Problem 73 - Chemistry: The Central Science

Question

(a) You have a stock solution of \(14.8 \mathrm{M} \mathrm{NH}_{3}\). How many milliliters of this solution should you dilute to make \(1000.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{NH}_{3} ?\) (b) If you take a 10.0-mL portion of the stock solution and dilute it to a total volume of \(0.500 \mathrm{~L}\), what will be the concentration of the final solution?

Step-by-Step Solution

Answer

(a) To make 1000.0 mL of 0.250 M NH3 solution, you should dilute 16.9 mL of the 14.8 M NH3 stock solution. (b) The concentration of the final solution after diluting 10.0 mL of the stock solution to a total volume of 0.500 L will be 2.96 M.

Step 1: Part (a): Find the volume of stock solution needed for dilution

We are given: M1 = 14.8 M (concentration of the stock NH3 solution) M2 = 0.250 M (concentration of the final NH3 solution) V2 = 1000.0 mL (volume of the final NH3 solution) We need to find V1 (volume of the stock NH3 solution to be diluted). Using the dilution formula, M1V1 = M2V2, we can find V1: V1 = (M2 * V2) / M1 Plug in the given values and calculate V1: V1 = (0.250 * 1000.0) / 14.8 = 250/14.8 = 16.9 mL Therefore, 16.9 mL of the stock solution should be diluted to make 1000.0 mL of 0.250 M NH3 solution.

Step 2: Part (b): Concentration of the final solution after dilution

We are given: V1 = 10.0 mL (volume of the stock NH3 solution) M1 = 14.8 M (concentration of the stock NH3 solution) V2 = 500.0 mL (total volume of the final NH3 solution after dilution) We need to find M2 (concentration of the final NH3 solution). Using the dilution formula, M1V1 = M2V2, we can find M2: M2 = (M1 * V1) / V2 Plug in the given values and calculate M2: M2 = (14.8 * 10.0) / 500.0 = 148/50 = 2.96 M Therefore, the concentration of the final solution after dilution will be 2.96 M.

Key Concepts

Dilution Formula

Understanding the dilution formula is essential when working with solutions in chemistry. It helps calculate the amount of solvent needed to achieve a desired concentration of a solution, or conversely, to determine the concentration after dilution has occurred. The formula can be expressed as:

\[ M_1V_1 = M_2V_2 \]
where:

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

In practice, scientists often start with a concentrated 'stock' solution. By adding a calculated volume of solvent (such as water), they can prepare a less concentrated solution suitable for various experiments. This method ensures precision and consistency in the preparation of solutions in the laboratory.

Molarity

When we talk about the molarity (M) of a solution, we are referring to its concentration, specifically the moles of solute per liter of solution. It's one of the most common ways to express concentration in chemistry and is calculated as follows:

\[ Molarity (M) = \frac{moles\ of\ solute}{liters\ of\ solution} \]
When you're performing dilutions, keeping track of the molarity is crucial because it tells you how 'strong' or 'weak' the solution is. Imagine you have lemon concentrate; the molarity can tell you how much water you need to add to achieve the lemonade flavor you desire. By changing the volume of the solution while keeping the amount of solute constant, you can adjust the molarity to your requirements.

Concentration of Solutions

The concentration of a solution represents the proportion of one substance (the solute) dissolved within another (the solvent). The higher the concentration, the more solute is present in a given volume of solution. It's a fundamental concept not just in chemistry but also in biology and environmental sciences, where the effects of various substances on organisms or ecosystems often depend on their concentrations.

Concentration can be expressed in various units such as molarity, molality, normality, or percent composition, each suitable for different scenarios. This variety allows scientists to choose the best way to express and communicate the amount of a substance in a given solution, depending on the context of their work. For instance, while molarity is typically used for reactions in solutions, percent composition can be a more intuitive way to describe the concentration of components in consumer products.

Volumetric Analysis

Volumetric analysis, also known as titrimetry, is a technique in analytical chemistry that measures the volume of a solution as it reacts with another substance. The precise measurement of volume allows for the determination of an unknown concentration. It involves a sequence of adding measured volumes of reactants, the use of indicators to denote the end of a reaction, and calculations to find the sought-after concentration.

Techniques in Volumetric Analysis

There are several types of volumetric analysis, including but not limited to acid-base titrations, redox titrations, and precipitation titrations. Each type is suited for specific kinds of chemical reactions and provides information vital to identifying substance concentrations.

In educational settings, volumetric analysis teaches students accuracy and precision in measuring and titration. Meanwhile, in industry, it is used for quality control to ensure that products meet specified standards concerning their chemical components.