To determine the volume of the diluted solution that will give you a concentration of 2.0 mol/L from a stock solution of 5.0 mol/L, you can use the dilution equation:
\[ C_1V_1 = C_2V_2 \]
Where:
- \( C_1 \) is the concentration of the stock solution (5.0 mol/L)
- \( V_1 \) is the volume of the stock solution to use (in mL)
- \( C_2 \) is the concentration of the diluted solution (2.0 mol/L)
- \( V_2 \) is the final volume of the diluted solution (in mL)
Since we are trying to find \( V_2 \), let's rearrange the equation:
\[ V_2 = \frac{C_1V_1}{C_2} \]
To perform the dilution calculation, we need to decide how much of the stock solution we want to use. Let's say we want to use the full volume available, which is 500.0 mL.
\[ C_1 = 5.0 , \text{mol/L} \] \[ V_1 = 500.0 , \text{mL} \] \[ C_2 = 2.0 , \text{mol/L} \]
Now, substituting the values into the equation:
\[ V_2 = \frac{(5.0 , \text{mol/L})(500.0 , \text{mL})}{2.0 , \text{mol/L}} \]
Calculating this gives:
\[ V_2 = \frac{2500.0 , \text{mol mL/L}}{2.0 , \text{mol/L}} = 1250.0 , \text{mL} \]
Thus, the total volume of the diluted solution will be 1250.0 mL.
Now, converting this to liters with four decimal places:
\[ 1250.0 , \text{mL} = 1.2500 , \text{L} \]
So, the final volume of the diluted solution is 1250.0 mL, or 1.2500 L.
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