This figure shows the distribution of molecular speeds for a gases at 300 K. Which of these statements is true? Select all that apply.

Question

BlackTom AI · Accepted Answer

To analyze the statements, I’ll go option by option and connect them to the features of a Maxwell–Boltzmann speed distribution as shown in the figure.
Option 1: 'More than half of the particles are moving at speeds that are less than or equal to the most probable speed (the peak maximum).' In a right-skewed Maxwell–Boltzmann distribution, the peak corresponds to the most probable speed, but the area under the curve to the left of the peak is not greater than 0.5. The distribution is not symmetric, and the mean speed is greater than the most probable speed, so the fraction of particles with speeds less than or equal to the most probable speed is less than half. Therefore this statement is false.
Option 2: 'The number of particles that are moving at a given range of speeds is proportional to the area under the distribution curve.' This is a direct reflection of how a probability density function works: the fraction (or number) of particles with speeds in a given interval is given by the area under the curve over that speed interval. Thus this statement is true.
Option 3: 'This function that describes the distribution of molecular speeds is called a Maxwell–Boltzmann distribution.' Indeed, the curve shown is the Maxwell–Boltzmann distribution, which characterizes speeds in an ideal gas at a given temperature. This statement is true.
Option 4: 'The majority of the particles in the gas sample are moving at speeds greater than 2000 m/s.' The peak of the distribution is near around 1000–1500 m/s, and the tail to high speeds (above 2000 m/s) contains far fewer particles than the peak region. Therefore, the majority are not moving above 2000 m/s; this statement is false.

This figure shows the distribution of molecular speeds for a gases at 300 K. Which of these statements is true? Select all that apply.多项选择题

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