1.6 Mathematical treatment of measurement results  (Page 6/9)

Complete the following conversions between SI units.

(a) 612 g = ________ mg

(b) 8.160 m = ________ cm

(c) 3779 μg = ________ g

(d) 781 mL = ________ L

(e) 4.18 kg = ________ g

(f) 27.8 m = ________ km

(g) 0.13 mL = ________ L

(h) 1738 km = ________ m

(i) 1.9 Gg = ________ g

Gasoline is sold by the liter in many countries. How many liters are required to fill a 12.0-gal gas tank?

Milk is sold by the liter in many countries. What is the volume of exactly 1/2 gal of milk in liters?

A long ton is defined as exactly 2240 lb. What is this mass in kilograms?

Make the conversion indicated in each of the following:

(a) the men’s world record long jump, 29 ft 4¼ in., to meters

(b) the greatest depth of the ocean, about 6.5 mi, to kilometers

(c) the area of the state of Oregon, 96,981 mi ² , to square kilometers

(d) the volume of 1 gill (exactly 4 oz) to milliliters

(e) the estimated volume of the oceans, 330,000,000 mi ³ , to cubic kilometers.

(f) the mass of a 3525-lb car to kilograms

(g) the mass of a 2.3-oz egg to grams

Make the conversion indicated in each of the following:

(a) the length of a soccer field, 120 m (three significant figures), to feet

(b) the height of Mt. Kilimanjaro, at 19,565 ft the highest mountain in Africa, to kilometers

(c) the area of an 8.5 t 11-inch sheet of paper in cm ²

(d) the displacement volume of an automobile engine, 161 in. ³ , to liters

(e) the estimated mass of the atmosphere, 5.6 t 10 ¹⁵ tons, to kilograms

(f) the mass of a bushel of rye, 32.0 lb, to kilograms

(g) the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)

Many chemistry conferences have held a 50-Trillion Angstrom Run (two significant figures). How long is this run in kilometers and in miles? (1 Å = 1 $\times$ 10 ⁻¹⁰ m)

A chemist’s 50-Trillion Angstrom Run (see [link] ) would be an archeologist’s 10,900 cubit run. How long is one cubit in meters and in feet? (1 Å = 1 $\times$ 10 ⁻⁸ cm)

The gas tank of a certain luxury automobile holds 22.3 gallons according to the owner’s manual. If the density of gasoline is 0.8206 g/mL, determine the mass in kilograms and pounds of the fuel in a full tank.

As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?

To prepare for a laboratory period, a student lab assistant needs 125 g of a compound. A bottle containing 1/4 lb is available. Did the student have enough of the compound?

A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds?

In a recent Grand Prix, the winner completed the race with an average speed of 229.8 km/h. What was his speed in miles per hour, meters per second, and feet per second?

Solve these problems about lumber dimensions.

(a) To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness $\times$ width $\times$ length dimensions are 1.50 in. $\times$ 3.50 in. $\times$ 8.00 ft in the US. What are the dimensions in cm $\times$ cm $\times$ m?

(b) This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters?

The mercury content of a stream was believed to be above the minimum considered safe—1 part per billion (ppb) by weight. An analysis indicated that the concentration was 0.68 parts per billion. What quantity of mercury in grams was present in 15.0 L of the water, the density of which is 0.998 g/ml? $\text{(1 ppb Hg}=\frac{\text{1 ng Hg}}{\text{1 g water}}\text{)}$

Calculate the density of aluminum if 27.6 cm ³ has a mass of 74.6 g.

Osmium is one of the densest elements known. What is its density if 2.72 g has a volume of 0.121 cm ³ ?

Calculate these masses.

(a) What is the mass of 6.00 cm ³ of mercury, density = 13.5939 g/cm ³ ?

(b) What is the mass of 25.0 mL octane, density = 0.702 g/cm ³ ?

Calculate these masses.

(a) What is the mass of 4.00 cm ³ of sodium, density = 0.97 g/cm ³ ?

(b) What is the mass of 125 mL gaseous chlorine, density = 3.16 g/L?

Calculate these volumes.

(a) What is the volume of 25 g iodine, density = 4.93 g/cm ³ ?

(b) What is the volume of 3.28 g gaseous hydrogen, density = 0.089 g/L?

Calculate these volumes.

(a) What is the volume of 11.3 g graphite, density = 2.25 g/cm ³ ?

(b) What is the volume of 39.657 g bromine, density = 2.928 g/cm ³ ?

Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin.

Convert the temperature of scalding water, 54 °C, into degrees Fahrenheit and kelvin.

Convert the temperature of the coldest area in a freezer, −10 °F, to degrees Celsius and kelvin.

Convert the temperature of dry ice, −77 °C, into degrees Fahrenheit and kelvin.

Convert the boiling temperature of liquid ammonia, −28.1 °F, into degrees Celsius and kelvin.

The label on a pressurized can of spray disinfectant warns against heating the can above 130 °F. What are the corresponding temperatures on the Celsius and kelvin temperature scales?

The weather in Europe was unusually warm during the summer of 1995. The TV news reported temperatures as high as 45 °C. What was the temperature on the Fahrenheit scale?