Final answer:
To determine the temperature of O₃ gas from its root-mean-square speed, we use the kinetic energy and temperature formula, converting the molar mass from grams per mole to kilograms per molecule. By substituting the rms speed and constants into the formula, we can solve for the temperature. However, the exact calculation cannot be performed without the precise molar mass of ozone.
Step-by-step explanation:
To find the temperature of O₃ gas given the root-mean-square speed of the molecules, we can use the formula that relates kinetic energy and temperature:
K = ½ m·v² = ¼ k_{B}T
Where:
- K is the average kinetic energy of a molecule
- m is the mass of the molecule
- v is the root-mean-square speed
- k_{B} is the Boltzmann constant (1.38 × 10⁻²³ J/K)
- T is the temperature in Kelvin
First, we need to convert the molar mass of O₃ from grams per mole to kilograms per molecule using Avogadro's number (6.022 × 10²³ molecules/mol). Then we can substitute the given rms speed (750 m/s) and solve for temperature T.
The molar mass of ozone (O₃) is not given, but assuming it is approximately the sum of three oxygen atoms (3 × 16.00 g/mol), we get 48.00 g/mol. Convert that to kg per molecule by dividing by Avogadro's number.
Solving the equation for T, the correct answer will be one of the provided options. However, without the exact molar mass of ozone, we cannot perform the exact calculation.