Question

A laboratory assistant needs to prepare \(225 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{CaCl}_{2}\) solution. How many grams of calcium chloride will she need?

Short answer

The laboratory assistant will need 3.748 grams of calcium chloride to prepare a 0.150 M CaCl2 solution with a volume of 225 mL.

Step-by-step solution

Convert the volume of solution into liters.

The given volume of solution is 225 mL. We need to convert this into liters before using the formula for molarity. To do this, divide the volume in milliliters by 1000 mL/L: \( \frac{225 \,\text{mL}}{1000\, \text{mL/L}} = 0.225 \,\text{L} \)

Calculate the moles of solute needed for the solution.

The formula for molarity (M) is: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \) We will solve this equation for the number of moles of solute, which is the amount of calcium chloride needed: Moles of solute \( = M \times \text{liters of solution} = 0.150 \, \text{M} \times 0.225 \, \text{L} \) Calculate the moles of calcium chloride needed: Moles of calcium chloride \(= 0.150 \, \mathrm{M} \times 0.225 \, \mathrm{L} = 0.03375 \, \mathrm{mol} \)

Calculate the grams of solute needed for the solution.

Next, we need to convert the moles of solute into grams using the molar mass of calcium chloride: For calcium chloride, CaCl2: \( \mathrm{Molar\ mass\ of\ CaCl_2} = \mathrm{Molar\ mass\ of\ Ca} + 2 \times \mathrm{Molar\ mass\ of\ Cl} \) The molar mass of Ca (calcium) is \( 40.08 \ \mathrm{g/mol} \), and the molar mass of Cl (chlorine) is \( 35.45 \ \mathrm{g/mol} \). Calculate the molar mass of CaCl2: CaCl2 molar mass \( = 40.08 \, \mathrm{g/mol} + 2 \times 35.45 \, \mathrm{g/mol} = 110.98\, \mathrm{g/mol} \) Now, multiply the moles of calcium chloride by its molar mass to find the mass (grams) needed: Grams of calcium chloride \( = \mathrm{moles} \times \mathrm{molar\ mass} = 0.03375 \, \mathrm{mol} \times 110.98 \, \mathrm{g/mol} \) Calculate the grams of calcium chloride needed: Grams of calcium chloride \( = 0.03375 \, \mathrm{mol} \times 110.98 \, \mathrm{g/mol} = 3.748 \, \mathrm{g} \)

Conclusion.

The laboratory assistant will need 3.748 grams of calcium chloride to prepare a 0.150 M CaCl2 solution with a volume of 225 mL.

Key concepts

Molarity Calculation

Molarity is a key concept in chemistry that measures the concentration of a solution. It is defined as the number of moles of solute per liter of solution. To calculate molarity, you use the formula: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]When you're tasked with finding out how much solute you need to achieve a certain molarity in a given volume of solution, you'll often need to rearrange this formula. For instance, if you know the desired molarity and the volume of the solution, you can solve for the moles of solute required by multiplying the molarity by the volume in liters.
In the case of the calcium chloride solution preparation, the assistant calculated the moles required by multiplying the given molarity \(0.150 \, \text{M}\) by the solution volume in liters \(0.225 \, \text{L}\), resulting in \(0.03375 \, \text{mol}\). This value indicates the amount of calcium chloride needed to achieve the desired concentration.

Molar Mass

Molar mass is another fundamental topic in chemistry, essential for converting between moles and grams. Every element has a molar mass, which is the mass of one mole of its atoms, typically expressed in grams per mole (g/mol). The periodic table provides the molar masses of all elements.
To find the molar mass of a compound like calcium chloride \(\text{CaCl}_2\), you need to add the molar masses of all the constituent atoms. Calcium \(\text{Ca}\) has a molar mass of \(40.08 \, \text{g/mol}\), and chlorine \(\text{Cl}\) has a molar mass of \(35.45 \, \text{g/mol}\). Since calcium chloride has two chlorine atoms, its molar mass is calculated as: \[40.08 \, \text{g/mol} + 2 \times 35.45 \, \text{g/mol} = 110.98 \, \text{g/mol}\]
This value is crucial for converting the moles of calcium chloride, calculated in the molarity step, into grams. By using the molar mass, the assistant converted \(0.03375 \, \text{mol}\) of calcium chloride into \(3.748 \, \text{g}\).

Concentration Units

Concentration units are essential for expressing how much solute is present in a given volume of solution. Molarity is just one of several concentration units used in chemistry. Other common ones include:

• Molality (m): Moles of solute per kilogram of solvent. Used when temperature variations are involved, since it is not affected by temperature changes.
• Weight Percent (wt%): Mass of solute divided by total mass of the solution, multiplied by 100%. Helpful when dealing with solid solutions or mixtures.
• Volume Percent (v/v%): Volume of solute divided by the total volume of the solution, multiplied by 100%. Mostly used for liquid-liquid solutions.

Molarity is particularly useful because it ties the amount of solute to the volume of solution, a vital relationship in laboratory settings where volumetric measurements are standard.
Understanding how to convert between different concentration units is important for various chemical calculations and ensures accurate solution preparation. In the laboratory task described, molarity provided a straightforward measure for determining how much calcium chloride to dissolve to attain the desired solution concentration.