Problem 1 - Chemical Principles in the Laboratory

Question

7.0 mL of 6.0 M NaOH are diluted with water to a volume of 400 mL. You are asked to find the molarity of the resulting solution. a. First find out how many moles of NaOH there are in 7.0 mL of 6.0 M NaOH. Use Equation 1. Note that the volume must be in liters. ____________ moles b. Since the total number of moles of NaOH is not changed on dilution, the molarity after dilution can also be found by Equation 1, using the final volume of the solution. Calculate that molarity. ____________ M

Step-by-Step Solution

Answer

The final molarity is 0.105 M.

Step 1: Convert Volume to Liters

First, convert the given volume of NaOH from milliliters (mL) to liters (L). We know that 1000 mL is equal to 1 L. So, we have: \( 7.0 \text{ mL} = \frac{7.0}{1000} \text{ L} = 0.007 \text{ L} \).

Step 2: Calculate Moles of NaOH

Use the molarity formula \( C = \frac{n}{V} \) to find the moles of NaOH. Given the molarity \( C = 6.0 \text{ M} \) and the initial volume \( V = 0.007 \text{ L} \), we calculate the moles \( n = C \times V = 6.0 \text{ M} \times 0.007 \text{ L} = 0.042 \text{ moles} \).

Step 3: Use Dilution Formula for Final Molarity

Since the number of moles before and after dilution remains constant, use the formula for molarity \( C' = \frac{n}{V'} \), where \( n = 0.042 \text{ moles} \) (from Step 2) and \( V' = 400 \text{ mL} = \frac{400}{1000} \text{ L} = 0.4 \text{ L} \). Substitute to find the final molarity: \( C' = \frac{0.042 \text{ moles}}{0.4 \text{ L}} = 0.105 \text{ M} \).

Key Concepts

Dilution

In chemistry, dilution is a crucial concept where you reduce the concentration of a solute in a solution, typically by adding more solvent. It’s important to understand that during dilution, the amount of solute, in this case, sodium hydroxide (NaOH), stays the same. What changes is the concentration. Think of making a pitcher of lemonade less sweet by adding more water.

In our exercise, you start with a concentrated solution of NaOH at 6.0 M and transform it into a more dilute form by adding water until the total volume reaches 400 mL. The key here is realizing that while the volume increases, the number of moles of the solute remains constant. This is because you haven't added or removed any NaOH, just more water. Understanding this balance helps you use equations correctly to calculate new concentrations.

Moles

Moles are a fundamental unit in chemistry used to express amounts of a chemical substance. It connects the microscopic world of atoms and molecules with the macroscopic world we experience. One mole contains Avogadro's number (\( 6.022 imes 10^{23} \)), which allows chemists to count particles by weighing them.

In the case of our NaOH solution, moles give you a precise measure of how much NaOH you have, regardless of changes in volume. To find the moles of NaOH in a solution, you multiply the molarity (concentration) by the volume in liters. In our problem, the results show us that 0.042 moles of NaOH are present before dilution. This amount of substance stays constant even as the solution's volume is increased.

Volume Conversion

Converting volumes from milliliters (mL) to liters (L) is a necessary skill in chemistry calculations that involve concentrations and stoichiometry. One liter equals 1000 milliliters, making the conversion straightforward yet crucial for accurate calculations.

In our example, the initial volume of NaOH is given in milliliters and needs to be converted to liters to use in the molarity equation. By dividing the volume in mL by 1000 (\( 7.0 \text{ mL} = 0.007 \text{ L} \)), you can perform correct calculations that comply with the units required for scientific accuracy. Always be diligent with units, as small mistakes can lead to significant errors in results.

Chemistry Education

Chemistry education emphasizes understanding concepts rather than rote memorization. Solving problems like this one helps build a strong foundation in scientific reasoning.

Learning involves more than finding the correct answer— it’s about comprehending the "why" behind it. By working through exercises involving dilution, moles, and volume conversion, students develop critical thinking and problem-solving skills applicable to a wide range of scientific inquiries. In a classroom setting, consider experimenting with physical solutions to better grasp these abstract concepts.

• Engage in experiments to observe dilution in action.
• Use simulations to visualize mole quantities and concentration changes.
• Practice converting units to build proficiency.

Remember, chemistry is a dynamic field, evolving as it supports a better understanding of the natural world. Continuous practice makes you adept at handling various chemical calculations.