Question

A beaker containing \(150.0 \mathrm{~mL}\) of \(0.1 M\) glucose is represented by (a). Which of the drawings (b)-(d) represents the solution that results when \(50.0 \mathrm{~mL}\) is withdrawn from (a) and then diluted hy a factor of \(4 ?\)

Short answer

Drawing with 0.025 M concentration in 200 mL.

Step-by-step solution

Understand Initial Conditions

The initial solution is 150.0 mL of 0.1 M glucose. This means there are 0.015 moles of glucose in the beaker because moles = volume (L) × molarity = 0.150 L × 0.1 M.

Calculate Amount Withdrawn

We withdraw 50.0 mL of the solution. Since the concentration is consistent, we can find the moles in the withdrawn volume: moles = 0.050 L × 0.1 M = 0.005 moles.

Consider Dilution Process

After withdrawing, the solution containing 0.005 moles of glucose is then diluted by a factor of 4. This means that the new total volume of the solution is four times the withdrawn volume: 50.0 mL × 4 = 200.0 mL.

Calculate New Concentration

The new concentration is calculated by dividing the moles of glucose by the new volume in liters: \(\text{New Molarity} = \frac{0.005 \text{ moles}}{0.200 \text{ L}} = 0.025 M\).

Identify the Correct Drawing

Look among drawings (b)-(d) and identify which one represents a solution with a concentration of 0.025 M in a 200 mL volume. Choose the drawing consistent with these numbers.

Key concepts

Molarity

Molarity is an important concept in chemistry that refers to the concentration of a solution. It is defined as the number of moles of a solute (the substance being dissolved) divided by the total volume of the solution in liters. The formula to calculate molarity is \( M = \frac{n}{V} \), where \( M \) is the molarity, \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters.

For example, if you have a solution with 0.1 moles of glucose dissolved in 1 liter of water, the molarity of the solution is 0.1 M. This unit is often used in laboratory settings to specify the concentration of chemical solutions. When performing dilution calculations, knowing the molarity of a solution allows you to determine how much of a solution is needed to achieve a desired concentration.

Understanding molarity helps in titration and many other chemical calculations. It allows chemists to properly balance reactions and prepare solutions with precise concentrations.

Solution Concentration

Solution concentration is a measure of the amount of solute that is dissolved in a given quantity of solvent. It can be expressed in several ways, such as molarity, molality, or percentage concentration. In our context, we focus on molarity because it's particularly useful in calculating changes during dilution.

To assess the concentration of a solution, consider the initial number of moles present and how they change when the solution is altered. For instance, if you begin with 0.015 moles of glucose in 150 mL of solution, withdrawing 50 mL will proportionally decrease the moles present. Ultimately, understanding these shifts helps draw the correct connections between the properties of the solution.

The ability to modify solution concentration is crucial in many chemical processes. Balancing concentrations ensures reactions occur efficiently and desired products are formed correctly.

Volume Conversion

Volume conversion is a fundamental skill needed when dealing with solutions, as volumes may need to be adjusted or converted when calculating concentrations. In the metric system, common units of volume like milliliters (mL) and liters (L) must be convertible seamlessly.

For example, remember that 1,000 mL equals 1 L. When calculating molarity or performing dilution, it's essential to work in consistent units. This means converting all volumes to liters when needed. If the original exercise involves withdrawing 50 mL from a solution, converting this to liters by dividing by 1,000 gives 0.050 L, simplifying further calculations.

• Keep units consistent to avoid errors during conversion.
• Always double-check calculations to ensure accuracy.

By mastering volume conversion, you safeguard against avoidable calculation mistakes and ensure accuracy in chemical problem-solving.