To determine the concentration of a solution made by diluting 45 mL of 6.0 M HCl to a final volume of 750 mL, we'll use the dilution formula which is based on the principle of conservation of moles. This states that the number of moles of solute before dilution is equal to the number of moles of solute after dilution.
The dilution formula is:
[tex]\[ C_1 \times V_1 = C_2 \times V_2 \][/tex]
Where:
- [tex]\( C_1 \)[/tex] is the initial concentration of the solution.
- [tex]\( V_1 \)[/tex] is the initial volume of the solution.
- [tex]\( C_2 \)[/tex] is the final concentration of the solution.
- [tex]\( V_2 \)[/tex] is the final volume of the solution.
Let's apply the given values to this formula:
1. The initial concentration ([tex]\( C_1 \)[/tex]) is 6.0 M.
2. The initial volume ([tex]\( V_1 \)[/tex]) is 45 mL.
3. The final volume ([tex]\( V_2 \)[/tex]) is 750 mL.
We need to find the final concentration ([tex]\( C_2 \)[/tex]). Rearrange the formula to solve for [tex]\( C_2 \)[/tex]:
[tex]\[ C_2 = \frac{C_1 \times V_1}{V_2} \][/tex]
Substitute the given values into the equation:
[tex]\[ C_2 = \frac{6.0 \, \text{M} \times 45 \, \text{mL}}{750 \, \text{mL}} \][/tex]
Perform the multiplication in the numerator:
[tex]\[ 6.0 \, \text{M} \times 45 \, \text{mL} = 270 \, \text{mL} \cdot \text{M} \][/tex]
Next, divide by the final volume (750 mL):
[tex]\[ C_2 = \frac{270 \, \text{mL} \cdot \text{M}}{750 \, \text{mL}} \][/tex]
Simplify the division:
[tex]\[ C_2 = 0.36 \, \text{M} \][/tex]
Therefore, the concentration of the solution after dilution is [tex]\( 0.36 \)[/tex] M.
