So that ions do not collide with each other over the large distances they must t

Question

So that ions do not collide with each other over the large distances they must travel to be mass analyzed, mass spectrometers are operatd under high or ultra-high vacuum conditions. At these low pressures, a reasonable mean free path is maintained. The mean free path () is the average distance a molecule can travel at a given pressure before colliding with another molecule. It is calculated using the following equation, where k is the Boltzmann constant, T is the temperature (in kelvin), P is the pressure (in pascals), and d is the diameter (in meters) of the molecule. KT A) A quadrupole mass spectrometer is operated under a high vacuum at a pressure of 1.00 x 104 mbar, What is the mean free path of an ion with a diameter of 1.488 nm at 27.0 °C in the mass spectrometer? Number Im B) A time-of-flight (TOF) mass spectrometer is operated under an ultra-high vacuum at a pressure of 1.00 x 10-11 mbar. What is the mean free path of an ion with a diameter of 1.661 nm at 28.0 in the mass spectrometer? Number In

Explanation / Answer

A)

The answer is very straight forward, you just need to change some of the units:

1mbar=100Pa

K=°C+273

just need to change the nm into m (1m has 1x109nm)

and k =1.38x10-23m2kg/s2K

(1.38x10-23m2kg/s2K)(300K)/(2)1/2(pi)(1.488x10-9m)2(0.01Pa)

Plugging in the equation yields: 0.042m

B)

Just as the previous

(1.38x10-23m2kg/s2K)(301K)/(2)1/2(pi)(1.661x10-9m)2(1x10-9Pa)

plugging in the equation yields: 338876.49m

C)

since it is not specified the charge of the ions, you need to assum each measurment as the mass of the molecule, you jus need to calcuate the average and standar deviation:

6612.994 6172.204 5786.555 5446.237 5143.759 4873.103 Average 5672.47533 SD 650.697955

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