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Chapter 10: Problem 80

Suppose you have two 1 -L flasks, one containing \(\mathrm{N}_{2}\) at \(\mathrm{STP}\), the other containing \(\mathrm{CH}_{4}\) at STP. How do these systems \(\mathrm{com}\) pare with respect to (a) number of molecules, (b) density, (c) average kinetic energy of the molecules, \((\mathbf{d})\) rate of effusion through a pinhole leak?

Short Answer

Expert verified
(a) The number of molecules in both flasks is the same, as they contain equal moles of gas at STP. (b) The density of N2 is higher than the density of CH4, as its molar mass is greater. (c) The average kinetic energy of the molecules is equal for both gases, as they are at the same temperature. (d) The rate of effusion of CH4 is greater than the rate of effusion of N2, as its molar mass is lower.

Step by step solution

01

a) Number of molecules

At STP, the pressure is 1 atm and the temperature is 273.15 K. To find the number of molecules, we will use the Ideal Gas Law Equation. PV = nRT Here, P = 1 atm, T = 273.15 K, R (gas constant) = 0.0821 atm L/mol K For N2: Molar Mass of N2 = 28 g/mol For CH4: Molar Mass of CH4 = 16 g/mol First, we need to find the moles of each gas in the flask, then multiply by Avogadro's number to find the number of molecules. n_N2 = (PV) / (RT) n_CH4 = (PV) / (RT) Based on the values of n_N2 and n_CH4, we will then find the number of molecules.
02

b) Density

Density of a gas is given by: Density = Mass / Volume Density_N2 = (Mass of N2) / (Volume of flask) Density_CH4 = (Mass of CH4) / (Volume of flask) We can find the mass of each gas using the moles and molar mass, then divide by volume (1 L) to obtain the densities of N2 and CH4.
03

c) Average kinetic energy of the molecules

The average kinetic energy of a gas depends on temperature alone and is given by: KE_avg = (3/2) * R * T Since both gases are at the same temperature (STP), their average kinetic energies are equal.
04

d) Rate of effusion through a pinhole leak

Rate of effusion is given by Graham's Law of Effusion: Rate1 / Rate2 = sqrt(MolarMass2 / MolarMass1) Here, Rate1 refers to the rate of effusion of N2, and Rate2 refers to the rate of effusion of CH4. Using the molar masses of N2 and CH4, we can calculate the rate of effusion through a pinhole leak for both gases and compare them.

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Most popular questions from this chapter

An ideal gas at a pressure of \(152 \mathrm{kPa}\) is contained in a bulb of unknown volume. A stopcock is used to connect this bulb with a previously evacuated bulb that has a volume of \(0.800 \mathrm{~L}\) as shown here. When the stopcock is opened, the gas expands into the empty bulb. If the temperature is held constant during this process and the final pressure is \(92.66 \mathrm{kPa}\), what is the volume of the bulb that was originally filled with gas?

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Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of \(85.7 \% \mathrm{C}\) and \(14.3 \% \mathrm{H}\) by mass. \((\mathbf{a})\) If $1.56 \mathrm{~g}\( of cyclopropane has a volume of \)1.00 \mathrm{~L}$ at 99.7 \(\mathrm{kPa}\) and \(50.0^{\circ} \mathrm{C}\), what is the molecular formula of cyclopropane? (b) Judging from its molecular formula, would you expect cyclopropane to deviate more or less than Ar from ideal-gas behavior at moderately high pressures and room temperature? Explain. (c) Would cyclopropane effuse through a pinhole faster or more slowly than methane, \(\mathrm{CH}_{4} ?\)
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