times \text{Total volume in L}}$

$\text{Molarity of } \mathrm{Ca}^{2+} = \text{Molarity of } \mathrm{CaCl}_{2} + \text{Molarity of } \mathrm{CaSO}_{4}$ (since both contribute to the $\mathrm{Ca}^{2+}$ concentration)

a) and b) Answer

[Insert grams of $\mathrm{CaCl}_{2}$ and $\mathrm{CaSO}_{4}$ here]

c), d) and e) Answer

[Insert molarity of $\mathrm{Ca}^{2+}$, $\mathrm{CaCl}_{2}$, and $\mathrm{CaSO}_{4}$ here]

Key Concept

Calculating the mass and molarity of ions in a solution requires understanding of ppm concentration and molar mass.

Explanation

The mass of ions needed is calculated from ppm, which is then used to determine the mass of each compound to add. Molarity is found by dividing the mass of each compound by its molar mass and the total volume of the solution.

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