Go to some metric unit conversions

**Problem #1:** A material will float on the surface of a liquid if the material has a density less than that of a liquid. Given that the density of water is approximately 1.0 g/mL, will a block of material having a volume of
1.2 x 10^{4} in^{3} and weighing 350 lb float or sink when replaced in a reservoir of water?

**Solution:**

1) Convert cubic inches to cubic centimeters, then to mL:

1 in^{3}= 1 in x 1 in x 1 insince 1 inch = 2.54 cm:

1 in^{3}= 2.54 cm x 2.54 cm x 2.54 cm = 16.387 cm^{3}since 1 mL = 1 cm

^{3}, we know this:16.387 cm^{3}= 16.387 mL

2) Convert the cubic inches of the block of material to mL:

1.2 x 10^{4}in^{3}x 16.387 mL/in^{3}= 196644 mL

3) Convert pounds to grams:

350 lb x 453.6 g lb¯^{1}= 158760 g

4) Calculate the density of the material and compare it to the density of water:

158760 g / 196644 ml = 0.807 g/mLSince this is less than the density of water, we conclude that the block of material will float.

**Problem #2:** Convert 0.02515 ft^{3} to cm^{3}

**Solution:**

1) Convert 1 foot to inches, then centimeters:

1 foot = 12 inches (by definition)12 inches x (2.54 cm / 1 inch) = 30.48 cm

2) Calculate what one cubic foot would be in cubic centimeters:

30.48 cm x 30.48 cm x 30.48 cm = 28317 cm^{3}

3) Determine answer to problem:

0.02515 ft^{3}x (28317 cm^{3}/ one ft^{3}) = 712.2 cm^{3}

Now, go to Google and type this in the search box:

convert 0.02515 cubic foot to cubic centimeters

Pretty amazing!

**Problem #3:** Gasoline has a density of 0.76 g/mL. Find the mass of 4.25 gallons in pounds.

**Solution:**

1) Convert g/mL to pounds per mL:

0.76 g/mL x (one lb / 453.59 g) = 0.0016755 lb/mL

Convert lb/mL to lb/gal:

0.0016755 lb/mL x (3 785.4 mL/1 gal) = 6.34244 lb/galTry this in Google: convert 0.76 g/mL to pounds/gallon

3) Find the mass of 4.25 gal:

6.34244 lb/gal x 4.25 gal = 27.0 pounds

**Problem #4:** How many slugs are there in 54.29 kg?

Hint: use Google to convert slugs to kilograms

A slug is a very old school unit of mass. The ChemTeam has heard of it (as well as dyne and erg), but has never used it in a computation, either as a student or as a teacher.

The ChemTeam would shout "Erg!" when putting the shot in high school and college. He thought this was quite funny, knowing that the erg is a unit of energy.

The ChemTeam is easily amused!

**Problem #5:** If a container measures 3.2 gallons of volume, how many liters does it occupy?

Hie thee off to the great Googlizer!

**Problem #6:** The three dimensions of a box are measured to be 1.3 in, 3.4 in, and 5.9 in. What is the volume of the box in liters?

**Solution:**
A video of the solution to problem #6

**Problem #7:** The density of water is 1.00 g/cm^{3}. What is the density of water expressed in lb/ft^{3}?

**Solution:**

1) Convert 1.00 ft^{3} to cm^{3}:

one foot = 12 inches (by definition)12 inches times (2.54 cm/inch) = 30.48 cm

30.48 cm x 30.48 cm x 30.48 cm = 28316.8466 cm

^{3}

2) Convert 28316.8466 grams to pounds:

28316.8466 grams divided by 453.59237 grams/pound = 62.43 poundsThere are 62.43 lb/ft

^{3}

I used 28316.8466 g because water has a density of 1.00 g/cm^{3}.

**Problem #8:** Suppose your dorm room is 11.8 ft wide by 12 ft long and 8.5 ft high and has an air conditioner that exhanges air at a rate of 1200 L/min. How long would it take the air conditioner to exhange the air in your room once?

**Solution:**

1) Convert feet to decimeters:

from Google, one foot = 3.048 dmtherefore:

11.8 ft times 3.048 dm/ft = 35. 9664 dm

12 ft times 3.048 dm/ft = 36.576 dm

8.5 ft times 3.048 dm/ft = 25.908 dm

2) Calculate the volume in cubic decimeters:

35. 9664 dm times 36.576 dm times 25.908 dm = 34082.156 dm^{3}

3) Compute time required:

34082.156 dm^{3}/ 1200 L/min = 28.40 minRemember, L = dm

^{3}, so those two units cancel exactly.

**Problem #9:** Analysis of an air sample reveals that it contains 3.5 x 10^{-6} g/L of carbon monoxide. Express the concentration of carbon monoxide in lb/ft^{3}. (1 lb = 453.6 g, 1 m = 3.27 ft)

**Solution:**

1) Convert grams to pounds:

3.5 x 10^{-6}g/L times (1 lb/453.6 g) = 7.716 x10^{-9}lb/L

2) Construct the L to ft^{3} conversion:

we know this by definition: 1 L = 1 dm^{3}we know this: 1 dm

^{3}= 1 dm x 1 dm x 1 dmor expressed another way: 1 dm

^{3}= 0.1 m x 0.1 m x 0.1 mwe know this: 0.1 m = 0.327 ft

Therefore: 1 L = 0.327 ft x 0.327 ft x 0.327 ft = 3.496 x 10

^{-2}ft^{3}

3) Convert L to cubic feet:

7.716 x10^{-9}lb/L times (1 L / 3.496 x 10^{-2}ft^{3}) = 2.2 x 10^{-7}lb/ft^{3}(to two sig figs)

**Problem #10:** Convert 22.43 gal/min to L/seconds.

**Solution:**

1) Convert gallons to liters:

22.43 gal/min x (3.7854 L/gal) = 84.9067863 L/minAll I did when I typed up this solution was go to Google and type "convert 22.43 gal to L" and it gave me the answer I pasted in above.

2) Convert minutes to seconds:

84.9067863 L/min x (1 min / 60 sec) = 1.415 L/sec

**Problem #10:** Convert 35.50 mi/hr to km/s.

**Solution:**

1) Convert hours to seconds:

35.5 mi/hr times (1 hr / 3600 s) = 0.009861 mi/s

2) Convert miles to km:

0.009861 mi/s times (1.609 km / mi) = 0.01587 km/s

3) Click this sentence. It will go to a Google conversion of this problem.