Webassign 2 -- Measurement and Density.

1. Use appropriate metric prefixes to write the following measurements without use of exponents.

• a) 6.42 10^-2 L to mL
• (6.42e-2 L / 1) * (1000 mL / 1 L) = 64.2 mL (to 3 significant figures)
• b) 5.1 10^-6 s to microseconds
• (5.1e-6 sec / 1) * (1,000,000 us / 1 sec) = 5.1 us (to 2 significant figures)
• c) 9.7 10^-4 m to mm
• (9.7e-4 m / 1) * (1000 mm / 1 m) = 0.97 mm (to 2 significant figures)
• d) 4.38 10^-9 m³ to microliters
• (4.38e-9 m^3 / 1) * (100 cm / 1 m)^3 * (1 mL / 1 cm^3) * (1000 uL / 1 mL) = 4.38 uL (to 3 significant figures)
• e) 1.33 10^-7 kg to mg
• (1.33e-7 kg / 1) * (1000 g / 1 kg) * (1000 mg / 1 g) = 0.133 mg (to 3 significant figures)
• f) 3.2 10^-10 g to nanograms
• (3.2e-10 g / 1) * (1.0e9 ng / 1 g) = 0.32 ng (to 2 significant figures)
• g) 6.42 10⁹ femtoseconds to microseconds
• (6.42e9 fs / 1) * (1.0e-15 sec / 1 fs) * (1,000,000 ms / 1 sec) = 6.42 us (to 3 significant figures)

2.

• a) A sample of carbon tetrachloride, a liquid once used in dry cleaning, has a mass of 39.00 g and a volume of 24.5 mL at 25°C. What is its density in grams per cm³?
• density = mass/volume. Mass is given as 39.00, volume is 24.5 since 1 mL = 1 cm³
• density = (39.00 grams / 24.5 mL) = 1.59 g/cm³ (to 3 significant figures)
• b) The density of platinum is 23.4 g/cm³ at 20°C. Calculate the mass of 75.8 cm³ of platinum at this temperature. 
• (75.8 cm³ Pt / 1) * (23.4 g Pt / 1 cm³ pt) = 1770 g Pt. (to 3 significant figures)
• c) The density of magnesium is 1.74 g/cm³ at 20°C. What is the volume of 275 g of this metal at this temperature?
• (275 g Mg / 1) * (1 cm³ Mg/ 1.74 g Mg) = 158 cm³ Mg (to 3 significant figures)

 3.

• a) Gold can be hammered into extremely thin sheets called gold leaf. If a 185 mg piece of gold (density = 19.32 g/cm³) is hammered into a sheet measuring 2.4 1.0 ft, what is the average thickness of the sheet in meters? 
• Convert grams of Au to cubic centimeters of Au:
• (185 mg Au / 1) * (1 g Au / 1000 mg Au) * (1 cm³ Au / 19.32 g Au) = 0.009575 cm³ Au
• Convert 2.4 and 1.0 feet to centimeters:
• (2.4 ft / 1) * (12 in / 1 ft) * (2.54 cm / 1 in) = 73.152 cm
• (1.0 ft / 1) * (12 in / 1 ft) * (2.54 cm / 1 in) = 30.48 cm
• Using the equation volume = length * width * height, solve for height:
• v = lwh
• 0.009575 cm³ Au = (73.152 cm) * (30.48 cm) * (x)
• x = 4.29435e-6 cm
• Convert your answer to meters:
• (4.29435e-6 cm / 1) * (1 m / 100 cm) = 4.3e-8 m (to 2 significant figures)
• b) How might the thickness be expressed without exponential notation, using an appropriate metric prefix?
• Convert your answer in meters to nanometers: 43 nm (to 2 significant figures)

4. What is the number of significant figures in each of the following measured quantities?  

• a) 350. kg     (Answer: 3)
• b) 0.051 s     (Answer: 2)
• c) 6.3010 cm     (Answer: 5)
• d) 0.0121 L     (Answer: 3)
• e) 6.9500e-4 cm     (Answer: 5)

5.  Indicate the number of significant figures in each of the following measured quantities.

• a) 1.281 10^-3 km     (Answer: 4)
• b) 0.0317 m²     (Answer: 3)
• c) 172.080 g     (Answer: 6)
• d) 488.410 K     (Answer: 6)
• 6.58762e+06 cm     (Answer: 6)

6. Carry out the following operations, and express the answer with the appropriate number of significant figures.

• a) 320.66 - (3104.0/1.5)     (Answer: -1700) (to 2 significant figures)
• b) [(285.4 10⁵) - (3.400 10³)] 2.8944     (Answer: 8.260e7) (to 4 significant figures)
• c) (0.0049 20014.0) + (3200. 40.)     (Answer: 1.3e5) (to 2 significant figures)
• d) 857 [1242 - (3.52 100.)]     (Answer: 7.63e5) (to 3 significant figures)

7.

• a) A sample of ascorbic acid (vitamin C) is synthesized in the laboratory. It contains 1.50 g of carbon and 2.00 g of oxygen. Another sample of ascorbic acid isolated from citrus fruits contains 6.58 g of carbon. How many grams of oxygen does it contain? 
• Set up a proportion: (1.5 g Carbon / 2.00 g Oxygen) = (6.58 g Carbon / x g Oxygen)
• Solve for x.     (Answer: 8.77 g Oxygen) (to 3 significant figures)
• b) Which law are you assuming in answering this question?     (Answer: Law of constant composition)

8. What type of quantity (for example, length, volume, density) do the following units indicate?

• a) mL     (Answer: volume)
• b) cm²     (Answer: area)
• c) mm³    (Answer: volume)
• d) mg/L     (Answer: density)
• e) ps     (Answer: time)
• f) nm     (Answer: length)
• g) K     (Answer: temperature)

9. 

• a) A 25.67 g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.0 mL. The solid and toluene together weigh 49.53 g. The density of toluene at the temperature of the experiment is 0.864 g/mL. What is the density of the solid?
• Calculate the amount of Toluene present in the flask:
• (49.53 grams Toluene + sample) - (25.67 g sample) = 23.86 g Toluene
• Calculate the volume of the sample by subtracting the volume of the liquid:
• (23.86 g Toluene / 1) * (1 mL Toluene / 0.864 g Toluene) = 27.6157 mL Toluene
• Volume of sample = (50 mL Toluene + sample) - (27.6157 mL Toluene) = 22.3843 mL sample
• Calculate the density of the sample given its mass and volume:
• Density = mass/volume
• Density = 25.67 g / 22.3843 mL
• Density = 1.15 g/mL (to 3 significant figures)