If \(6.04 \mathrm{~mL}\) of a \(2.75 \mathrm{M}\) solution of calcium acetate is added to enough orange juice to make \(1.50 \mathrm{~L}\) of orange juice, what will the molarity of calcium acetate be in the calcium-fortified orange juice?

Short Answer

Expert verified
The molarity of calcium acetate in the fortified juice is approximately 0.0108 M.

Step by step solution

01

Determine Amount of Solute

Calculate the amount of calcium acetate in moles present in the original solution using the molarity equation, which is moles of solute divided by volume of solution in liters. Molarity (M) = moles of solute (n) / volume of solution (V). Thus, n = M × V. Here, M = 2.75 M and V = 6.04 mL, which is 0.00604 L. So, n = 2.75 M × 0.00604 L.
02

Convert Volume to Liters

Since the final volume of the orange juice solution is given in liters, ensure that all volume measurements are in the same units. Convert the initial volume of the calcium acetate solution from mL to L by dividing by 1000. Therefore, 6.04 mL is 0.00604 L.
03

Calculate Final Molarity

Add the volume of the calcium acetate solution to the volume of the orange juice to get the total volume of the calcium-fortified juice. Then, use the moles of calcium acetate calculated in Step 1 and the total volume of juice to find the final molarity. The new molarity (M_f) is calculated by dividing the number of moles of calcium acetate (n) by the final volume (V_f = 1.50 L + 0.00604 L). M_f = n / V_f.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemistry Education
Chemistry education lays the foundational knowledge required to understand the composition, structure, properties, and changes of matter. It equips students with the skills to solve quantitative problems, such as those involving molarity calculations, which are central to the study of solution chemistry. Through exercises like calculating the molarity of a calcium-fortified orange juice, students can apply theoretical concepts to practical scenarios, enhancing their comprehension of chemical processes and analytical methods. To truly grasp these concepts, one needs to practice and apply the steps learned, such as the proper conversion of units, and utilization of the molarity formula. This hands-on approach aids in solidifying a student's understanding of real-world chemical applications.
Solution Concentration
Solution concentration conveys the amount of solute present in a given volume of solvent and is a fundamental concept in chemistry. Molarity, one of the ways to express concentration, is defined as the number of moles of solute per liter of solution. Understanding how to calculate molarity is crucial for preparing solutions with desired properties, conducting stoichiometric calculations, and interpreting the results of chemical reactions. For example, to know how much calcium acetate to add to orange juice to achieve a specific molarity, you need to be adept at converting volumes and applying the molarity formula. The molarity calculation is instrumental for accurately determining the strength of a solution, which can impact its reactivity, osmotic pressure, and other characteristics important in both academic research and industry applications.
Stoichiometry
Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is used to calculate reactant and product quantities, both in moles and mass, and to understand the ratios and proportions in which substances react. This principle extends to solution preparation, where the molarity formula plays a key role in determining how much of a substance is present in a solution. In the exercise of fortifying orange juice with calcium acetate, stoichiometry helps us understand the relationship between the volume of solution and moles of solute–critical for ensuring sufficient calcium content without precipitating excess solute. Recognizing stoichiometric principles in such mixtures ensures consistency in chemistry lab work and industrial processes alike, and is pivotal for advancements in fields like pharmacology, where precise medication dosages are required.

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