Question

If \(3.5 \mathrm{~L}\) of a \(4.8 \mathrm{M} \mathrm{SrCl}_{2}\) solution is diluted to \(45 \mathrm{~L},\) what is the molarity of the diluted solution?

Short answer

The molarity of the diluted solution is 0.37 M.

Step-by-step solution

Understand the Concept of Dilution

Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. The total amount of solute remains the same, so we can use the equation M1V1 = M2V2, where M1 and V1 are the molarity and volume of the initial concentrated solution, and M2 and V2 are the molarity and volume of the final diluted solution.

Identify Known Values

The initial molarity (M1) is 4.8 M, and the initial volume (V1) is 3.5 L. The final volume (V2) after dilution is 45 L. The molarity of the diluted solution (M2) is unknown and is what we are solving for.

Set Up the Dilution Equation

We use the dilution equation: M1V1 = M2V2. Substituting the known values we have: (4.8 M)(3.5 L) = (M2)(45 L).

Solve for the Molarity of the Diluted Solution

We rearrange the equation to solve for M2: M2 = (M1V1) / V2. Substitute the given values to find M2: M2 = (4.8 M * 3.5 L) / 45 L.

Perform the Calculation

Performing the calculation gives M2 = (16.8) / 45 = 0.3733 M. The molarity of the diluted solution is 0.3733 M, which can be rounded to two significant figures based on the precision of the given values, resulting in 0.37 M.

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution. It represents the number of moles of a substance in one liter of solution, and it's expressed in units of moles per liter (M or mol/L). To calculate molarity, you divide the number of moles of the solute by the volume of the solution in liters.

Understanding molarity is crucial for many chemistry calculations because it allows scientists and students to comprehend and predict the number of particles involved in chemical reactions. When you have a given molarity, it's understood that you are referring to a specific volume of solution, which makes it easier to scale the reactions up or down, like in dilution processes or when preparing solutions for experiments.

Dilution Equation

The dilution equation is a simple formula used to determine the new concentration of a solution after it has been diluted. It's given as: \(M_1V_1 = M_2V_2\), where \(M_1\) is the initial molarity, \(V_1\) is the initial volume, \(M_2\) is the final molarity, and \(V_2\) is the final volume of the solution.

This equation is based on the principle of conservation of mass, which states that the amount of solute remains constant before and after dilution. By rearranging the equation, you can solve for any unknown variable. For example, if you know the initial concentration and volume and the final volume, you can solve for the final concentration after dilution, which is common in laboratory work to prepare solutions of desired concentrations.

Concentration of Solution

The concentration of a solution describes how much solute is present in a given quantity of solvent. It can be expressed in various ways, including molarity, molality, weight percent, and volume percent. Molarity is one of the most frequently used measures because it directly relates to the volume of solution, which is easy to measure in a lab setting.

It is important to note that the concentration can change by adding more solute to the solution or by changing the amount of solvent, typically through processes such as evaporation or dilution. Understanding the concentration of a solution is fundamental in chemistry as it affects the rate of chemical reactions and the extent of reaction that can occur.

Stoichiometry

Stoichiometry is the section of chemistry that involves calculating the amounts of reactants and products in a chemical reaction. It's based on the conservation of mass and the concept of the mole, allowing chemists to predict the yield of products from a given quantity of reactants.

The calculations involve using balanced chemical equations and unit conversion known as the mole ratio. Stoichiometry can be complex but mastering this tool is essential for conducting accurate chemical reactions and for practical applications, such as calculating medication dosages in pharmacy, determining the fuel efficiency in combustion engines, or optimizing the use of reactants in industrial processes.