Problem 43 - General Chemistry: Principles and Modern Applications

Question

A 10.00 mL sample of \(2.05 \mathrm{M} \mathrm{KNO}_{3}\) is diluted to a volume of \(250.0 \mathrm{mL}\). What is the concentration of the diluted solution?

Step-by-Step Solution

Answer

The concentration of the diluted solution is 0.082 M.

Step 1: Identify the Knowns

First identify all the known values. The volume of the initial solution (V1) is given as 10.00 mL or 0.01 L since the volumes in this formula must be in Liters. The molarity of the initial solution (M1) is given as 2.05 M. The final volume after dilution (V2) is given as 250.0 mL or 0.25 L. The goal is to find the molarity of the solution after dilution (M2), which is currently unknown.

Step 2: Apply Dilution Formula

To determine the molarity of the diluted solution, use the molarity dilution equation: M1V1 = M2V2. Plug all known values into the equation: (2.05 M)*(0.01 L) = M2* (0.25 L).

Step 3: Solve for the Unknown

Next, rearrange the equation by dividing both sides by 0.25 L to solve for M2, the molarity of the diluted solution. This leads to the following calculation: M2 = (2.05 M * 0.01 L) / 0.25 L.

Step 4: Calculate Molarity of the Diluted Solution

Perform the calculation in Step 3, leading to a result: M2 = 0.082 M. This is the molarity of the diluted potassium nitrate solution.

Key Concepts

Molarity

The concept of molarity is a fundamental aspect of chemistry. Molarity (M) refers to the concentration of a solution and is defined as the number of moles of solute per liter of solution. It's a way to express how much of a given substance is present in a certain volume of liquid. For example, if you have a solution labeled as `2.05 M KNO3`, it means that there are 2.05 moles of potassium nitrate dissolved in every liter of the solution. Understanding molarity is crucial in many areas of chemistry, including reaction stoichiometry, where knowing the exact concentration allows for the precise calculation of reactants and products. Molarity is typically used in the context of liquids where substances are dissolved in water or another solvent, making it important for laboratory work and industrial applications.

Volume Conversion

Volume conversion is an essential step in many chemical calculations, particularly when you are working with different units. In chemistry, volume is often expressed in milliliters (mL) or liters (L). However, most equations, like the dilution equation used in our example, require the volume to be in liters.

• 1 liter (L) is equal to 1000 milliliters (mL).
• To convert from milliliters to liters, divide the number of milliliters by 1000.

For instance, when given a volume of `250.0 mL`, converting to liters involves dividing by 1000, yielding `0.25 L`. This conversion is crucial because using the correct unit ensures that the values work properly in calculations, reducing the risk of errors.

Dilution Formula

The dilution formula is a simple yet powerful tool in chemistry. The formula, expressed as \( M_1V_1 = M_2V_2 \), is used to relate the concentrations and volumes of two solutions before and after dilution. This equation can be particularly useful when trying to determine the final concentration of a solution after adding solvent.Here's a breakdown of what each term represents:

• \( M_1 \) is the initial molarity (concentration) of the solution.
• \( V_1 \) is the initial volume of the solution.
• \( M_2 \) is the final molarity after dilution.
• \( V_2 \) is the final volume of the solution.

In our original exercise, knowing the initial concentration and volume allows us to apply this formula to determine the new concentration after dilution. When we rearrange to solve for \( M_2 \), the resulting formula becomes \( M_2 = \frac{M_1V_1}{V_2} \). This approach ensures accurate predictions regarding how dilution affects solution concentration, making it an essential concept for mixing solutions in both laboratory and industrial settings.