What is the estimated concentration of aspirin in solution X after diluting 2.5 mL of solution X in 50 mL of buffer?
Understand the Problem
The question is asking for the estimated concentration of aspirin in solution X after diluting 2.5 mL of it to a total volume of 50 mL. The user needs to use the appropriate calculations to find this concentration.
Answer
The estimated concentration in solution X is $1000 \, \text{mg/L}$.
Answer for screen readers
The estimated concentration in solution X is $1000 , \text{mg/L}$.
Steps to Solve
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Identify the dilution formula
To find the concentration after dilution, we use the formula:
$$ C_1V_1 = C_2V_2 $$
Where:
- ( C_1 ) = initial concentration (unknown)
- ( V_1 ) = initial volume (2.5 mL)
- ( C_2 ) = final concentration after dilution (what we want to find)
- ( V_2 ) = final volume (50 mL)
-
Rearrange the formula for concentration
To solve for ( C_2 ), rearrange the equation:
$$ C_2 = \frac{C_1V_1}{V_2} $$ -
Substitute known values
We need the initial concentration ( C_1 ) of solution X to proceed. If ( C_1 ) is given or assumed, substitute that value along with ( V_1 = 2.5 , \text{mL} ) and ( V_2 = 50 , \text{mL} ) into the rearranged formula.
Example: If ( C_1 = 20 , \text{mg/mL} ), we compute:
$$ C_2 = \frac{20 , \text{mg/mL} \times 2.5 , \text{mL}}{50 , \text{mL}} $$ -
Calculate the final concentration
Carrying out the calculation:
$$ C_2 = \frac{50}{50} = 1 , \text{mg/mL} $$ -
Convert units if necessary
If required by the problem, convert ( C_2 ) to ( \text{mg/L} ):
$$ C_2 = 1 , \text{mg/mL} \times 1000 = 1000 , \text{mg/L} $$
The estimated concentration in solution X is $1000 , \text{mg/L}$.
More Information
This calculation demonstrates dilution principles widely used in chemistry and biology to determine concentrations of solutions. Knowing how to adjust concentrations through dilution is crucial for accurate experimental results.
Tips
- Not rearranging the formula correctly: Ensure that you isolate ( C_2 ) properly.
- Forgetting to convert units: Always double-check if the units match what is needed (mg/mL vs. mg/L).
- Confusing initial and final volumes: Be careful to use ( V_1 ) for the volume of the concentrated solution and ( V_2 ) for the total diluted volume.
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