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Chapter 10: Problem 14

What volume of a \(0.580-M\) solution of \(\mathrm{CaCl}_{2}\) contains \(1.28 \mathrm{g}\) solute?

Short Answer

Expert verified
The volume of a \( 0.580\,\mathrm{M} \) solution of CaCl₂ that contains 1.28 g solute is approximately 19.88 mL.

Step by step solution

01

Calculate the molar mass of CaCl₂

To find the moles of CaCl₂, we first need to determine its molar mass. CaCl₂ consists of one calcium (Ca) atom, and two chlorine (Cl) atoms. We will look up their atomic masses on the periodic table and sum them up to find the molar mass of CaCl₂. Molar mass of Ca = 40.08 g/mol Molar mass of Cl = 35.45 g/mol Molar mass of CaCl₂ = (40.08) + 2 × (35.45) = 40.08 + 70.90 = 110.98 g/mol
02

Calculate the moles of CaCl₂ in the 1.28 g solute

Now, we'll use the molar mass of CaCl₂ to convert the mass of solute (1.28 g) into moles. moles of CaCl₂ = (mass of solute)/(molar mass of CaCl₂) = \( \frac{1.28\,\mathrm{g}}{110.98\,\mathrm{g/mol}} \) = 0.01153 mol
03

Use the molarity formula to find the volume of the solution

The molarity formula relates moles, volume, and concentration: Molarity (M) = \( \frac{moles\,of\,solute}{volume\,of\,solution\,(L)} \) We are given the molarity (0.580 M) and the moles of solute (0.01153 mol). We will solve for the volume of the solution (in liters). 0.580 M = \( \frac{0.01153\,\mathrm{mol}}{volume\,(L)} \) Now, we'll solve for the volume: volume (L) = \( \frac{0.01153\,\mathrm{mol}}{0.580\,\mathrm{M}} \) = 0.01988 L
04

Convert the volume from liters to milliliters

To make the volume more practical, we'll convert it from liters to milliliters (mL) using the conversion factor: 1 L = 1,000 mL volume (mL) = 0.01988 L × 1,000 mL/L = 19.88 mL The volume of a 0.580 M solution of CaCl₂ that contains 1.28 g solute is approximately 19.88 mL.

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