A student requires 2.00 L of [tex]$0.100 M NH _4 NO _3$[/tex] from a [tex]$1.75 M NH _4 NO _3$[/tex] stock solution. What is the correct way to get the solution?
Use [tex]$M_i V_f=M_f V_f$[/tex].
A. Measure 114 mL of the 1.75 M solution, and dilute it to 1.00 L.
B. Measure 114 mL of the 1.75 M solution, and dilute it to 2.00 L.
C. Measure 8.75 mL of the 1.75 M solution, and dilute it to 2.00 L.
D. Measure 8.75 mL of the 0.100 M solution, and dilute it to 2.00 L.
Answer (1)
Use the formula M i V i = M f V f to calculate the volume of stock solution needed.
Substitute the given values: M i = 1.75 M , M f = 0.100 M , and V f = 2.00 L .
Solve for V i : V i = 1.75 M 0.100 M × 2.00 L = 0.1142857 L ≈ 114 m L .
Measure 114 mL of the 1.75 M solution, and dilute it to 2.00 L. The answer is M e a s u re 114 m L o f t h e 1.75 M so l u t i o n , an d d i l u t e i t t o 2.00 L .
Explanation
Problem Setup We are given a stock solution of 1.75 MN H 4 N O 3 and we need to prepare 2.00 L of 0.100 MN H 4 N O 3 solution. We will use the formula M i V i = M f V f to find the volume of the stock solution needed.
Identifying Variables Here, M i = 1.75 M is the initial concentration of the stock solution, V i is the initial volume of the stock solution we need to find, M f = 0.100 M is the final desired concentration, and V f = 2.00 L is the final desired volume.
Applying the Formula Plugging the values into the formula, we get:
1.75 M × V i = 0.100 M × 2.00 L
Calculating the Volume Now, we solve for V i :
V i = 1.75 M 0.100 M × 2.00 L = 1.75 0.200 L = 0.1142857 L
Converting this to milliliters, we multiply by 1000:
V i = 0.1142857 L × 1000 L m L = 114.2857 m L
Rounding to a reasonable number of significant figures, we get V i ≈ 114 m L .
Preparing the Solution Therefore, to prepare the solution, you should measure approximately 114 mL of the 1.75 MN H 4 N O 3 stock solution and dilute it with enough solvent (usually water) to reach a final volume of 2.00 L.
Final Answer The correct way to get the solution is to measure 114 mL of the 1.75 M solution, and dilute it to 2.00 L.
Examples
In a lab setting, you often need to dilute stock solutions to create solutions of a specific concentration for experiments. For example, if you have a concentrated acid and need a less concentrated solution for a reaction, you would use the dilution formula to calculate how much of the stock solution to use and how much water to add. This ensures accurate concentrations, which is crucial for reliable experimental results. Similarly, pharmacists use dilutions to prepare medications at the correct dosage for patients.
