You have two samples of the same gas in the same size container, with the same pressure. the gas in the first container has a kelvin temperature four times that of the gas in the other container. . 1) the ratio of the number of moles of gas in the first container compared to that in the second is? . 2) the ratio of the average velocity of particles in the first container compared to that in the second is? . explain.

We assume that the gases in the container both behave as ideal gas. The number of moles (n) is calculated through the ideal gas law,
                                       n = PV / RT
From the two gases,
                                n1 / n2 = (PV / R(4T2)) / (PV / RT2)
The value of n1:n2 is therefore equal to 1:4. 
The equation for the average velocity of the gas particles is sqrt (3RT/M). Substituting,
                                 u1 / u2 = sqrt (3R(4T2)/M) / sqrt (3RT2/M)
Simplifying gives an answer of 2:1. 

The formula for the ideal gas law is PV = nRT. Manipulating the variables we get n = PV/RT.

so if the first container has a Kelvin temperature four times than the other container, n = PV/R(4T), then the ratio of the number of moles of gas in the first container compared to that in the second is 1/4.

following the kinetic energy of a molecule whcih is represented by squared speed = sqrt(3RT/M), the ratio of the average velocity of particles in the first container compared to that in the second is
squared speed = sqrt(3R(4T)/M)
squared speed = sqrt(12RT/M)
squared speed = 2sqrt(3RT/M)
2 times that of the other container