The correct dimensional analysis equation is shown here:
[tex]3.00 L CaCl_2 \times \frac{0.100 mol CaCl_2}{1 L} \times \frac{2 mol AgNO_3}{1 mol CaCl_2} \times \frac{1 L}{0.100 mol AgNO_2}[/tex]
Did you perform the calculation correctly?
A. Yes, I got the correct answer.
B. Yes, but I got the wrong answer because of a math error.
C. No, I did not set up the calculation correctly.
Answer (2)
The dimensional analysis equation is analyzed to check if the units cancel out correctly.
The units are tracked through each step of the calculation.
The final unit is L A g N O 3 , which is the desired unit.
Therefore, the dimensional analysis equation is set up correctly, and the answer is: Yes, I got the correct answer.
Explanation
Analyze the Dimensional Analysis Equation We are given a dimensional analysis equation and asked if it is set up correctly. The equation is: 3.00 L C a C l 2 \t × \t 1 L 0.100 m o lC a C l 2 \t × \t 1 m o lC a C l 2 2 m o l A g N O 3 \t × \t 0.100 m o l A g N O 2 1 L We need to check if the units cancel out correctly to arrive at the correct final units.
Track the Units Let's analyze the units in each step:
Starting unit: L C a C l 2
First conversion: L C a C l 2 \t × \t L C a C l 2 m o lC a C l 2 = m o lC a C l 2
Second conversion: m o lC a C l 2 \t × \t m o lC a C l 2 m o l A g N O 3 = m o l A g N O 3
Third conversion: m o l A g N O 3 \t × \t m o l A g N O 3 L A g N O 3 = L A g N O 3
So, the final unit is L A g N O 3 .
Conclusion Since the initial units are L C a C l 2 and the final units are L A g N O 3 , the dimensional analysis is set up correctly. The equation converts the volume of C a C l 2 to the volume of A g N O 3 using the given molarities and stoichiometric ratio.
Final Answer The dimensional analysis equation is set up correctly, so the correct answer is: Yes, I got the correct answer.
Examples
Dimensional analysis is a powerful tool used in chemistry and other sciences to convert between different units. For example, if you want to determine how many grams of a product will be formed in a chemical reaction given a certain amount of reactant, you can use dimensional analysis to convert from moles of reactant to moles of product, and then to grams of product. This method ensures that your units are consistent throughout the calculation, reducing the risk of errors. It's also used in everyday life, such as converting kilometers to miles or calculating cooking ingredient quantities.
The dimensional analysis for converting liters of CaCl2 to liters of AgNO3 is correctly set up, as all units cancel out properly. Therefore, the correct answer is: A. Yes, I got the correct answer.
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