Final answer:
Without the temperature, it's not possible to calculate the translational root mean square speed (Urms) of sulfur dioxide (SO2) molecules, as temperature is essential for determining the kinetic energy and speed of gas particles.
Step-by-step explanation:
To find the translational root mean square speed (Urms) of sulfur dioxide (SO2) molecules, we can use the equation derived from the kinetic theory of gases:
Urms = sqrt((3 * P) / (ρ))
where P is the pressure of the gas, ρ is the density of the gas, and the square root of the average squared speed is used to find Urms. We first need to find the density (ρ) of the gas using the ideal gas law (PV = nRT) rearranged to solve for ρ (density = nM / V), where n is the number of moles, M is the molar mass, V is the volume, R is the universal gas constant (8.314 J/mol·K), and T is the temperature (which is not given in the question and assumed to be at standard conditions unless otherwise stated).
Unfortunately, without the temperature, we cannot proceed to calculate Urms since temperature is a crucial component in determining the kinetic energy and hence the speed of gas molecules. The temperature must be provided or assumed to be at standard conditions of temperature and pressure (STP) to continue with the calculation.