4. Ideal gases A.md
2024-4-11|2024-4-12
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- Understand: What is the significance of 'amount of substance' in SI units? Answer: The 'amount of substance' is one of the seven base quantities in the International System of Units (SI). Its base unit is the mole (mol), which is used to express the amount of a chemical substance.
- Use: How is the concept of a mole used in relation to the Avogadro constant? Answer: One mole of any substance is the amount that contains a number of particles (atoms, molecules, ions, etc.) equal to the Avogadro constant, . This number, approximately , is the number of atoms in 12 grams of carbon-12.
- Understand: What is an ideal gas? Answer: An ideal gas is a hypothetical gas that perfectly follows the ideal gas law, , at all ranges of pressure and temperature. In this law, is the pressure, is the volume, and is the thermodynamic temperature. Ideal gases are assumed to consist of a large number of small particles that interact only through elastic collisions.
- Recall and Use: What is the equation of state for an ideal gas? Answer: The equation of state for an ideal gas can be expressed in two ways: , where is the amount of substance (number of moles), is the ideal gas constant, and is the temperature; and , where is the number of molecules and is the Boltzmann constant.
- Recall: What is the Boltzmann constant and how is it related to the ideal gas constant and the Avogadro constant? Answer: The Boltzmann constant () is a fundamental physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It is given by , where is the ideal gas constant and is the Avogadro constant.
- State: What are the basic assumptions of the kinetic theory of gases?Answer: The basic assumptions of the kinetic theory of gases are:
- T The time of a collision is negligible compared to the time between collisions
- F There are no forces of attraction or repulsion between the molecules
- R The molecules are in continuous random motion
- E Molecules of gas behave as identical, hard, perfectly elastic spheres
- V The volume of the molecules is negligible compared to the volume of the container
- Explain: How does molecular movement cause the pressure exerted by a gas?Answer: The pressure exerted by a gas is caused by the constant collisions of the gas molecules with the walls of the container. Each collision exerts a small force on the wall, and the pressure is the total force exerted by these collisions per unit area.
- Derive and Use: What is the relationship between pressure, volume, and the mean-square speed of gas molecules?Answer: The relationship between pressure (p), volume (V), the number of molecules (N), and the mean-square speed () in a gas can be expressed as .
- Understand: What is the root-mean-square speed of a gas molecule?Answer: The root-mean-square speed (crms) of a gas molecule is a measure of the average speed of the gas particles, and it is given by the square root of the mean-square speed, i.e., .
- Compare: What can be deduced by comparing and ?
Answer: By comparing these two equations, we can deduce that the average translational kinetic energy of a molecule is given by , where k is the Boltzmann constant and T is the temperature. This shows that the average kinetic energy of a molecule in a gas is directly proportional to its absolute temperature.
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