Question

1. if the temperature of a gas is increased, which of the following describes the most likely change in the motion of the molecules of the gas?

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b. blurry
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1. according to kinetic molecular theory, as the temperature of a confined gas increases, which of the following is true about the gas molecules?

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1. a sample of gas is heated in a rigid container. which of the following will occur as the gas molecules collide with the sides of the container?

a. the density of the gas will decrease.
b. the pressure of the gas will increase.
c. the pressure of the gas will decrease.
d. the density of the gas will increase.

Explanation:

Question 9 (Assuming it's about gas temperature and molecular energy)

The average kinetic energy of gas molecules is directly proportional to the absolute temperature (Kelvin scale) of the gas. The formula is $KE_{avg}=\frac{3}{2}kT$ (where $k$ is Boltzmann constant and $T$ is absolute temperature). So if temperature increases, average kinetic energy of molecules increases. Among the options (assuming options are about temperature - energy relation), the correct one would be related to higher temperature meaning higher molecular energy. But since the original options are a bit unclear in the image, if we assume standard options like "Increase in temperature increases molecular energy", but based on typical questions, if the question is "If the temperature of a gas of particles in a container is increased, which describes the average kinetic energy of the molecules of the gas?" and options are about increase/decrease:

• Temperature and average kinetic energy of gas molecules are directly related (kinetic theory of gases). So as temperature increases, average kinetic energy increases. So the correct option (say if options are A: Increase, B: Decrease etc.) would be the one saying increases.

Kinetic molecular theory states that the temperature of a gas (in Kelvin) is directly proportional to the average kinetic energy of its molecules. Temperature is related to the average kinetic energy, and among the properties:

• Density: Depends on mass and volume ($

ho=\frac{m}{V}$), not directly on temperature alone (depends on $T$ and $P$ via ideal gas law $PV = nRT$).

• Number of molecules: Depends on amount of substance (moles), not temperature directly.
• Speed: The average speed of gas molecules is related to temperature ($v_{rms}=\sqrt{\frac{3RT}{M}}$), but temperature is a measure of average kinetic energy.
• Average kinetic energy: By kinetic molecular theory, temperature (Kelvin) is a measure of the average kinetic energy of gas molecules. So the property that temperature is a measure of is average kinetic energy.

A rigid container means volume ($V$) is constant. The ideal gas law is $PV = nRT$.

• Density: $

ho=\frac{m}{V}$, mass ($m$) and volume ($V$) are constant (rigid container, fixed amount of gas), so density remains same. So options A (density increases) and D (density decreases) are wrong.

• Pressure: From $PV = nRT$, with $V$, $n$, $R$ constant, $P\propto T$. So if temperature ($T$) increases, pressure ($P$) increases. So option B (pressure increases) is correct, option C (pressure decreases) is wrong.

Answer:

(Assuming the correct option is the one stating that the average kinetic energy increases with temperature, e.g., if option A is "Increase" then) A. Increase

Question 10 (Kinetic molecular theory and gas temperature - property relation)