Question

At what temperature (in degrees Celsius) will xenon atoms have the same average speed that Cl2 molecules have at 45 ∘C? Express the temperature in degrees Celsius to two significant digits.

Answer 1

We know that, the average speed of gas particles is given by v =

here, R= Real gas constant, T= Temp in kelvin, M= Molar mass

Now, the expression for average speed of Xe gas particles is v= --------- (1)

and the expression for average speed of Cl2 gas particles is v= ---------- (2)

Now equating eq-(1) & (2) and squaring on both sides & simplifying we have

T1/M1 = T2/M2

Here, T1 = Temp of Xe gas particles , M1 = molar mass of Xe = 131.3 g/mol

T2= Temp of Cl2 gas particles = 45 deg C = 318 K , M2 = molar mass of Cl2 = 70.9 g/mol

now T1 = T2 x M1 / M2 = 318 x 131.3 / 70.9 = 588.9 K = 315.9 deg C [deg C = deg K - 273]

Therefore, the temperature at which the xenon atoms have the same average speed that Cl2 molecules have at 45 ∘C is 315.9 deg C.