- Analyze the definition of molar concentration as mol/L, independent of solution volume.
- List the concentration for each solution: \(1.0\text{ M}\), \(10\text{ M}\), \(10\text{ M}\), and \(10.5\text{ M}\).
- Compare the values to identify that \(10.5\text{ M}\) is the maximum.
- Identify the solution corresponding to \(10.5\text{ M}\) as the most concentrated: \(\boxed{2.0\text{ mL of } 10.5\text{ M H}_2\text{O}_2}\).
Explanation
- Understanding the Definition of Concentration
To determine which solution is the most concentrated, we need to compare the molarity (concentration) values provided for each solution. Concentration, typically measured in Molarity (\(M\)), is defined as the amount of solute in moles per liter of solution (\(mol/L\)). The problem specifically asks for the "most concentrated" solution, which means we are looking for the solution with the highest numerical value for its molar concentration. It is important to note that the volume of the solution provided (e.g., \(5.0\text{ mL}\), \(100\text{ mL}\)) does not affect the concentration value itself; it only describes the quantity of the specific solution being considered.
- Extracting and Comparing Molarity Values
Now, we extract the molarity (\(M\)) for each of the four solutions provided:
- Solution 1: \(5.0\text{ mL}\) of \(1.0\text{ M PbSO}_4\). The concentration is \(C_1 = 1.0\text{ M}\).
- Solution 2: \(2.0\text{ mL}\) of \(10\text{ M H}_2\text{SO}_4\). The concentration is \(C_2 = 10\text{ M}\).
- Solution 3: \(100\text{ mL}\) of \(10\text{ M NaCl}\). The concentration is \(C_3 = 10\text{ M}\).
- Solution 4: \(2.0\text{ mL}\) of \(10.5\text{ M H}_2\text{O}_2\). The concentration is \(C_4 = 10.5\text{ M}\).
- Conclusion and Final Answer
We compare the four concentration values: \(1.0\text{ M}\), \(10\text{ M}\), \(10\text{ M}\), and \(10.5\text{ M}\).
Clearly, \(10.5\text{ M} > 10\text{ M} > 1.0\text{ M}\).
Since \(10.5\text{ M}\) is the highest value among the options, the fourth solution is the most concentrated. Therefore, the \(2.0\text{ mL}\) of \(10.5\text{ M H}_2\text{O}_2\) solution has the highest concentration.
Examples
In chemistry laboratories, identifying concentration is essential for safely diluting reagents. For example, if a researcher needs to perform an oxidation reaction using hydrogen peroxide (\(H_2O_2\)), knowing that a \(10.5\text{ M}\) solution is more concentrated than a \(1.0\text{ M}\) lead sulfate solution allows the researcher to determine which reagent needs more significant dilution to reach a desired working strength, ensuring both safety and experimental precision.