Simple dimensional analysis problem, thanks for any help

In summary, the problem involves calculating the number of micrograms of Cu^2+ ions in one spot of a Cu(NO_3)_2 solution. Using simple dimensional analysis, the conversion factors of 10^6 micrograms/1g and 10^6 microliters/1L can be used. Multiplying these factors by the given concentration of 6g Cu^2+/L and the volume of 10 microliters/spot, the result is 60 micrograms/spot. However, this answer is not correct and further calculations are needed to determine the accurate number of micrograms of Cu^2+ ions in one spot.
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Homework Statement


It requires 10 microliters of a Cu(NO_3)_2 solution to produce a spot of 1cm in diameter. If the Cu(NO_3)_2 solution contains about 6g Cu^2+ per liter, then how many micrograms of Cu^2+ ions are there in one spot?

Homework Equations


simple dimensional analysis problem:
1st conversion factor is 10^6micrograms / 1g = 1
2nd conversion factor is 10^6 microliters/1L = 1
also please note that u = mu symbol

The Attempt at a Solution


6g/L * 10^6ug/1g * 1L/10^6uL = 6ug/uL

problem states that 10uL of solution required to make one spot, so multiply 6ug/uL by factor of 10 = 60 ug/uL

It doesn't look right to me but I don't know why. Thanks for any help
 
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  • #2
You need to multiply by 10 microliters/spot, not just by 10. In this type of dimensional analysis, you multiply the original item by factors/fractions that are always equal to 1. ## \\ ## The answer you get is not 60 micrograms per microliter=that is incorrect, (you calculated that it is 6 micrograms/microliter=that is correct and it doesn't change), Edit: I'll let you compute what the answer should be, given these inputs...
 
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1. What is dimensional analysis and why is it useful in scientific calculations?

Dimensional analysis is a method used in science to convert units of measurement and check for consistency in mathematical equations. It is useful because it allows for easier comparison and manipulation of different quantities and units, and helps to identify errors in calculations.

2. How do you solve a simple dimensional analysis problem?

To solve a simple dimensional analysis problem, start by writing down all the given information and the units of measurement for each quantity. Then, use conversion factors to cancel out unwanted units and ensure that the final units match the desired answer. Finally, perform the necessary mathematical operations to arrive at the solution.

3. What are some common conversion factors used in dimensional analysis?

Common conversion factors include those for length (e.g. 1 meter = 100 centimeters), mass (e.g. 1 kilogram = 1000 grams), and time (e.g. 1 hour = 60 minutes). There are also conversion factors for more specific units, such as those for temperature, volume, and pressure.

4. Can dimensional analysis be used for any type of measurement?

Yes, dimensional analysis can be used for any type of measurement as long as the units are known and can be converted. It is commonly used in fields such as physics, chemistry, and engineering.

5. What are some common mistakes to avoid when using dimensional analysis?

Some common mistakes to avoid when using dimensional analysis include using incorrect conversion factors, not properly cancelling out units, and performing the wrong mathematical operations. It is important to double check all steps and units before arriving at a final answer.

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