How would you prepare a \(6.00 M \mathrm{HNO}_{3}\) solution if only \(3.00 \mathrm{M}\) and \(12.0 \mathrm{M}\) solutions of the acid are available for mixing?

Understanding the concentration of solutions is a cornerstone in chemistry, especially when preparing a specific solution from different concentrations. The concentration of a solution is a measure of the amount of solute that is dissolved in a given quantity of solvent or solution. Imagine if you have a glass of lemonade: the sugar and lemon juice mixed with the water determine the concentration - more sugar means a sweeter (more concentrated) drink.

When a student encounters a problem related to preparing solutions, knowing the concentration concept is crucial. Concentration can be expressed in various ways, such as molarity, molality, or parts per million (ppm), with molarity being the most commonly used in academic settings. By adjusting the concentration, students can learn to control reactions and understand their mechanisms, which is a valuable skill in laboratory and industrial settings.

Molarity is a term that comes up frequently in chemistry and is symbolized by 'M'. It's defined as the number of moles of solute per liter of solution. The moles of a substance are a measurement of particles, often molecules or atoms. If you have a 1.00 M sugar solution, this means you have 1 mole of sugar dissolved in 1 liter of water. It's like saying you have a certain number of sugar packets per jug of water — a way of quantifying the 'strength' of your solution.

To calculate molarity, you use the formula:
\( M = \frac{{moles\text{{ of solute}}}}{{volume\text{{ of solution in liters}}}} \). This formula embodies the heart of preparing solutions in chemistry, allowing students to calculate the exact amount to mix to achieve a desired concentration. Remember, accurate measurements are key to getting reliable results in any experiment!

The principle of mixtures plays a crucial role when combining two solutions to achieve a target molarity. It's based on the concept that when you combine solutions, their volumes are additive, and the amount of substance in the combined volume is the sum from each original solution.

Understanding Volume Addition

When you pour 50 mL of water into a 100 mL of alcohol, you don't get 150 mL of solution due to volume contraction, but when solving chemistry problems, we assume volumes are additive for simplicity. In the exercise given, we assume that mixing 3.00 M and 12.0 M \( \text{{HNO}}_3 \) solutions will give us a simple sum of their volumes.

Applying the Equation

By understanding this principle and applying the equation \( C_1V_1 + C_2V_2 = C_fV_f \), students can calculate the correct proportions of each solution to mix to get the desired concentration. It's like following a recipe to get the perfect flavor - you need to know the right amount of each ingredient to add. Just as a chef uses the principle of mixtures to combine flavors, chemists use it to create solutions of needed strength and volume for their experiments.