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Sia

15240672380's Question
Chemistry
Posted 9 months ago

7.) Suppose you are brewing a batch of beer. You need to have a total of 101ppm2101 \mathrm{ppm}^{2} of Ca2+\mathrm{Ca}^{2+} in 12.0 gallons of water for the mash. You must have equal parts of CaCl2\mathrm{CaCl}_{2} and CaSO4\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 Ca2+,CaCl2\mathrm{Ca}^{2+}, \mathrm{CaCl}_{2}, and CaSO4\mathrm{CaSO}_{4} in the resulting solution?
(Ca2+=40.078 g/mol,CaCl2=110.984 g/mol,CaSO4=136.140 g/mol,1.000gal.=3.785 L)
\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 9 months ago
Solution
1
Calculate the total mass of $\mathrm{Ca}^{2+}$ needed: First, we need to calculate the total mass of Ca2+\mathrm{Ca}^{2+} required for 12.0 gallons of water. Since 1 ppm is equivalent to 1 mg/L, we can convert the concentration to mg/L and then to grams
$101 \mathrm{ppm} \times 12.0 \text{ gallons} \times 3.785 \text{ L/gallon} \times \frac{1 \text{ g}}{1000 \text{ mg}} = \text{mass of } \mathrm{Ca}^{2+} \text{ in grams}$
2
Determine the mass of each compound: Since equal parts of CaCl2\mathrm{CaCl}_{2} and CaSO4\mathrm{CaSO}_{4} are needed, we divide the total mass of Ca2+\mathrm{Ca}^{2+} by 2 to find the mass of Ca2+\mathrm{Ca}^{2+} in each compound. Then, we use the molar mass of each compound to find the mass of each compound to add
$\text{Mass of } \mathrm{Ca}^{2+} \text{ from each compound} = \frac{\text{Total mass of } \mathrm{Ca}^{2+}}{2}$
$\text{Mass of } \mathrm{CaCl}_{2} = \text{Mass of } \mathrm{Ca}^{2+} \text{ from } \mathrm{CaCl}_{2} \times \frac{\text{Molar mass of } \mathrm{CaCl}_{2}}{\text{Molar mass of } \mathrm{Ca}^{2+}}$
$\text{Mass of } \mathrm{CaSO}_{4} = \text{Mass of } \mathrm{Ca}^{2+} \text{ from } \mathrm{CaSO}_{4} \times \frac{\text{Molar mass of } \mathrm{CaSO}_{4}}{\text{Molar mass of } \mathrm{Ca}^{2+}}$
3
Calculate the molarity of each compound: To find the molarity, we divide the mass of each compound by its molar mass and then divide by the total volume of the solution in liters
$\text{Molarity of } \mathrm{CaCl}_{2} = \frac{\text{Mass of } \mathrm{CaCl}_{2}}{\text{Molar mass of } \mathrm{CaCl}_{2} \times \text{Total volume in L}}$
$\text{Molarity of } \mathrm{CaSO}_{4} = \frac{\text{Mass of } \mathrm{CaSO}_{4}}{\text{Molar mass of } \mathrm{CaSO}_{4} \times \text{Total volume in L}}$
$\text{Molarity of } \mathrm{Ca}^{2+} = \text{Molarity of } \mathrm{CaCl}_{2} + \text{Molarity of } \mathrm{CaSO}_{4}$ (since both contribute to the $\mathrm{Ca}^{2+}$ concentration)
a) and b) Answer
[Insert grams of CaCl2\mathrm{CaCl}_{2} and CaSO4\mathrm{CaSO}_{4} here]
c), d) and e) Answer
[Insert molarity of Ca2+\mathrm{Ca}^{2+}, CaCl2\mathrm{CaCl}_{2}, and CaSO4\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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