Question

which of the following statements are true? check all that apply. view available hint(s) there are gas molecules that move faster than the average. the average kinetic energy of gas molecules increases with increasing temperature. the average speed of gas molecules increases with increasing temperature. there are gas molecules that move slower than the average. all the gas molecules in a sample have the same kinetic energy. submit previous answers incorrect; try again you have not selected all of the correct options. increasing the temperature increases the kinetic energy of the molecules, causing them to as a whole. you may want to review hint 1. the relationship among temperature, average kinetic energy, and speed.

Explanation:

• For the statement "There are gas molecules that move faster than the average": In a gas sample, molecular speeds follow a distribution (e.g., Maxwell - Boltzmann distribution). So, there are always molecules with speeds above the average.
• For "The average kinetic energy of gas molecules increases with increasing temperature": The formula for the average kinetic energy of gas molecules is \(\bar{K}E=\frac{3}{2}kT\) (where \(k\) is the Boltzmann constant and \(T\) is the temperature in Kelvin). As \(T\) increases, \(\bar{K}E\) increases.
• For "The average speed of gas molecules increases with increasing temperature": The average speed of gas molecules is given by \(\bar{v}=\sqrt{\frac{8RT}{\pi M}}\) (where \(R\) is the universal gas constant, \(T\) is temperature, and \(M\) is the molar mass). As \(T\) increases, \(\bar{v}\) increases.
• For "There are gas molecules that move slower than the average": Due to the molecular speed distribution (e.g., Maxwell - Boltzmann distribution), there are always molecules with speeds below the average.
• For "All the gas molecules in a sample have the same kinetic energy": Molecular speeds are distributed (Maxwell - Boltzmann distribution), so kinetic energies (\(K E=\frac{1}{2}mv^{2}\), where \(m\) is molecular mass and \(v\) is molecular speed) are also distributed.

Answer:

There are gas molecules that move faster than the average, The average kinetic energy of gas molecules increases with increasing temperature, The average speed of gas molecules increases with increasing temperature, There are gas molecules that move slower than the average.