How many grams of $CaCl_2$ are in 250 mL or $2.0 M CaCl_2$?
$\square$ $g CaCl_2$
Answer (2)
Convert the volume of the solution from mL to L: 250 mL = 0.25 L .
Calculate the number of moles of C a C l 2 : 2.0 M × 0.25 L = 0.5 moles .
Determine the molar mass of C a C l 2 : 40.08 + 2 × 35.45 = 110.98 g/mol .
Calculate the mass of C a C l 2 : 0.5 moles × 110.98 g/mol = 55.49 g .
Explanation
Problem Analysis We are asked to find the mass of C a C l 2 in grams present in 250 mL of a 2.0 M C a C l 2 solution.
Volume Conversion First, we need to convert the volume from milliliters (mL) to liters (L). We know that 1 L = 1000 mL, so: V o l u m e ( L ) = 1000 mL/L 250 mL = 0.25 L
Calculating Moles Next, we calculate the number of moles of C a C l 2 using the definition of molarity: M o l a r i t y = Volume of solution (in L) Moles of solute We can rearrange this to solve for moles: Moles of C a C l 2 = M o l a r i t y × V o l u m e ( L ) = 2.0 M × 0.25 L = 0.5 moles
Molar Mass Calculation Now, we need to find the molar mass of C a C l 2 . The molar mass is the sum of the atomic masses of each element in the compound. The atomic mass of Calcium (Ca) is approximately 40.08 g/mol, and the atomic mass of Chlorine (Cl) is approximately 35.45 g/mol. Therefore: M o l a r mass of C a C l 2 = 40.08 + 2 × 35.45 = 40.08 + 70.9 = 110.98 g/mol
Calculating Mass Finally, we can calculate the mass of C a C l 2 in grams using the formula: M a ss = M o l es × M o l a r mass = 0.5 moles × 110.98 g/mol = 55.49 g Therefore, there are 55.49 grams of C a C l 2 in 250 mL of a 2.0 M C a C l 2 solution.
Final Answer The mass of C a C l 2 in 250 mL of a 2.0 M solution is 55.49 grams.
Examples
In chemistry, calculating the mass of a solute needed to create a solution of a specific molarity is a fundamental skill. For example, if you're preparing a solution of C a C l 2 to use as a de-icer on roads, you need to calculate the precise amount of C a C l 2 to dissolve in a known volume of water to achieve the desired concentration. This ensures the de-icer is effective at lowering the freezing point of water and preventing ice formation. Similarly, in a lab setting, accurate solution preparation is crucial for experiments and analyses, where precise concentrations of reagents are required for reliable results. The calculation we performed ensures that the solution has the correct concentration for its intended use.
In 250 mL of a 2.0 M solution of C a C l 2 , there are 55.49 grams of C a C l 2 . This is calculated by converting the volume to liters, determining the number of moles based on the molarity, and using the molar mass to find the mass in grams.
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