The two isotopes of uranium, 238U and 235U, can be separated by effusion of the corresponding UF6 gases. What is the ratio (in the form of a decimal) of the root-mean-square speed of 238UF to that of 235UF6 at constant temperature?
u(rms) = sqrt(3RT/M)
Calculate rms for UF6(238) and do the same for UF6(235), take the ratio of 238/235.
Use 8.314 for R.
I got the square root of 238/235 is 1, and I know that R mutiplied by 3 is 24.9, but I'm stuck right there.
Do what DrBob has suggested
Write an expression for the rms for UF6(238) and do the same for UF6(235), take the ratio of (rms) 238/235.
so
rms(238)=sqrt(3RT/238)
rms(235)=sqrt(3RT/235)
ratio=rms(238)/rms(235)
=sqrt(3RT/238)/sqrt(3RT/235)
as 3RT will cancel
ratio= sqrt(1/238)/sqrt(1/235)
=sqrt(1/238)/(1/235)
=sqrt(235/238)
from there how do we right the ratio?
To find the ratio of the root-mean-square (rms) speed of 238UF6 to that of 235UF6 at constant temperature, we can use the concept of the kinetic theory of gases. According to the kinetic theory, the rms speed of a gas molecule is directly proportional to the square root of its molar mass.
First, we need to find the molar masses of the two isotopes of uranium, 238U and 235U, and their corresponding UF6 molecules.
The molar mass of 238U is 238 g/mol, and the molar mass of 235U is 235 g/mol.
The molar mass of UF6 can be calculated by adding the molar mass of uranium (238 or 235 g/mol) to six times the molar mass of fluorine (19 g/mol) since there are six fluorine atoms in UF6.
For 238UF6:
Molar mass = Molar mass of uranium + 6 × Molar mass of fluorine
= 238 g/mol + 6 × 19 g/mol
= 238 g/mol + 114 g/mol
= 352 g/mol
For 235UF6:
Molar mass = 235 g/mol + 6 × 19 g/mol
= 235 g/mol + 114 g/mol
= 349 g/mol
Now, we can calculate the ratio of the rms speeds of the two UF6 molecules using the formula:
Ratio = √(Molar mass of 238UF6 / Molar mass of 235UF6)
Ratio = √(352 g/mol / 349 g/mol)
To find this ratio in decimal form, we need to evaluate the square root:
Ratio ≈ √1.0086 ≈ 1.0043
Therefore, the ratio of the rms speed of 238UF6 to that of 235UF6 at constant temperature is approximately 1.0043.