Question

If 123 \(\mathrm{mL}\) of a 1.1 \(\mathrm{M}\) glucose solution is diluted to \(500.0 \mathrm{mL},\) what is the molarity of the diluted solution?

Short answer

The molarity of the diluted solution is \(\frac{1.1 \times 123}{500.0}\) M, which simplifies to around 0.272 M.

Step-by-step solution

Identify the Dilution Formula

To solve this problem, we use the dilution formula: \( C_1V_1 = C_2V_2 \), where \(C_1\) is the initial concentration, \(V_1\) is the initial volume, \(C_2\) is the final concentration, and \(V_2\) is the final volume.

Plug in the Known Values

The initial concentration \(C_1\) is 1.1 M, the initial volume \(V_1\) is 123 mL, and the final volume \(V_2\) is 500.0 mL. We need to find the final concentration \(C_2\). The equation with known values is: \(1.1 \text{ M} \times 123\text{ mL} = C_2 \times 500.0\text{ mL}\).

Solve for the Final Concentration

To find \(C_2\), divide both sides by the final volume \(V_2\): \(C_2 = \frac{1.1 \text{ M} \times 123\text{ mL}}{500.0\text{ mL}}\).

Calculate the Final Molarity

Perform the calculation: \(C_2 = \frac{1.1 \times 123}{500.0}\) M. This gives the molarity of the diluted solution.

Key concepts

Dilution Formula

Understanding the dilution formula is a key step in mastering solution chemistry. It allows you to calculate the concentration of a solution after it has been diluted. The fundamental dilution formula is expressed as: \( C_1V_1 = C_2V_2 \) where:\
\

• \(C_1\) is the initial concentration.
• \(V_1\) is the initial volume.
• \(C_2\) is the final concentration after dilution.
• \(V_2\) is the final volume.

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Using this formula, we can manipulate the concentration and volume of solutions to reach desired levels. For instance, in the exercise provided, we use the initial values and the final volume to find out the final concentration after the solution has been diluted. The key takeaway is that no matter the dilution, the amount of solute present stays the same, which is the foundation of this formula.

Molarity Concentration

Molarity, denoted by \(M\), is a measure of concentration in chemistry that describes the number of moles of a solute per liter of solution. It is crucial when preparing solutions and understanding their chemical properties. One mole corresponds to Avogadro's number of molecules or atoms, typically \(6.022 \times 10^{23}\). So, when we express a molarity of 1.1 M, as in our example, we're saying that in every liter of solution, there is 1.1 moles of glucose. Molarity is involved in a multitude of calculations, such as those involving chemical reactions and dilutions. For students and chemists alike, being adept with molarity is essential for accuracy in both the laboratory and classroom settings.

Volume Conversion

In many scientific calculations, we need to convert volumes from one unit to another. A common conversion is from milliliters \(\mathrm{mL}\) to liters \(\mathrm{L}\) since molarity is moles per liter. Remember that \(1000 \mathrm{mL}\) is equivalent to \(1 \mathrm{L}\). When dealing with volume conversions, keeping track of the units is crucial to ensure the accuracy of your calculations. For example, if your original volume is in milliliters, but your concentration is given in molarity (moles per liter), you'll need to convert your volume to liters before using it in the dilution formula. This attention to detail can be the difference between a correct solution and a significant error in chemistry.

Solution Preparation

Preparing solutions with the correct concentration is a fundamental skill in chemistry. Whether it's for an experiment or a titration, the process involves measuring the solute and solvent accurately and mixing them thoroughly. When diluting, the goal is to decrease a solution's concentration by adding more solvent. In practice, to dilute a solution, you would measure the required volume of the original solution and then add solvent up to the desired final volume, as illustrated in the example exercise. It is important to mix the solution well after the dilution to ensure that the solute is evenly distributed throughout the new volume. Always remember to label the diluted solution correctly with the new concentration value to prevent any potential confusion during future use.