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Ch.5 - Thermochemistry
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.5 - ThermochemistryProblem 121b
Chapter 5, Problem 121b

At 20 °C (approximately room temperature) the average velocity of N2 molecules in air is 1050 mph. (b) What is the kinetic energy (in J) of an N2 molecule moving at this speed?

Verified step by step guidance
1
Convert the velocity of the N2 molecule from miles per hour (mph) to meters per second (m/s) using the conversion factor: 1 mph = 0.44704 m/s.
Calculate the mass of an N2 molecule. The molecular weight of N2 is approximately 28 g/mol. Convert this mass to kilograms (kg) by using the conversion factor: 1 g = 0.001 kg. Then, use Avogadro's number (6.022 \(\times\) 10^{23} molecules/mol) to find the mass of one molecule.
Use the kinetic energy formula: KE = \(\frac{1}{2}\)mv^2, where 'm' is the mass of the molecule in kg and 'v' is the velocity in m/s.
Plug the values of 'm' and 'v' into the kinetic energy formula to calculate the kinetic energy of the N2 molecule.
Ensure the final kinetic energy value is in Joules (J), as this is the standard unit for energy in the International System of Units (SI).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 0.5 * m * v², where m is the mass of the object and v is its velocity. For gas molecules like N₂, this concept is crucial for understanding how speed translates into energy at the molecular level.
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Molecular Mass

The molecular mass of a substance is the mass of a single molecule, typically expressed in atomic mass units (amu). For nitrogen (N₂), the molecular mass is approximately 28 amu, which is essential for calculating the kinetic energy of an individual N₂ molecule when given its velocity.
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Conversion of Units

In physics and chemistry, it is often necessary to convert units to ensure consistency in calculations. In this case, converting the speed from miles per hour (mph) to meters per second (m/s) is essential for using standard SI units in the kinetic energy formula, allowing for accurate energy calculations.
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Related Practice
Textbook Question

The Sun supplies about 1.0 kilowatt of energy for each square meter of surface area (1.0 kW/m2, where a watt=1 J/s). Plants produce the equivalent of about 0.20 g of sucrose (C12H22O11) per hour per square meter. Assuming that the sucrose is produced as follows, calculate the percentage of sunlight used to produce sucrose. 12 CO2(g) + 11 H2O(l) → C12H22O11 + 12 O2(g) H = 5645 kJ

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Textbook Question

Consider two solutions, the first being 50.0 mL of 1.00 M CuSO4 and the second 50.0 mL of 2.00 M KOH. When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to 27.7 °C. (a) Before mixing, how many grams of Cu are present in the solution of CuSO4?

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Textbook Question

Depending on their specific usage, fuels are judged in part on energy released per unit volume and energy released per unit mass. Three prospective fuels are listed in the following table, along with their densities and molar enthalpies of combustion.

a. Rank the three fuels according to their enthalpy produced per gram.

b. Rank them according to their enthalpy produced per cm3:

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