CHEM 101: ChemActivity 2C - Multistep Unit Conversion Problems

This document provides a comprehensive solution to ChemActivity 2C, focusing on multistep unit conversion problems. It covers various aspects including the application of conversion factors, derived units, and density calculations. The solution includes step-by-step answers to critical thinking questions, detailed explanations, and solution maps for converting between different units such as feet to centimeters and yards to kilometers. The assignment also explores concepts like the SI unit for volume and density, and provides examples to calculate volume and density using given data. Furthermore, it includes a practical application of these concepts, such as determining the volume of titanium needed for a bicycle frame and the conversion between cubic inches and cubic centimeters. The document also defines and explains the concept of a solution map. The document references relevant sources to support the presented information.

MORE WITH CONVERSIONS
CHEMACTIVITY 2C
MODEL 1: MULTISTEP UNIT CONVERSION PROBLEMS
Useful Conversion Factors
1 cm = 0.01 m 1 yd = 3 ft 1 in = 2.54 cm
12 in = 1 ft 1 km = 1000 m
CRITICAL THINKING QUESTIONS
1. What is 1 x 1 x 1 x 1?
1 x 1 x 1 x 1 = 1
The product of a 1-unit sided 4-D dimensional figure is 1.
2. If every conversion factor has the numerical value of 1, does multiplying a
quantity by multiple conversion factors change the quantity?
No. A conversion factor of value 1 implies that two measurement units are equal thus
multiplying a quantity by multiple conversion factors does not change the quantity.
3. Convert 5.4 ft to cm by completing the following:
12 in 2.54
5.4 ft × × =164.592 cm
1 in1
5.4ft × ( 12inc
1 )× ¿= 164.592cm
4. If you only know the equalities in the model, complete the “solution map” you could use to
convert from yards to km:
yd ft _______cm _______km
Yard Ft cm km
3 0.032808 1/100000
5. In the solution map above, write the relevant conversion factor under each arrow.
Answered in Question (4)
6. If you run the 100-‐yard dash, how many km have you run? Write out all your
conversion factors in glorious detail.
1 yd = 0.0009km
100yd = 100*0.0009 = 0.09km
7. Define “solution map
A solution map is a tool for creating ideas, solving problems, sharing knowledge, and
strategy processes (Salamon, 2013; Pietkun, 2017). Solution maps are used to test dilemmas
and new ideas with the aim of getting a solution by involving stakeholders through
discussions.
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INFORMATION
You may have been taught to do unit conversions by using proportionality. This works for
problems like the ones in ChemActivity 2B, but it is very tedious to use proportionalities to solve
problems like the one in CTQ 6, since you need to do multiple individual conversions instead of
doing them all at once as shown above.
MODEL 2: DERIVED UNITS AND DENSITY
The base units are commonly combined to form new units, called derived units, for other sorts
of quantities. For example, volume is the product of three lengths, so it can be measured in m x
m x m = m3. Derived units can also be formed from units with prefixes (mm3).
CRITICAL THINKING QUESTIONS
8. Is m an SI base unit? Is m3 an SI base unit?
m is An SI base unit for length
m3 an SI base unit for volume
9. What is the SI unit for volume? Remember that volume is the product of three lengths.
The SI unit for volume is m3
Volume = L (in m) ×L (in m) ×L (in m)
10. Velocity is a measure of the distance traversed in a certain amount of time
(calculated as distance divided by time). What is the SI unit for velocity?
SI unit for velocity = ms−1
11. Density is a measure of the mass per unit of volume. What is the SI unit for density?
SI unit for density = kg m−3
12. One liter (abbreviated L) is the volume of a box that is 1 dm on each side. How long is
the side of that box in meters?
1dm = 0.1m
Therefore, the length of the side of the box = 0.1m
13. One mL is what fraction of a liter?
1ml = 0.001liters
1ml= 1
1000liters
14. Is L the SI unit for volume?
L is not the SI unit of volume. The SI unit of volume is m3
15. The density of titanium is 4.5 g/cm3. Is this an SI unit? Write it as an equality.
g/cm3 is not the SI unit of density.
4.5g =1 cm3
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16. Use the equality in CTQ 15 to write two conversion factors: one to convert from
mass to volume and one to convert from volume to mass.
Mass to volume: 1g = 1
4.5 cm3
Volume to mass: 4.5g =1 cm3
17. What volume of titanium is needed to make a bicycle frame that weighs 1590 g?
4.5g of titanium takes 1 cm3
If 4.5g =1 cm3
Then 1590g bicycle frame will require 1590∗1
4.5 = 353.33 cm3
MODEL 3: A ONE-‐INCH CUBE
This cube is exactly one inch on each side. The lines on the faces of the cube are marked at one-‐
centimeter increments.
CRITICAL THINKING QUESTIONS
18. How long is one side of the cube in inches?
Length of the cube = 1inch
19. What is the volume of the cube in cubic inches (in3)?
Volume = s3
Volume = 1*1*1= 1 in3
20. How many centimeters equal one inch?
2.54 cm = 1 inch
21. How long is one side of the cube in centimeters?
Length of one side = 2.54 cm
22. What is the volume of the cube in cubic centimeters (cm3)?
Volume = s3
But 2.54 cm = 1 inch
Thus
Volume = 2.543 = 16.387 cm3
23. Using your answers to CTQ 19 and CTQ 22, complete the
following 1 in3 = 16.387 cm
24. Which of the following is a correct conversion factor from cm3 to in3? Circle all that apply.
1 in! 1 in ! 1 in!
2.54 cm!
2.54 cm 16.4 cm!

The correct conversion rate is ( 1 ¿3
16.4 cm3 )
25. Recall that 1 L is a cube 1 dm on a side. How many 1 L cubes would you have to line up
end to end to make 1 m?
1dm3= 1 L
But
1000 dm3=1 m3
¿
1000L = 1 m3
Thus calculating the cube root of gives;
√1000 d m3= √1 m3
10dm = 1m
Therefore, we need to line up 10 1L cubes to make 1 L
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References
Salamon, J. (2013). Sensitivity analysis of the solution map of parametric operator equilibrium
problems. Publicationes Mathematicae Debrecen, 83(4), 625-642. doi:
10.5486/pmd.2013.5630
Pietkun, R. (2017). On some properties of the solution set map to Volterra integral
inclusion. Topological Methods In Nonlinear Analysis, 48(1), 1. doi:
10.12775/tmna.2017.006
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