Question

Calculate what volume of the following solutions is required to obtain \(0.250 \mathrm{~mol}\) of each solute. (a) \(0.250 \mathrm{M} \mathrm{AlCl}_{3}\) (b) \(3.00 \mathrm{MHCl}\)

Short answer

The volume required for 0.250 mol AlCl3 is 1.00 litre and for 0.250 mol HCl is 0.083 litres or 83 milliliters.

Step-by-step solution

Finding the volume for 0.250 M AlCl3

Use the formula Volume = Moles of solute / Molarity to find the volume of solution needed to get 0.250 mol of AlCl3. Rearranging the equation we get:Volume (L) = 0.250 mol / 0.250 M

Performing the calculation for AlCl3

Dividing 0.250 moles by 0.250 M gives a result of 1 litre.

Finding the volume for 3.00 M HCl

Now use the same formula to find the volume of solution for HCl. Plugging the given values into the equation we get:Volume (L) = 0.250 mol / 3.00 M

Performing the calculation for HCl

Dividing 0.250 moles by 3.00 M gives a result of approximately 0.083 litres, or 83 milliliters (as 1 litre equals 1000 milliliters).

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution. It indicates how many moles of a substance are present in one liter of a solution. Molarity is expressed in units of moles per liter (mol/L), and it is often symbolized by the capital letter M.
For example, a 0.250 M AlCl extsubscript{3} solution means that 0.250 moles of Aluminum Chloride are dissolved in a total volume of one liter of solution.

• The higher the molarity, the more concentrated the solution.
• Molarity helps us understand the relative amounts of solute and solvent in a given volume of solution.

To calculate molarity, you can use the formula: \[Molarity (M) = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}\]
This concept is integral to various fields of chemistry, particularly when solutions need to be prepared with precise concentrations for reactions and analyses.

Volume Calculation

The volume of a solution required for a specific amount of solute can be determined using the molarity formula rearranged as follows: \[Volume (L) = \frac{\text{Moles of solute}}{\text{Molarity (M)}}\]
This equation helps to directly find out how much of a solution you need if you know the molarity and the desired moles of solute.

• For example, to obtain 0.250 mol of AlCl extsubscript{3} with concentrations of 0.250 M, the calculation is straightforward: 0.250 mol / 0.250 M, resulting in 1 liter.
• Similarly, for 3.00 M HCl, the volume required to provide 0.250 mol is calculated as 0.250 mol / 3.00 M, equaling approximately 0.083 liters or 83 mL.

Volume calculations are essential for designing and scaling chemical experiments, where knowing the precise quantity of reactants is necessary for successful reactions.

Chemical Solutions

Chemical solutions consist of a solute, the substance being dissolved, and a solvent, the medium that dissolves the solute. Solutions are homogeneous mixtures where the composition is uniform throughout.

• The solute and solvent interact at the molecular level, forming a single-phase environment where chemical reactions can occur.
• Understanding the properties of chemical solutions, such as their concentration, is essential for many scientific and industrial processes.

Making a solution involves dissolving a precise amount of solute into a known volume of solvent. The process is affected by factors such as temperature, pressure, and the nature of solute-solvent interactions. By changing these factors, you can influence how solutes dissolve and how the solutions function.
Chemical solutions are fundamental in everyday applications, from manufacturing to pharmaceutical formulations. In laboratory settings, the precise preparation and understanding of solutions are critical for the accuracy and repeatability of experiments.