Problem 89
What is the density of lithium metal (in \(\mathrm{g} / \mathrm{cm}^{3}\) ) if a cube measuring \(0.82 \mathrm{~cm} \times 1.45 \mathrm{~cm} \times 1.25 \mathrm{~cm}\) has a mass of \(0.794 \mathrm{~g}\) ?
Problem 90
Ethanol produced by fermentation has a specific gravity of 0.787 at \(25^{\circ} \mathrm{C}\). What is the volume of \(125 \mathrm{~g}\) of ethanol at this temperature? (The density of water at \(25^{\circ} \mathrm{C}\) is \(0.997 \mathrm{~g} / \mathrm{mL} .\) )
Problem 91
Ethane- 1,2 -diol, commonly used as automobile antifreeze, has a specific gravity of 1.1088 at room temperature \(\left(25^{\circ} \mathrm{C}\right) .\) What is the mass of \(1.00 \mathrm{~L}\) of ethane- 1,2 -diol at this temperature?
Problem 92
Another temperature scale is the Rankine scale. It represents an absolute temperature scale similar to the Kelvin scale, with a common absolute zero (i.e., \(0.0 \mathrm{~K}=0.0{ }^{\circ} \mathrm{R}\) ). However, whereas a change of \(1.0 \mathrm{~K}\) is the same as a change of \(1.0^{\circ} \mathrm{C}\), a change of \(1.0{ }^{\circ} \mathrm{R}\) is the same as \(1.0{ }^{\circ} \mathrm{F}\). Absolute zero on the Rankine scale equals \(-459.67{ }^{\circ} \mathrm{F}\). Water freezes at \(32{ }^{\circ} \mathrm{F}\) (or \(\left.0.0{ }^{\circ} \mathrm{C}\right)\) and boils at \(212{ }^{\circ} \mathrm{F}\) \(\left(100.0^{\circ} \mathrm{C}\right)\). Convert these temperatures to their equivalent temperatures on the Rankine scale.
Problem 93
A white solid with a melting point of \(730^{\circ} \mathrm{C}\) is melted. When electricity is passed through the resultant liquid, a brown gas and a molten metal are produced. Neither the metal nor the gas can be broken down into anything simpler by chemical means. Classify each-the white solid, the molten metal, and the brown gas - as a mixture, a compound, or an element.
Problem 95
Gemstones are weighed in carats, where 1 carat \(=200 \mathrm{mg}\) exactly. What is the mass in grams of the Hope diamond, the world's largest blue diamond, at 44.4 carats?
Problem 96
The relationship between the nutritional unit for energy and the metric unit is 1 Calorie \(=1 \mathrm{kcal}\). (a) One donut contains 350 Calories. Convert this to calories and joules. (b) If the energy in one donut was used to heat \(35.5 \mathrm{~kg}\) of water, calculate the increase in temperature of the water \(\left(\right.\) in \(\left.^{\circ} \mathrm{C}\right)\)
Problem 97
Drug dosages are typically prescribed in units of milligrams per kilogram of body weight. A new drug has a recommended dosage of \(9 \mathrm{mg} / \mathrm{kg}\). (a) How many milligrams would a \(55 \mathrm{~kg}\) woman have to take to obtain this dosage? (b) How many \(125 \mathrm{mg}\) tablets should a \(18 \mathrm{~kg}\) child take to receive the recommended dosage?
Problem 98
A clinical report gave the following data from a blood analysis: iron, \(39 \mathrm{mg} / \mathrm{dL} ;\) calcium, \(8.3 \mathrm{mg} / \mathrm{dL} ;\) cholesterol, \(224 \mathrm{mg} / \mathrm{dL}\). Express each of these quantities in grams per deciliter, writing the answers in scientific notation.
Problem 99
A weather balloon has a volume of \(2.027 \times 10^{5} \mathrm{ft}^{3}\). (a) Convert this volume to \(\mathrm{L}\). (b) When in operation it is filled with helium gas. If the density of helium at room temperature is \(0.179 \mathrm{~g} / \mathrm{L}\), calculate the mass of helium in the blimp. (c) What is the mass of air occupying the same volume? The density of air at room temperature is \(1.20 \mathrm{~g} / \mathrm{L}\).
