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Chapter 10: Problem 93

To minimize the rate of evaporation of the tungsten filament, \(1.4 \times 10^{-5}\) mol of argon is placed in a \(600-\mathrm{cm}^{3}\) lightbulb. What is the pressure of argon in the lightbulb at \(23^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The pressure of argon in the lightbulb at \(23^{\circ}\mathrm{C}\) is approximately \(5.66 \times 10^{-4}\) atm.

Step by step solution

01

Convert the temperature to Kelvin

To convert the temperature from Celsius to Kelvin, add 273.15 to the Celsius temperature. T(K) = T(掳C) + 273.15 T(K) = 23 + 273.15 T(K) = 296.15 K
02

Convert volume to liters

To convert the volume from cm鲁 to liters (L), divide the volume in cm鲁 by 1000: V(L) = V(cm鲁) / 1000 V(L) = 600 / 1000 V(L) = 0.6 L
03

Use Ideal Gas Law to solve for Pressure

Now we have all the values we need to plug into the Ideal Gas Law equation: PV = nRT P = nRT / V To solve for pressure (P), we will use the number of moles (n = 1.4 x 10鈦烩伒 mol), volume in liters (V = 0.6 L), temperature in Kelvin (T = 296.15 K), and gas constant (R = 0.0821 L atm/mol K). P = (1.4 x 10鈦烩伒 mol) * (0.0821 L atm/mol K) * (296.15 K) / (0.6 L) Now, we can calculate the pressure of argon in the lightbulb: P = 5.66 x 10鈦烩伌 atm The pressure of argon in the lightbulb at 23掳C is approximately 5.66 x 10鈦烩伌 atm.

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Most popular questions from this chapter

Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30 , the other a gas of molar mass 60 , both at the same temperature. The pressure in flask \(\mathrm{A}\) is \(\mathrm{X} \mathrm{atm}\), and the mass of gas in the flask is \(1.2 \mathrm{~g}\). The pressure in flask B is \(0.5 \mathrm{X} \mathrm{atm}\), and the mass of gas in that flask is \(1.2 \mathrm{~g}\). Which flask contains gas of molar mass 30 , and which contains the gas of molar mass 60 ?

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In one hour the average cockroach running at \(0.08 \mathrm{~km} / \mathrm{hr}\) consumed \(0.8 \mathrm{~mL}\) of \(\overline{\mathrm{O}_{2}}\) at 1 atm pressure and \(24^{\circ} \mathrm{C}\) per gram of insect weight. (a) How many moles of \(\mathrm{O}_{2}\) would be consumed in \(1 \mathrm{hr}\) by a \(5.2-\mathrm{g}\) cockroach moving at this speed? (b) This same cockroach is caught by a child and placed in a \(1-\) qt fruit jar with a tight lid. Assuming the same level of continuous activity as in the research, will the cockroach consume more than \(20 \%\) of the available \(\mathrm{O}_{2}\) in a \(48-\mathrm{hr}\) period? (Air is 21 mol percent \(\mathrm{O}_{2}\).)

A mixture containing \(0.477\) mol \(\mathrm{He}(g), 0.280\) mol \(\mathrm{Ne}(g)\), and \(0.110 \mathrm{~mol} \mathrm{Ar}(g)\) is confined in a \(7.00\) -L vessel at \(25^{\circ} \mathrm{C}\). (a) Calculate the partial pressure of each of the gases in the mixture. (b) Calculate the total pressure of the mixture.

A gas of unknown molecular mass was allowed to effuse through a small opening under constant-pressure conditions. It required \(105 \mathrm{~s}\) for \(1.0 \mathrm{~L}\) of the gas to effuse. Under identical experimental conditions it required \(31 \mathrm{~s}\) for \(1.0\) L of \(\mathrm{O}_{2}\) gas to effuse. Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; that is, rate and time are inversely proportional.)

Indicate which of the following statements regarding the kinetic-molecular theory of gases are correct. For those that are false, formulate a correct version of the statement. (a) The average kinetic energy of a collection of gas molecules at a given temperature is proportional to \(\mathrm{m}^{1 / 2}\). (b) The gas molecules are assumed to exert no forces on each other. (c) All the molecules of a gas at a given temperature have the same kinetic energy. (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained.
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