To calculate the concentration of a diluted solution, you typically use a simple formula that relates the concentrations and volumes of the original and diluted solutions.
The formula you'll generally use to calculate dilutions is:
C1V1 = C2V2
Where:
- C1 is the concentration of the original, more concentrated stock solution.
- V1 is the volume of the original stock solution that you will use for the dilution.
- C2 is the desired concentration of the final, diluted solution.
- V2 is the desired final volume of the diluted solution.
Here's a breakdown of how to apply this formula:
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Identify the known values: Determine the values for C1, V1, C2, and V2 based on the information given in the problem.
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Rearrange the formula (if needed): Depending on what you're trying to find, you might need to rearrange the formula. For example, if you need to find V1 (the volume of the stock solution needed), you would rearrange the formula as:
- V1 = (C2V2) / C1
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Plug in the values: Substitute the known values into the formula. Make sure the units for volume are consistent (e.g., both in mL or both in L).
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Solve for the unknown value: Perform the calculation to find the unknown concentration or volume.
Example:
Let's say you have a stock solution of 1 M NaCl (C1 = 1 M) and you want to make 500 mL (V2 = 500 mL) of a 0.1 M NaCl solution (C2 = 0.1 M). How much of the 1 M stock solution do you need?
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Identify knowns:
- C1 = 1 M
- C2 = 0.1 M
- V2 = 500 mL
- V1 = ? (This is what we want to find)
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Rearrange formula:
- V1 = (C2V2) / C1
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Plug in values:
- V1 = (0.1 M * 500 mL) / 1 M
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Solve:
- V1 = 50 mL
Therefore, you would need 50 mL of the 1 M NaCl stock solution, and you would dilute it with enough solvent (typically water) to reach a final volume of 500 mL.
