Question

When a concentrated stock solution is diluted to prepare a less concentrated reagent, the number of ____________ is the same both before and after the dilution.

Short answer

When a concentrated stock solution is diluted to prepare a less concentrated reagent, the number of moles of solute is the same both before and after the dilution. This is confirmed through the equation \(C_1V_1 = C_2V_2\) and the derived relationship \(n_1 = n_2\).

Step-by-step solution

Identify the property that remains constant during dilution

When a concentrated stock solution is diluted to prepare a less concentrated reagent, the number of moles of solute (the substance being dissolved) remains the same before and after the dilution.

Express the relationship between initial and final conditions

To confirm the property that remains the same before and after the dilution, we can use the equation relating the initial and final conditions of the solution: \(C_1V_1 = C_2V_2\) where: - \(C_1\) is the initial concentration of the stock solution - \(V_1\) is the initial volume of the stock solution - \(C_2\) is the final concentration of the diluted solution - \(V_2\) is the final volume of the diluted solution

Derive the relationship between moles of solute

Recall that moles can be calculated by multiplying the concentration by the volume. Therefore, we can rewrite the above equation in terms of moles: \(n_1 = n_2\) where: - \(n_1 = C_1V_1\) represents the moles of solute in the stock solution - \(n_2 = C_2V_2\) represents the moles of solute in the diluted solution Since this equation demonstrates that \(n_1 = n_2\), the number of moles of solute remains the same before and after the dilution process. Therefore, the answer to the exercise is: The number of moles of solute is the same both before and after the dilution.

Key concepts

Understanding Concentration

Concentration in chemistry refers to the amount of a substance, typically called a solute, present in a specific volume of solution. It helps in indicating how much of a solute is mixed with the solvent. Concentration is commonly expressed in molarity (M), which is defined as the number of moles of solute per liter of solution.
This measure allows chemists to create solutions with accurate chemical compositions. To calculate concentration, you use the formula:

• Concentration (C) = Moles of Solute (n) / Volume of Solution (V)

By manipulating this equation, you can also find either the quantity of solute present for a given solution or the amount of solvent required to achieve a desired concentration.
Understanding concentration is key in dilution, where a stock solution (a more concentrated solution) is used to create a solution of interest with a lower concentration.

Significance of Moles of Solute

The concept of moles is fundamental in chemistry for measuring quantities of a substance. One mole corresponds to Avogadro's number, which is approximately 6.022 x 10²³ entities (atoms, ions, or molecules). The use of moles allows chemists to count particles in reactions and solutions efficiently.
The number of moles of solute before and after a dilution remains constant. This is because dilution involves only adding more solvent without altering the amount of substance (solute) present in the solution.
Mathematically, this is why the equation,

• \(n_1 = n_2\)

where \(n_1\) is the initial moles of solute and \(n_2\) is the final moles of solute, holds true.
This principle ensures that while you may have changed the concentration through altering the volume, the total amount of solute remains unchanged.

Role of Stock Solution

A stock solution is a concentrated solution that serves as a starting point for producing solutions of lower concentrations. In laboratories, stock solutions are invaluable for saving time and ensuring consistency when preparing series of solutions with varying concentrations.
When using a stock solution, a portion of it is mixed with a solvent to achieve the desired concentration. It's important to utilize the dilution equation,

• \(C_1V_1 = C_2V_2\)

to ensure the number of moles of solute remains the same.
In practical terms, this allows one to precisely dilute a highly concentrated solution while maintaining the consistency and accuracy of chemical reactions. Hence, stock solutions simplify the logistic and practical aspects of preparing solutions by ensuring that concentration is accurately adjusted without wastage.