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# Unknown Gases: Hydrohalic Acids

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You have two unknown gases that are hydrohalic acids (i.e., HF, HCl, HBr, and HI). You don't know which is which. So, you decided to do an experiment. This experiment involves a ten meter, exactly, long glass cylinder that can be evacuated. At one end of the glass cylinder is a compartment, which has a small hole so that the gases can escape, into which the unknown gases can be put. At the other end is a detector that can detect when the gas molecules reach that point. You place the gases, at 25 EC, in to the compartment, the cylinder is evacuated, and the hole is opened. The detector indicates that one gas reaches it in 0.032984 sec and the second
gas reaches the detector in 0.041472 sec. What two hydrohalic acids are these?

Hint:
KE = ½mv2, but it also equals 3/2kT, where k is Boltzmann's constant, which, actually equals the gas constant, R, divided by Avogadro's number (NA). Fully justify your answer.

https://brainmass.com/chemistry/bonding/unknown-gases-hydrohalic-acids-516703

## SOLUTION This solution is FREE courtesy of BrainMass!

The kinetic energy is given by:
(1.1)
Where M is the molecule's mass and v is the molecule's speed.
However, the kinetic energy is also a function of the temperature T:
(1.2)
Equating both expressions and solving for M we get:
(1.3)
If it takes the molecule time  to transverse the length L, the molecule's speed is:
(1.4)
Thus, the molecule's mass is:
(1.5)

Plugging in the numbers:

This molecule's mass is about 81 atomic mass units, hence the halide that is bonded to the hydrogen has atomic mass of about 80 which corresponds to Bromine (Br)

The molecule is therefore HBr

The second molecule:

This molecule's mass is about 128 atomic mass units, hence the halide that is bonded to the hydrogen has atomic mass of about 127 which corresponds to Iodine (I)
The molecule is HI

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