A student takes a measured volume of 3.00 M HCl to prepare a 50.0 mL sample of 1.80 M HCl. What volume of 3.00 M HCl did the student use to make the sample? Use [tex]M_i V_i=M_f V_f[/tex].
A. 3.70 mL
B. 16.7 mL
C. 30.0 mL
D. 83.3 mL
Answer (2)
Use the dilution formula: M i V i = M f V f .
Substitute the given values: M i = 3.00 M , M f = 1.80 M , and V f = 50.0 mL .
Solve for V i : V i = M i M f V f = 3.00 M ( 1.80 M ) ( 50.0 mL ) .
Calculate V i : V i = 30.0 mL .
The volume of 3.00 M HCl the student used is 30.0 mL .
Explanation
Understanding the Problem We are given the initial concentration of HCl ( M i ), the final concentration of HCl ( M f ), and the final volume of HCl ( V f ). We need to find the initial volume of HCl ( V i ) using the formula M i V i = M f V f .
Given Values We are given: M i = 3.00 M (initial concentration) M f = 1.80 M (final concentration) V f = 50.0 mL (final volume) We need to find V i (initial volume).
Formula Rearrangement Using the formula M i V i = M f V f , we can rearrange it to solve for V i :
V i = M i M f V f
Calculation Now, we substitute the given values into the formula: V i = 3.00 M ( 1.80 M ) ( 50.0 mL ) V i = 3.00 90.0 mL V i = 30.0 mL
Final Answer Therefore, the student used 30.0 mL of 3.00 M HCl to make the sample.
Examples
Imagine you're a chef needing to dilute a strong sauce to a desired concentration for a dish. This problem is similar to calculating how much of the concentrated sauce you need to mix with other ingredients to achieve the perfect flavor. By using the dilution formula, you can accurately determine the initial volume of the concentrated sauce required to create the final, diluted sauce with the desired concentration and volume, ensuring your dish tastes just right. This principle is also used in pharmacies to prepare medications at specific concentrations.
The student used 30.0 mL of 3.00 M HCl to prepare a 50.0 mL sample of 1.80 M HCl. This was calculated using the dilution formula M i V i = M f V f . By substituting the values and solving for V i , we find the required initial volume.
;
