How much concentrated 12 M hydrochloric acid is needed to prepare 100.0 mL of a 2.0 M solution?
16.67
To determine the amount of concentrated 12 M hydrochloric acid needed to prepare a 2.0 M solution, you can use the concept of dilution.
The formula for dilution is:
\(C_1V_1 = C_2V_2\)
Where:
- \(C_1\) is the initial concentration of the solution (in this case, 12 M)
- \(V_1\) is the initial volume of the solution (what we need to find)
- \(C_2\) is the final concentration of the solution (2.0 M)
- \(V_2\) is the final volume of the solution (100.0 mL)
Substituting the given values into the equation, we have:
\(12\, \text{M} \times V_1 = 2.0\, \text{M} \times 100.0\, \text{mL}\)
Now, let's solve for \(V_1\):
\(12\, \text{M} \times V_1 = 2.0\, \text{M} \times 100.0\, \text{mL}\)
Divide both sides of the equation by 12 to isolate \(V_1\):
\(V_1 = \frac{{2.0\, \text{M} \times 100.0\, \text{mL}}}{{12\, \text{M}}}\)
Calculating this expression:
\(V_1 = \frac{{200.0\, \text{mL}}}{{12\, \text{M}}}\)
\(V_1 \approx 16.7\, \text{mL}\)
Therefore, you will need approximately 16.7 mL of concentrated 12 M hydrochloric acid to prepare 100.0 mL of a 2.0 M solution.