Question

The graph shows the distribution of energy in the particles of two gas samples at different temperatures, T1 and T2. A, B, and C represent individual particles.
A graph is shown with two inverted graph curves running close to each other. One of the curves labeled T1 is slightly more spread out than the other labeled T2. The x axis of the graph has the title Kinetic Energy. The y axis of the graph has the title Number of Particles. A vertical line perpendicular to the x axis is shown. This vertical line is labeled Activation Energy. A point labeled B is shown on the right hand side of the vertical line. A point labeled A is shown in the lower left side of the vertical line. A particle labeled C is shown in the upper left side of the vertical line.

Based on the graph, which of the following statements is likely to be true?
Particle A and C are more likely to participate in the reaction than particle B.
Most of the particles of the two gases have very high speeds.
A fewer number of particles of gas at T1 are likely to participate in the reaction than the gas at T2.
The average speed of gas particles at T2 is lower than the average speed of gas particles at T1.

Answer 1

Answer:

• The average speed of gas particles at T₂ is lower than the average speed of gas particles at T₁.

Explanation:

Particles A and C are shown as if they are on the same vertical line, which means with the same kinetic energy. Both particle A and C are to the lett of particle B, which means that the formers have a lower kinetic energy than the latter.

Since the likelyhood of a particle to participate in the reaction increases with the kinetic energy, particle B is more likely to participate in the reaction than particles A and C. Hence, the first choice is incorrect.

The graph, although not perfectly symmetrical, does show a bell shape, hence there are many particles will low kinetic energy and many particles with high kinetic energy. You cannot assert that most of the particles of the two gases have high high speeds. Hence, second statement is incorrect, too.

At high values of kinetic energy (toward the right of the curve), the line labeled T₁ is higher than the line labeled T₂, meaning that at T₁ more particles have an elevated kinetic energy than the number of particles that have an elevated kinetic energy at T₂.

On the other hand, at low values of kinetic energy (toward the left of the curve) the line T₂ is higher than the line T₁, meaning that at T₂ more particles have a low kinetic energy than the number of particles that have low kinetic energy at T₁.

Hence, the last two paragraphs are telling that the average kinetic energy of gas particles at T₂ is is lower than the average kinetic energy of gas particles at T₁.

Since the average speed is proportional the the square root of the temperature, the same trend for the average kinetic energy is true for the average speed, and you conclude that the last statement is true: "The average speed of gas particles at T₂ is lower than the average speed of gas particles at T₁".

Since more particles at T₁ have high kinetic energy than the number of particles at T₂ that have a high kinetic energy, more particles of gas at T₁ are likely to participate in the reaction  than the gas at T₂, and the third statement is incorrect.