Which statement best explains how the solution should be made?
A. Add 1.5 mL of [tex]$0.50 M H _2 SO _4$[/tex] to 10.5 mL of water to get 12 mL of [tex]$4 M H _2 SO _4$[/tex].
B. Add 1.5 mL of [tex]$4.00 M H _2 SO _4$[/tex] to 10.5 mL of water to get [tex]$12- mL$[/tex] of [tex]$0.50 M H _2 SO _4$[/tex].
C. Add 1.5 mL of [tex]$4.00 M H _2 SO _4$[/tex] to 12 mL of water to get [tex]$0.50 M H _2 SO _4$[/tex].
Answer (2)
Use the dilution formula M 1 V 1 = M 2 V 2 to calculate the final concentration ( M 2 ) for each statement.
For statement 1: M 2 = 12 m L 0.50 M × 1.5 m L = 0.0625 M .
For statement 2: M 2 = 12 m L 4.00 M × 1.5 m L = 0.50 M .
For statement 3: M 2 = 13.5 m L 4.00 M × 1.5 m L ≈ 0.444 M .
Statement 2 is correct: Add 1.5 mL of 4.00 M H 2 S O 4 to 10.5 mL of water to get 12 mL of 0.50 M H 2 S O 4 .
Explanation
Understanding the Dilution Formula Let's analyze each statement to determine the correct dilution process. We'll use the dilution formula M 1 V 1 = M 2 V 2 , where:
M 1 is the initial concentration,
V 1 is the initial volume,
M 2 is the final concentration,
V 2 is the final volume.
Analyzing Statement 1 Statement 1: Add 1.5 mL of 0.50 M H 2 S O 4 to 10.5 mL of water to get 12 mL of 4 M H 2 S O 4 .
Here, M 1 = 0.50 M , V 1 = 1.5 m L , and V 2 = 12 m L . We want to find M 2 .
M 2 = V 2 M 1 V 1 = 12 m L 0.50 M × 1.5 m L = 0.0625 M This statement claims the final concentration is 4 M , but our calculation shows it's 0.0625 M . So, this statement is incorrect.
Analyzing Statement 2 Statement 2: Add 1.5 mL of 4.00 M H 2 S O 4 to 10.5 mL of water to get 12 mL of 0.50 M H 2 S O 4 .
Here, M 1 = 4.00 M , V 1 = 1.5 m L , and V 2 = 12 m L . We want to find M 2 .
M 2 = V 2 M 1 V 1 = 12 m L 4.00 M × 1.5 m L = 0.50 M This statement claims the final concentration is 0.50 M , and our calculation confirms this. So, this statement is correct.
Analyzing Statement 3 Statement 3: Add 1.5 mL of 4.00 M H 2 S O 4 to 12 mL of water to get 0.50 M H 2 S O 4 .
Here, M 1 = 4.00 M , V 1 = 1.5 m L , and V 2 = 1.5 m L + 12 m L = 13.5 m L . We want to find M 2 .
M 2 = V 2 M 1 V 1 = 13.5 m L 4.00 M × 1.5 m L ≈ 0.444 M This statement claims the final concentration is 0.50 M , but our calculation shows it's approximately 0.444 M . So, this statement is incorrect.
Conclusion Therefore, the statement that best explains the solution is:
Add 1.5 mL of 4.00 M H 2 S O 4 to 10.5 mL of water to get 12 mL of 0.50 M H 2 S O 4 .
Examples
Dilution is a common practice in chemistry, biology, and even cooking. For example, if you have a concentrated cleaning solution, you dilute it to the appropriate concentration for safe and effective use. Similarly, in a lab, scientists often dilute stock solutions to create working solutions of desired concentrations. Understanding dilution calculations ensures accuracy and safety in these applications. For instance, if you need a 0.1 M solution from a 1 M stock, you can calculate the exact volumes needed to achieve the desired concentration.
The correct method to make the solution is to add 1.5 mL of 4.00 M H2SO4 to 10.5 mL of water, resulting in 12 mL of 0.50 M H2SO4. This method is confirmed by the dilution formula, which yields the expected concentration. Therefore, the correct answer is Statement B.
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