/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 91 At \(20^{\circ} \mathrm{C}\) (ap... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 91

At \(20^{\circ} \mathrm{C}\) (approximately room temperature) the average velocity of \(\mathrm{N}_{2}\) molecules in air is \(1050 \mathrm{mph}\). (a) What is the average speed in \(\mathrm{m} / \mathrm{s}\) ? (b) What is the kinetic energy (in J) of an \(\mathrm{N}_{2}\) molecule moving at this speed? (c) What is the total kinetic energy of \(1 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) molecules moving at this speed?

Short Answer

Expert verified
(a) The average speed in meters per second is \(1050 \times \frac{1609.34}{3600} \approx 469.62 \, \mathrm{m/s}\). (b) The kinetic energy of a single N2 molecule is approximately \(KE \approx 6.389 \times 10^{-21} \, \mathrm{J}\). (c) The total kinetic energy of one mole of N2 molecules moving at this speed is approximately \(8.452 \times 10^{3} \, \mathrm{J}\).

Step by step solution

01

Convert velocity from mph to m/s

To convert the velocity given in mph (miles per hour) to m/s (meters per second), you can use the following conversion factor: 1 mile = 1609.34 meters and 1 hour = 3600 seconds. The average velocity of an N2 molecule is 1050 mph. Let's now convert it to m/s: Average velocity (m/s) = 1050 mph * (1609.34 m / 1 mile) * (1 hour / 3600 s) Calculating this will give us the average speed in m/s.
02

Calculate kinetic energy

Now, let's find the kinetic energy of a single N2 molecule moving at this speed. The formula for the kinetic energy is: KE = \(\frac{1}{2}\) * m * v^2 where KE is the kinetic energy, m is the mass of the molecule, and v is the average velocity. We are given the average velocity of N2 molecules in m/s from part (a) and the mass of one N2 molecule can be calculated as: Mass of one N2 molecule = (28 g/mol) * (1 mol / 6.022 * 10^23 molecules) * (1 kg / 1000 g) Now, substitute the values into the equation for the kinetic energy and calculate the result.
03

Calculate the total kinetic energy of one mole

For part (c), we need to find the total kinetic energy of one mole of N2 molecules moving at the average velocity given. We know there is exactly 6.022 脳 10^23 molecules per mole. So, the total kinetic energy for 1 mole of N2 molecules can be found by multiplying the kinetic energy of each single N2 molecule (found in part (b)) by the number of molecules in one mole: Total Kinetic Energy = Kinetic Energy of 1 molecule * number of molecules in 1 mole Now, just plug in the values and calculate the result.

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Most popular questions from this chapter

The heat of combustion of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), is \(-1367 \mathrm{~kJ} / \mathrm{mol}\). A batch of Sauvignon Blanc wine contains \(10.6 \%\) ethanol by mass. Assuming the density of the wine to be \(1.0 \mathrm{~g} / \mathrm{mL}\), what is the caloric content due to the alcohol (ethanol) in a 6-oz glass of wine \((177 \mathrm{~mL})\) ?

Assume that the following reaction occurs at constant pressure: $$ 2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s) $$ (a) If you are given \(\Delta H\) for the reaction, what additional information do you need to determine \(\Delta E\) for the process? (b) Which quantity is larger for this reaction? (c) Explain your answer to part (b).

Limestone stalactites and stalagmites are formed in caves by the following reaction: $$ \mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q) \longrightarrow \mathrm{CaCO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$ If \(1 \mathrm{~mol}\) of \(\mathrm{CaCO}_{3}\) forms at \(298 \mathrm{~K}\) under 1 atm pressure, the reaction performs \(2.47 \mathrm{~kJ}\) of \(P-V\) work, pushing back the atmosphere as the gaseous \(\mathrm{CO}_{2}\) forms. At the same time, \(38.95 \mathrm{~kJ}\) of heat is absorbed from the environment. What are the values of \(\Delta H\) and of \(\Delta E\) for this reaction?

The complete combustion of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), to form \(\mathrm{H}_{2} \mathrm{O}(g)\) and \(\mathrm{CO}_{2}(g)\) at constant pressure releases \(1235 \mathrm{~kJ}\) of heat per mole of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). (a) Write a balanced thermochemical equation for this reaction. (b) Draw an enthalpy diagram for the reaction.

You may have noticed that when you compress the air in a bicycle pump, the body of the pump gets warmer. (a) Assuming the pump and the air in it comprise the system, what is the sign of \(w\) when you compress the air? (b) What is the sign of \(q\) for this process? (c) Based on your answers to parts (a) and (b), can you determine the sign of \(\Delta E\) for compressing the air in the pump? If not, what would you expect for the sign of \(\Delta E\) ? What is your reasoning? [Section 5.2]
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