The volume of water that must be added in order to dilute 40 mL of 9.0 M HCl to a concentration of 6 — Solutions Chemistry Question

STEPS:

1. Identify the Core Concept: This problem involves the dilution of a solution. The fundamental principle of dilution is that while the concentration and volume change, the total number of moles of solute remains constant because no solute is added or removed.
2. Select the Appropriate Equation: The relationship between concentration (molarity) and volume during dilution is expressed by the equation:
$$M_1V_1 = M_2V_2$$
where $M$ is molarity and $V$ is volume.
3. Plug in the Known Variables: From the question, identify the specific values provided:
* Initial molarity ($M_1$) = 9.0 M
* Initial volume ($V_1$) = 40 mL
* Final desired molarity ($M_2$) = 6.0 M
* Final total volume ($V_2$) = unknown
4. Calculate the Final Total Volume ($V_2$): Rearrange the equation to solve for $V_2$:
$$(9.0\text{ M}) \times (40\text{ mL}) = (6.0\text{ M}) \times V_2$$
$$360 = 6.0 \times V_2$$
$$V_2 = \frac{360}{6.0} = \mathbf{60\text{ mL}}$$
5. Determine the Volume of Water Added: The final total volume of the solution ($V_2$) is the sum of the initial volume ($V_1$) and the volume of water added. To find the amount of water that must be added, subtract the initial volume from the calculated final volume:
$$\text{Volume of water added} = V_2 - V_1$$
$$\text{Volume of water added} = 60\text{ mL} - 40\text{ mL} = \mathbf{20\text{ mL}}$$
6. Conclusion: Adding 20 mL of water will increase the total volume from 40 mL to 60 mL, thereby reducing the concentration from 9.0 M to 6.0 M. This corresponds to option B.

WHY_OTHERS_WRONG:

• A) 10 mL: This value would result in a total volume of 50 mL ($40 + 10$), which would yield a concentration of 7.2 M ($360 / 50$), not the required 6.0 M.
• C) 30 mL: This might result from a calculation error or an incorrect assumption about the inverse relationship between concentration and volume.
• D) 40 mL: Adding 40 mL would double the initial volume to 80 mL. According to the dilution equation, doubling the volume results in halving the concentration, which would make the final solution 4.5 M rather than 6.0 M.
• E) 60 mL: This is a common "distractor" answer. 60 mL is the total final volume of the solution ($V_2$). However, the question specifically asks for the volume of water that must be added to the existing 40 mL to reach that final volume.