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Chapter 1: Problem 61

The density of air at ordinary atmospheric pressure and $25^{\circ} \mathrm{C}\( is \)1.19 \mathrm{~g} / \mathrm{L}$. What is the mass, in kilograms, of the air in a room that measures $4.5 \mathrm{~m} \times 5.0 \mathrm{~m} \times 2.5 \mathrm{~m} ?$

Short Answer

Expert verified
The mass of the air in the room can be found by first calculating the volume of the room, then converting the volume to liters, and finally using the given density to determine the mass. The calculated mass of the air in the room is approximately \(66.94\mathrm{~kg}\).

Step by step solution

01

Calculate the volume of the room

To calculate the volume of the room, simply multiply the lengths of all three dimensions:\ Volume = length × width × height\ Volume = \(4.5\mathrm{~m} × 5.0\mathrm{~m} × 2.5\mathrm{~m}\)\ Volume = \(56.25\mathrm{~m^3}\)
02

Convert the volume to liters

To convert cubic meters to liters, we use the conversion factor 1 cubic meter = 1000 liters:\ Volume_liter = Volume × 1000\ Volume_liter = \(56.25\mathrm{~m^3} × 1000\)\ Volume_liter = \(56250\mathrm{~L}\)
03

Calculate the mass of the air in the room

To find the mass of the air in the room, we will use the density formula:\ Density = Mass / Volume\ Mass = Density × Volume\ We were given the density of air as \(1.19\mathrm{~g/L}\). So we can find the mass as follows:\ Mass = \(1.19\mathrm{~g/L} × 56250\mathrm{~L}\)\ Mass = \(66937.5\mathrm{~g}\)
04

Convert the mass to kilograms

Lastly, we need to convert the mass from grams to kilograms. We use the conversion factor 1 kg = 1000 g:\ Mass_kg = Mass / 1000\ Mass_kg = \(66937.5\mathrm{~g} / 1000\)\ Mass_kg = \(66.9375\mathrm{~kg}\) The mass of the air in the room is approximately \(66.94\mathrm{~kg}\).

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Most popular questions from this chapter

Use appropriate metric prefixes to write the following measurements without use of exponents: (a) \(7.29 \times 10^{6} \mathrm{~g}\) (b) \(6.1 \times 10^{-10} \mathrm{~m}\) (c) \(1.828 \times 10^{-3} \mathrm{~s}\) (d) \(3.523 \times 10^{9} \mathrm{~m}^{3}\) (g) \(3.552 \times 10^{12} \mathrm{~L}\) (e) $9.62 \times 10^{2} \mathrm{~m} / \mathrm{s}(\mathbf{f}) 8.923 \times 10^{-12} \mathrm{~kg}$

(a) To identify a liquid substance, a student determined its density, Using a graduated cylinder, she measured out a \(45-\mathrm{mL}\). sample of the substance. She then measured the mass of the sample, finding that it weighed \(38.5 \mathrm{~g}\). She knew that the substance had to be either isopropyl alcohol (density \(0.785 \mathrm{~g} / \mathrm{mL}\) ) or toluene (density \(0.866 \mathrm{~g} / \mathrm{mL}\) ). What are the calculated density and the probable identity of the substance? (b) An experiment requires $45.0 \mathrm{~g}\( of ethylene glycol, a liquid whose density is \)1.114 \mathrm{~g} / \mathrm{mL}$. Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use? (c) Is a graduated cylinder such as that shown in Figure 1.21 likely to afford the (d) A cubic piece of metal accuracy of measurement needed? measures $5.00 \mathrm{~cm}\( on each edge. If the metal is nickel, whose density is \)8.90 \mathrm{~g} / \mathrm{cm}^{3}$, what is the mass of the cube?

(a) If an electric car is capable of going \(225 \mathrm{~km}\) on a single charge, how many charges will it need to travel from Seattle, Washington, to San Diego, California, a distance of \(1257 \mathrm{mi}\), assuming that the trip begins with a full charge? (b) If a migrating loon flies at an average speed of $14 \mathrm{~m} / \mathrm{s}$, what is its average speed in mi/hr? (c) What is the engine piston displacement in liters of an engine whose displacement is listed as 450 in. ${ }^{3} ?(\mathbf{d})\( In March \)1989,$ the Exxon Valdezranagroundand spilled 240,000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to 42 gal. How many liters of netroleum were spilled?

A \(40-1 b\) container of peat moss measures \(14 \times 20 \times 30\) in. A 40-lb container of topsoil has a volume of 1.9 gal. (a) Calculate the average densities of peat moss and topsoil in units of \(\mathrm{g} / \mathrm{cm}^{3}\). Would it be correct to say that peat moss is "lighter" than topsoil? (b) How many bags of peat moss are needed to cover an area measuring $15.0 \mathrm{ft} \times 20.0 \mathrm{ft}$ to a depth of 3.0 in.?

By using estimation technique, determine which of the following is the heaviest and which is the lightest: a \(10-1 \mathrm{~b}\) bag of fertilizer, a \(10-\mathrm{kg}\) bag of rice, or 2 gal of olive oil (density $\left.=0.918 \mathrm{~g} / \mathrm{cm}^{3}\right)$
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