To determine the final concentration of a hydrochloric acid (HCl) solution after diluting 10.0 mL of 12.3 M HCl to 2.00 liters, we can use the concept of dilution, which states that the product of the initial concentration and volume is equal to the product of the final concentration and volume. The equation used is:
[tex]\[ C_1 \times V_1 = C_2 \times V_2 \][/tex]
Here:
- [tex]\( C_1 \)[/tex] is the initial concentration
- [tex]\( V_1 \)[/tex] is the initial volume
- [tex]\( C_2 \)[/tex] is the final concentration
- [tex]\( V_2 \)[/tex] is the final volume
Let’s break down the steps:
1. Identify the initial concentration ([tex]\( C_1 \)[/tex]):
- The initial concentration of HCl is [tex]\( 12.3 \)[/tex] M.
2. Identify the initial volume ([tex]\( V_1 \)[/tex]):
- The initial volume of the HCl solution is [tex]\( 10.0 \)[/tex] mL.
3. Identify the final volume ([tex]\( V_2 \)[/tex]):
- The final volume of the solution after dilution is [tex]\( 2.00 \)[/tex] liters.
- Convert [tex]\( 2.00 \)[/tex] liters to milliliters (since our initial volume is in milliliters):
[tex]\[ 2.00 \, \text{L} = 2.00 \times 1000 \, \text{mL} = 2000 \, \text{mL} \][/tex]
4. Calculate the final concentration ([tex]\( C_2 \)[/tex]):
- Using the dilution equation [tex]\( C_1 \times V_1 = C_2 \times V_2 \)[/tex], solve for [tex]\( C_2 \)[/tex]:
[tex]\[ C_2 = \frac{C_1 \times V_1}{V_2} \][/tex]
Substituting the known values:
[tex]\[ C_2 = \frac{12.3 \, \text{M} \times 10.0 \, \text{mL}}{2000 \, \text{mL}} \][/tex]
[tex]\[ C_2 = \frac{123.0 \, \text{M} \cdot \text{mL}}{2000 \, \text{mL}} \][/tex]
[tex]\[ C_2 = 0.0615 \, \text{M} \][/tex]
Therefore, the approximate concentration of the hydrochloric acid solution after dilution is [tex]\( 0.0615 \)[/tex] M.
