Question

How would you prepare from the solid and pure water (a) \(0.400 \mathrm{~L}\) of \(0.155 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2} ?\) (b) \(1.75 \mathrm{~L}\) of \(0.333 \mathrm{M}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3} ?\)

Short answer

In summary, to prepare 0.400 L of 0.155 M \(\mathrm{Sr}(\mathrm{OH})_{2}\) solution, 7.541 g of solid \(\mathrm{Sr}(\mathrm{OH})_{2}\) is needed. And to prepare 1.75 L of 0.333 M $\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}$ solution, 56.0 g of solid $\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}$ is required.

Step-by-step solution

Calculate moles of solute needed

To determine the moles of \(\mathrm{Sr}(\mathrm{OH})_{2}\) needed for the solution, we can use the formula: Moles of solute = Molarity × Volume Moles of \(\mathrm{Sr}(\mathrm{OH})_{2}\) = \(0.155 \mathrm{M} \times 0.400 \mathrm{~L} = 0.062 \mathrm{~mol}\)

Convert moles to grams

We need to convert the moles of \(\mathrm{Sr}(\mathrm{OH})_{2}\) to grams by using its molar mass (which can be found in the periodic table). The molar mass of \(\mathrm{Sr}(\mathrm{OH})_{2}\) is: \(137.63 + 2(15.9994 + 1.0079) = 121.6342 \mathrm{~g/mol}\) Now we can convert moles to grams: Mass of \(\mathrm{Sr}(\mathrm{OH})_{2}\) = \(0.062 \mathrm{~mol} \times 121.6342 \mathrm{~g/mol} = 7.541 \mathrm{~g}\)

Mix the solid with water

Weigh 7.541 g of solid \(\mathrm{Sr}(\mathrm{OH})_{2}\) and add it to a volumetric flask. Then, carefully add pure water to the flask until it reaches the 0.400 L mark. Mix the solution thoroughly to ensure that the solute is completely dissolved in thewater. #(b) Preparing 1.75 L of 0.333 M $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}$

Calculate moles of solute needed

To determine the moles of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}\) needed for the solution, we can use the formula: Moles of solute = Molarity × Volume Moles of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}\) = \(0.333 \mathrm{M} \times 1.75 \mathrm{~L} = 0.58275 \mathrm{~mol}\)

Convert moles to grams

We need to convert the moles of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}\) to grams by using its molar mass (which can be found in the periodic table). The molar mass of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}\) is: \(2(1.0079 \times 4) + 2(1.0079) + 12.011 + 3(15.9994) = 96.086 \mathrm{~g/mol}\) Now we can convert moles to grams: Mass of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}\) = \(0.58275 \mathrm{~mol} \times 96.086 \mathrm{~g/mol} = 56.0 \mathrm{~g}\)

Mix the solid with water

Weigh 56.0 g of solid \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{CO}_{3}\) and add it to a volumetric flask. Then, carefully add pure water to the flask until it reaches the 1.75 L mark. Mix the solution thoroughly to ensure that the solute is completely dissolved in the water.

Key concepts

Molarity Calculations

Understanding molarity is essential in preparing solutions in chemistry. Molarity, denoted as M, measures the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters. To calculate molarity, you use the formula:

\[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \
\]
For instance, to prepare a 0.155 M solution of \(\mathrm{Sr(OH)_2}\), you would first determine the volume of the solution (0.400 L) and then use the molarity to find the moles needed. Once you know the moles required, you multiply it by the volume to get:

\[ 0.155 \, M \times 0.400 \, L = 0.062 \, mol \
\]
Using this fundamental concept helps students accurately prepare solutions with the desired concentration, ensuring successful experimental outcomes in any laboratory setting.

Moles to Grams Conversion

The bridge between the microscopic world of molecules and the macroscopic world we interact with daily is often crossed by converting between moles and grams. The link between these two is the substance's molar mass, which is the mass of one mole of a given substance and is measured in grams per mole (g/mol).

The molar mass can be calculated by summing the atomic masses of all atoms in a molecule, as found in the periodic table. So, the molar mass of \(\mathrm{Sr(OH)_2}\) is calculated through:

\[ 137.63 + 2(15.9994 + 1.0079) = 121.6342 \, g/mol \
\]
To determine the grams of a compound needed to prepare a solution, multiply the moles by this molar mass:

\[ 0.062 \, mol \times 121.6342 \, g/mol = 7.541 \, g \
\]
This conversion is a key step in the preparation of chemical solutions, providing a clear path from the specified molarity to the exact amount of substance required in grams.

Volumetric Flask Usage

A volumetric flask is a vital piece of glassware in the preparation of precise solution concentrations. It is designed to contain a specific volume of liquid with a high degree of accuracy. The volumetric flask is distinguished by its narrow neck with a marked line, which indicates the calibrated volume.

The process of using a volumetric flask properly includes adding the solute, such as weighed 7.541 g of \(\mathrm{Sr(OH)_2}\), to the flask first. After adding the solute, pure water is carefully poured into the flask until the bottom of the meniscus touches the calibration line. During this step, it's crucial to ensure that the solute is fully dissolved in the water. The final step is to stopper the flask and invert it multiple times to ensure uniform mixing of the solute and solvent. Proper use of a volumetric flask ensures the solution's concentration matches the precise intended molarity.