Question

Suppose the temperature of an object is raised from \(100^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) by heating it with a Bunsen burner. Which of the following will be true? (a) The average molecular kinetic energy will increase. (b) The total kinetic energy of all the molecules will increase. (c) The number of fast-moving molecules will increase. (d) The number of slow-moving molecules will increase. (e) The chemical potential energy will decrease.

Short answer

The correct statements are: (a) The average molecular kinetic energy will increase, (b) The total kinetic energy of all the molecules will increase, and (c) The number of fast-moving molecules will increase.

Step-by-step solution

Understanding Temperature and Molecular Kinetic Energy

Temperature is a measure of the average kinetic energy of the molecules in a substance. When the temperature of a substance increases, the average kinetic energy of its molecules also increases. This is because temperature is directly proportional to kinetic energy according to the equation for kinetic energy of gases, given by \( KE_{avg} = \frac{3}{2}kT \) where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.

Confirming the Increase in Total Kinetic Energy

As the average kinetic energy of the molecules increases with temperature, so does the total kinetic energy, because the total kinetic energy is just the sum of the kinetic energies of all the individual molecules. Therefore, an increase in temperature from \(100^\circ C\) to \(200^\circ C\) would result in an increase of both the average and the total kinetic energy.

Analyzing Distribution of Molecular Speeds with Temperature Change

According to the Maxwell-Boltzmann distribution, as temperature increases, the distribution of molecular speeds broadens and shifts to the right, meaning that more molecules will have higher speeds. Thus, the number of fast-moving molecules increases with an increase in temperature.

Evaluating the Number of Slow-Moving Molecules

Although the average speed of the molecules increases, the number of slow-moving molecules does not necessarily increase. In fact, as the distribution shifts to higher speeds, the relative number of slower molecules will typically decrease.

Understanding Changes in Chemical Potential Energy

Chemical potential energy is associated with the chemical bonds within a substance. Heating an object doesn't necessarily decrease its chemical potential energy unless a chemical change occurs. In the given scenario, only the heat content and kinetic energy are discussed, not chemical changes.

Key concepts

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution is a foundational concept in the study of thermodynamics and statistical mechanics, describing the distribution of speeds among the particles in a gas. This distribution is crucial for understanding how temperature influences molecular motion. As the temperature of a gas increases, the particles gain kinetic energy and move faster. The distribution curve becomes broader and flatter, indicating a greater range of molecular speeds with more molecules moving at higher velocities.

Visualize this curve as a hill: at lower temperatures, the hill is steep with most particles 'huddled' near the average speed; as temperature rises, the hill flattens out, allowing more particles to 'climb' to higher speeds, increasing the average and the tail of the distribution, where the faster particles reside. This shift underlines the direct relationship between the thermal energy provided by a heat source, like a Bunsen burner, and the kinetic behavior of gas particles.

Molecular Kinetic Energy

Understanding Molecular Kinetic Energy

Molecular kinetic energy is the energy that an object's molecules possess due to their motion, which can be translational, rotational, or vibrational. The kinetic energy of a single molecule is determined by both its mass and its velocity, following the equation
\( KE = \frac{1}{2}mv^2 \),
where \( m \) represents the mass and \( v \) the velocity. When it comes to a collection of gas molecules, the kinetic energy can be expressed as an average per molecule. This average kinetic energy is directly related to the temperature of the gas, as seen in the equation
\( KE_{avg} = \frac{3}{2}kT \),
with \( k \) being the Boltzmann constant and \( T \) the temperature in Kelvin.

This relationship implies a simple but profound insight: an increase in the substance's temperature, like from \(100^{\textdegree}C\) to \(200^{\textdegree}C\), leads to a proportional increase in molecular kinetic energy. Consequently, if you heat a substance, expect its molecules to move more vigorously, reflecting increased kinetic energy.

Chemical Potential Energy

Chemical potential energy is a form of potential energy stored within the chemical bonds between atoms in a molecule. This energy is a result of the positions of electrons relative to the nuclei and the arrangement of atoms within the molecules. When a substance undergoes a chemical reaction, this stored energy can be changed into other forms, such as kinetic energy or light.

Heating a substance typically raises its kinetic energy but does not necessarily alter its chemical potential energy. Chemical potential energy is only transformed during a chemical reaction or phase change, not simply by temperature changes. In the context of heating an object with a Bunsen burner, unless a chemical reaction or phase change occurs, the chemical potential energy remains unchanged, contrary to the rise in kinetic energy. Therefore, while heating can increase the kinetic energy of the molecules, it doesn't reduce their chemical potential energy unless a specific chemical transformation is triggered.