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]$M_j V_j=M_f V_f$[/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 (2)
Use the dilution formula M i V i = M f V f .
Substitute the given values: M i = 1.75 M , M f = 0.100 M , and V f = 2.00 L .
Calculate the required volume of the stock solution: V i = 1.75 M ( 0.100 M ) ( 2.00 L ) = 0.1142857142857143 L ≈ 114 m L .
Measure 114 mL of the 1.75 M solution and dilute it to 2.00 L. The final 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
Understanding the Problem We are given a problem where a student needs to prepare a solution of N H 4 N O 3 with a specific concentration and volume using a stock solution. We need to determine the correct volume of the stock solution to use and how to dilute it to achieve the desired solution. The formula M i V i = M f V f will be used, where:
M i is the initial concentration of the stock solution
V i is the initial volume of the stock solution needed
M f is the final concentration of the desired solution
V f is the final volume of the desired solution
Identifying Given Values We are given the following values:
M i = 1.75 M (concentration of the stock solution)
M f = 0.100 M (desired concentration of the final solution)
V f = 2.00 L (desired final volume of the solution) We need to find V i , the volume of the stock solution needed.
Calculating the Required Volume Using the formula M i V i = M f V f , we can rearrange to solve for V i :
V i = M i M f V f Substituting the given values: V i = 1.75 M ( 0.100 M ) ( 2.00 L ) V i = 1.75 0.200 L V i = 0.1142857142857143 L Converting this to milliliters (mL) by multiplying by 1000: V i = 0.1142857142857143 L × 1000 L m L = 114.2857142857143 m L Rounding to a reasonable number of significant figures, we get approximately 114 mL.
Preparing the Solution To prepare the solution, the student should measure 114 mL of the 1.75 M N 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 Therefore, 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 working solutions of lower concentrations. For example, if you have a concentrated acid or base, you would use the dilution formula to calculate how much of the stock solution to add to water to achieve the desired concentration for your experiment. This ensures accurate and safe preparation of chemical solutions.
To prepare 2.00 L of a 0.100 M NH₄NO₃ solution from a 1.75 M stock solution, use the dilution formula to calculate that you need 114 mL of the stock solution. Dilute this 114 mL with water until the total volume is 2.00 L. The correct answer is option B.
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