A chemist must dilute 78.3 ml. of 249. mM aqueous potassium dichromate K2Cr2O, solution until the concentration falts to 187. mM. He’ll do this by adding distilled water to the solution until it reaches a certain final volume
Calculate this final volume, in liters. Round your answer to 3 significant digits.
The Correct Answer and Explanation is :
To calculate the final volume of the diluted solution, we can use the dilution formula: C1⋅V1=C2⋅V2C_1 \cdot V_1 = C_2 \cdot V_2
Where:
- C1C_1 is the initial concentration of the solution (249. mM),
- V1V_1 is the initial volume of the solution (78.3 mL),
- C2C_2 is the final concentration of the solution (187. mM),
- V2V_2 is the final volume of the solution (which we are solving for).
Step 1: Plug in the known values
249. mM⋅78.3 mL=187. mM⋅V2249. \, \text{mM} \cdot 78.3 \, \text{mL} = 187. \, \text{mM} \cdot V_2
Step 2: Solve for V2V_2
Rearrange the equation to solve for V2V_2: V2=249. mM⋅78.3 mL187. mMV_2 = \frac{249. \, \text{mM} \cdot 78.3 \, \text{mL}}{187. \, \text{mM}}
Now, calculate: V2=249.⋅78.3187.=107.6 mLV_2 = \frac{249. \cdot 78.3}{187.} = 107.6 \, \text{mL}
Step 3: Convert the final volume to liters
Since the problem asks for the final volume in liters, we need to convert from milliliters to liters: V2=107.6 mL×1 L1000 mL=0.1076 LV_2 = 107.6 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.1076 \, \text{L}
Step 4: Round the answer to three significant digits
V2≈0.108 LV_2 \approx 0.108 \, \text{L}
Final Answer:
The final volume of the solution after dilution is 0.108 L.
Explanation:
This calculation demonstrates how dilution works in the context of molarity. When a solution is diluted, the number of moles of solute remains constant, but the concentration decreases as the volume increases. In this case, the chemist is diluting a 249 mM potassium dichromate solution to a lower concentration of 187 mM. By using the dilution equation C1⋅V1=C2⋅V2C_1 \cdot V_1 = C_2 \cdot V_2, we can calculate the final volume required to achieve the desired concentration. The resulting volume is converted to liters, as requested, and rounded to three significant digits for accuracy.
Let me generate the image for you!
Here’s a diagram illustrating the dilution process, which shows the initial solution concentration, the final volume, and how water is added to achieve the desired concentration. Let me know if you need further clarification!
To calculate the final volume of the diluted solution, we can use the dilution formula:
[
C_1 \cdot V_1 = C_2 \cdot V_2
]
Where:
- ( C_1 ) is the initial concentration of the solution (249. mM),
- ( V_1 ) is the initial volume of the solution (78.3 mL),
- ( C_2 ) is the final concentration of the solution (187. mM),
- ( V_2 ) is the final volume of the solution (which we are solving for).
Step 1: Plug in the known values
[
- \, \text{mM} \cdot 78.3 \, \text{mL} = 187. \, \text{mM} \cdot V_2
]
Step 2: Solve for ( V_2 )
Rearrange the equation to solve for ( V_2 ):
[
V_2 = \frac{249. \, \text{mM} \cdot 78.3 \, \text{mL}}{187. \, \text{mM}}
]
Now, calculate:
[
V_2 = \frac{249. \cdot 78.3}{187.} = 107.6 \, \text{mL}
]
Step 3: Convert the final volume to liters
Since the problem asks for the final volume in liters, we need to convert from milliliters to liters:
[
V_2 = 107.6 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.1076 \, \text{L}
]
Step 4: Round the answer to three significant digits
[
V_2 \approx 0.108 \, \text{L}
]
Final Answer:
The final volume of the solution after dilution is 0.108 L.
Explanation:
This calculation demonstrates how dilution works in the context of molarity. When a solution is diluted, the number of moles of solute remains constant, but the concentration decreases as the volume increases. In this case, the chemist is diluting a 249 mM potassium dichromate solution to a lower concentration of 187 mM. By using the dilution equation ( C_1 \cdot V_1 = C_2 \cdot V_2 ), we can calculate the final volume required to achieve the desired concentration. The resulting volume is converted to liters, as requested, and rounded to three significant digits for accuracy.
Let me generate the image for you!
Here’s a diagram illustrating the dilution process, which shows the initial solution concentration, the final volume, and how water is added to achieve the desired concentration. Let me know if you need further clarification!
