Question

How much slower is the root-mean-square speed of WF6 than Ar at 300 K...

A) Same speed
B) 1.25 times slower
C) 1.5 times slower
D) 2.0 times slower

Answer 1

The root-mean-square speed of WF6 is 1.5 times slower than Ar at 300 K.

Step-by-step explanation:

The root-mean-square speed (u) of a molecule is given by the formula:

u = sqrt(3RT/M)

Where R is the ideal gas constant, T is the temperature in kelvin, and M is the molar mass of the gas. In this case, we are comparing the root-mean-square speed of WF6 and Ar at 300 K.

The formula for the root-mean-square speed of WF6 is:

u(WF6) = sqrt(3RT/M(WF6))

The formula for the root-mean-square speed of Ar is:

u(Ar) = sqrt(3RT/M(Ar))

To find the ratio of the root-mean-square speeds, divide the speed of WF6 by the speed of Ar:

Ratio = u(WF6)/u(Ar) = sqrt((3RT/M(WF6))/(3RT/M(Ar))) = sqrt((M(Ar)/M(WF6)))

Since WF6 has a greater molar mass than Ar, the ratio will be greater than 1. Therefore, the root-mean-square speed of WF6 is slower than Ar.

Given the answer choices, the correct option is C) 1.5 times slower.