To what volume should 250 cm³ of 2M HCl be diluted in order to obtain a 0.1M solution of acid?
Answer (2)
Use the dilution formula: M 1 V 1 = M 2 V 2 .
Plug in the given values: M 1 = 2 M , V 1 = 250 cm 3 , M 2 = 0.1 M .
Solve for V 2 : V 2 = M 2 M 1 V 1 = 0.1 M ( 2 M ) ( 250 cm 3 ) .
Calculate the final volume: V 2 = 5000 cm 3 . The final answer is 5000 cm 3 .
Explanation
Understanding the Problem We are given an initial volume and concentration of HCI, and we want to dilute it to a lower concentration. We need to find the final volume after dilution.
Stating the Dilution Formula We can use the dilution formula, which states that the product of the initial molarity and volume is equal to the product of the final molarity and volume: M 1 V 1 = M 2 V 2 where:
M 1 is the initial molarity,
V 1 is the initial volume,
M 2 is the final molarity,
V 2 is the final volume.
Identifying Given Values We are given:
M 1 = 2 M (initial concentration)
V 1 = 250 cm 3 (initial volume)
M 2 = 0.1 M (final concentration) We need to find V 2 (final volume).
Calculating the Final Volume Rearrange the dilution formula to solve for V 2 :
V 2 = M 2 M 1 V 1 Plug in the given values: V 2 = 0.1 M ( 2 M ) ( 250 cm 3 ) V 2 = 0.1 M 500 M ⋅ cm 3 V 2 = 5000 cm 3
Final Answer Therefore, to obtain a 0.1 M solution of HCI, 250 cm³ of 2 M HCI should be diluted to a volume of 5000 cm³.
Examples
Dilution is a common practice in chemistry, biology, and medicine. For example, in a lab, you might have a concentrated stock solution of a chemical. To use it in an experiment, you often need to dilute it to a lower concentration. The dilution formula helps you calculate exactly how much solvent (usually water) to add to achieve the desired concentration. This is also relevant in everyday life, such as when you dilute concentrated juice or cleaning solutions to make them safe and effective for use.
To dilute 250 cm³ of 2M HCl to a 0.1M concentration, you should dilute it to a final volume of 5000 cm³ using the dilution formula: M 1 V 1 = M 2 V 2 . This ensures the final concentration of the solution is correct at 0.1M.
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