Question

Are the following instructions for diluting a \(10.0 M\) solution to a \(1.00 \mathrm{M}\) solution correct: "Take \(100.0 \mathrm{~mL}\) of the \(10.0 \mathrm{M}\) solution and add \(900.0 \mathrm{~mL}\) water"? Explain.

Short answer

Yes, the instructions are correct. Following them yields a \(1.00 \, M\) solution.

Step-by-step solution

- Identify Initial and Final Concentrations

The initial concentration is given as \(10.0 \, M\), and the final concentration is required to be \(1.00 \, M\).

- Determine Initial Volume

The initial volume of the \(10.0 \, M\) solution taken for dilution is \(100.0 \, mL\).

- State the Volume Addition

According to the instructions, \(900.0 \, mL\) of water is to be added to the initial solution.

- Calculate Final Volume

Add the initial volume of the solution to the volume of water added: \(100.0 \, mL + 900.0 \, mL = 1000.0 \, mL\). The total final volume is \(1000.0 \, mL\) or \(1.00 \, L\).

- Apply Dilution Formula

Use the dilution formula: \(C_1V_1 = C_2V_2\). Here, \(C_1 = 10.0 \, M\), \(V_1 = 100.0 \, mL\), \(C_2 = 1.00 \, M\), and \(V_2 = 1000.0 \, mL\).

- Verify the Calculations

Calculate if the final concentrations match: \(10.0 \, M \times 100.0 \, mL = 1.00 \, M \times 1000.0 \, mL\). The equation balances, indicating the dilution is correct.

- Conclusion

Based on calculations and the given instructions to add \(900.0 \, mL\) water to \(100.0 \, mL\) of \(10.0 \, M\) solution, the final concentration is indeed \(1.00 \, M\).

Key concepts

Molarity

Molarity is a measure of the concentration of a solution. It is defined as the number of moles of solute per liter of solution. The formula for molarity is: \( M = \frac{n}{V} \), where \(M\) is the molarity, \(n\) is the number of moles of solute, and \(V\) is the volume of the solution in liters.
For example, if you dissolve 1 mole of a substance in 1 liter of water, the molarity of the solution is \(1 \, M\).
Molarity helps in understanding how much of a substance is present in a given volume of solution.
It is an important concept in chemistry because it allows for the precise formulation of solutions for reactions.

Concentration

Concentration refers to the amount of a substance in a given volume. It can be expressed in different ways, such as molarity (\(M\)), mass percent, and volume percent.
In the exercise provided, we use molarity to express concentration. Understanding concentration helps to predict how substances interact in a mixture or solution.
The concentration changes when you dilute a solution. In the exercise, the initial concentration is \(10.0 \, M\), and we dilute it to achieve a target concentration of \(1.00 \, M\). Dilution involves adding more solvent (like water) to decrease the concentration of the solute without changing the number of moles of solute present.

Volume

Volume is the amount of space a substance occupies. In the context of solutions, volume is crucial in determining the final concentration after dilution.
When diluting, we need to add the volume of the initial solution to the volume of the solvent added. For instance, in our exercise, the initial volume is \(100.0 \, mL\) and \(900.0 \, mL\) of water is added, resulting in a total final volume of \(1000.0 \, mL\) or \(1.00 \, L\).
By understanding volume, we can use the dilution formula, \( C_1V_1 = C_2V_2 \), where \(C_1\) and \(C_2\) are the initial and final concentrations, and \(V_1\) and \(V_2\) are the initial and final volumes. This formula helps us determine if the final concentration meets the desired specification.