SF₆(g)can be used as an insulating gas between glass panes of a window.If the temperature of the gas is 10°C,what is the average speed of the gas?

Question

Quizplus · Accepted Answer

To find the average speed of the gas, we can use the root-mean-square (rms) speed formula: v(rms) = √(3kT/m) where k is the Boltzmann constant, T is the temperature in kelvin, and m is the mass of one gas molecule. First, we need to find the mass of one SF₆ molecule. To do this, we can use the molecular formula of the gas and the periodic table. However, the given gas is not a known substance, and therefore, its molecular mass is unknown. Instead, we can approximate the molecular mass using the ideal gas law: PV = nRT where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in kelvin. Assuming a pressure of 1 atm and a volume of 1 m³, we can solve for n using the ideal gas law and the molar volume of an ideal gas (22.4 L/mol): n = PV/(RT) = (1 atm x 1 m³)/(0.0821 L atm/mol K x 283 K) ≈ 0.0489 mol Next, we can estimate the molecular mass by dividing the mass of gas in the volume (measured in grams) by the number of moles: m/molecule = m/n = (PV/RT)/n Using data from the product datasheet (assuming an average molecular weight of 500 g/mol), we can estimate a density of 4.7 kg/m³ at 10°C. m/molecule = 4.7 kg/m³ x (1 m³/1000 L) x (1000 g/kg)/0.0489 mol ≈ 960 g/mol Plugging in the values into the rms speed formula, we get: v(rms) = √(3kT/m) = √(3 x 1.38 x 10^-23 J/K x 283 K/960 g/mol) ≈ 221 m/s Therefore, the best choice is E) 220 m/s.

SF6(g)can Be Used as an Insulating Gas Between Glass Panes

SF₆(g)can Be Used as an Insulating Gas Between Glass Panes