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]$M_i V_i=M_i V_t$[/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 formula M i V i = M f V f to find the required volume of the stock solution.
Plug in the known 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 ) = 0.114 L = 114 mL .
Measure 114 mL of the 1.75 M solution and dilute it to 2.00 L. The final answer is: Measure 114 mL of the 1.75 M solution, and dilute it to 2.00 L .
Explanation
Problem Setup and Formula We need to prepare 2.00 L of a 0.100 M N H 4 N O 3 solution using a 1.75 M N H 4 N O 3 stock solution. The formula M i V i = M f V f will help us determine the volume of the stock solution needed.
Identifying Variables Here, M i is the initial concentration (1.75 M), V i is the initial volume (what we need to find), M f is the final concentration (0.100 M), and V f is the final volume (2.00 L).
Rearranging the Formula We can rearrange the formula to solve for V i : V i = M i M f V f
Plugging in the Values Now, plug in the values: V i = 1.75 M ( 0.100 M ) ( 2.00 L )
Calculating the Volume Calculating V i : V i = 1.75 0.200 = 0.1142857142857143 L . To convert this to milliliters, we multiply by 1000: 0.1142857142857143 L × 1000 L mL = 114.28571428571429 mL . Rounding to a reasonable number of significant figures, we get approximately 114 mL.
Preparing the Solution Therefore, to prepare the solution, you should measure 114 mL of the 1.75 M N H 4 N O 3 stock solution and dilute it with enough water to reach a final volume of 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 instance, if you have a concentrated acid and need a less concentrated solution for a titration, you would use the M 1 V 1 = M 2 V 2 formula to calculate the necessary volume of the stock solution to dilute. This ensures accurate and safe preparation of chemical solutions, which is crucial in fields like chemistry, biology, and medicine.
To prepare 2.00 L of a 0.100 M N H 4 N O 3 solution from a 1.75 M stock solution, measure 114 mL of the stock solution and dilute it to 2.00 L. The calculation is based on the dilution formula M i V i = M f V f . Therefore, the correct option is B.
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