In a school's laboratory, students require 50.0 mL of [tex]$2.50 M H _2 SO _4$[/tex] for an experiment, but the only available stock solution of the acid has a concentration of 18.0 M. What volume of the stock solution would they use to make the required solution?
Use [tex]$M_i V_i=M_i V_r$[/tex].
A. 0.900 mL
B. 1.11 mL
C. 6.94 mL
D. 7.20 mL
Answer (2)
Use the dilution formula M i V i = M r V r .
Rearrange the formula to solve for the initial volume: V i = M i M r V r .
Substitute the given values: V i = 18.0 M ( 2.50 M ) ( 50.0 mL ) .
Calculate the initial volume: V i ≈ 6.94 mL . The final answer is 6.94 mL .
Explanation
Understanding the Problem We are given the following information:
Required volume of H 2 S O 4 : V r = 50.0 mL
Required concentration of H 2 S O 4 : M r = 2.50 M
Concentration of the stock solution: M i = 18.0 M
We need to find the volume of the stock solution ( V i ) required to prepare the required solution.
Stating the Formula We will use the dilution formula:
M i V i = M r V r
where:
M i is the initial concentration of the stock solution,
V i is the initial volume of the stock solution needed,
M r is the required concentration of the final solution, and
V r is the required volume of the final solution.
Rearranging the Formula We need to rearrange the formula to solve for V i :
V i = M i M r V r
Substituting the Values Now, we substitute the given values into the formula:
V i = 18.0 M ( 2.50 M ) ( 50.0 mL )
V i = 18 125 mL
V i ≈ 6.94 mL
Final Answer Therefore, the volume of the stock solution needed is approximately 6.94 mL.
Examples
Dilution calculations are essential in various fields, such as chemistry, biology, and medicine. For instance, when preparing medication, pharmacists must dilute concentrated drug solutions to achieve the correct dosage for patients. Similarly, in environmental science, scientists dilute water samples to measure pollutant concentrations accurately. Understanding dilution principles ensures precise and safe preparation of solutions for different applications.
To prepare 50.0 mL of a 2.50 M H 2 S O 4 solution from an 18.0 M stock solution, you need to use approximately 6.94 mL of the stock solution. This was calculated using the dilution formula. Therefore, the correct answer is option C: 6.94 mL.
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