Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

A student takes a measured volume of [tex]3.00\,M\,HCl[/tex] to prepare a [tex]50.0\,mL[/tex] sample of [tex]1.80\,M\,HCl[/tex]. What volume of [tex]3.00\,M\,HCl[/tex] did the student use to make the sample?

Use [tex]M_i V_i = M_f V_f[/tex].

A. [tex]3.70\,mL[/tex]
B. [tex]16.7\,mL[/tex]
C. [tex]30.0\,mL[/tex]
D. [tex]83.3\,mL[/tex]


Sagot :

To determine the volume of [tex]\(3.00 \, \text{M} \, \text{HCl}\)[/tex] needed to prepare a [tex]\(50.0 \, \text{mL}\)[/tex] sample of [tex]\(1.80 \, \text{M} \, \text{HCl}\)[/tex], we can use the dilution formula:

[tex]\[ M_i V_i = M_f V_f \][/tex]

where:
- [tex]\(M_i\)[/tex] is the initial concentration of the HCl solution.
- [tex]\(V_i\)[/tex] is the initial volume of the HCl solution that we need to find.
- [tex]\(M_f\)[/tex] is the final concentration of the diluted HCl solution.
- [tex]\(V_f\)[/tex] is the final volume of the diluted HCl solution.

Given values:
- [tex]\(M_i = 3.00 \, \text{M}\)[/tex]
- [tex]\(M_f = 1.80 \, \text{M}\)[/tex]
- [tex]\(V_f = 50.0 \, \text{mL}\)[/tex]

Substituting these values into the formula:

[tex]\[ 3.00 \, \text{M} \times V_i = 1.80 \, \text{M} \times 50.0 \, \text{mL} \][/tex]

Solving for [tex]\(V_i\)[/tex]:

[tex]\[ V_i = \frac{1.80 \, \text{M} \times 50.0 \, \text{mL}}{3.00 \, \text{M}} \][/tex]

Calculating the right-hand side:

[tex]\[ V_i = \frac{90.0 \, \text{M} \cdot \text{mL}}{3.00 \, \text{M}} \][/tex]

[tex]\[ V_i = 30.0 \, \text{mL} \][/tex]

Therefore, the volume of [tex]\(3.00 \, \text{M} \, \text{HCl}\)[/tex] used by the student to make the [tex]\(50.0 \, \text{mL}\)[/tex] sample of [tex]\(1.80 \, \text{M} \, \text{HCl}\)[/tex] is [tex]\(\boxed{30.0 \, \text{mL}}\)[/tex].