Molecular speed determination

According to the kinetic theory, the pressure of a gas results from the bombardment of container walls by molecules. Both the concentration of molecules (number per unit volume) and the average speed of the molecules are factors in determining this pressure. Molecular concentration and average speed determine the frequency of coUisions with the wall. Average molecular speed determines the average force of a coUision. 

The distribution of molecular speeds in gas can be determined experimentally. To du so, the gas is heated to the required temperature in an oven. The molecules then stream out of the oven through a small hole into an evacuated region. To ensure that the molecules form a narrow Iteam, they may also pass through a senes of slits, and the pressure must Ik kept very low so that collisions within the beam do not cause spreading. 

The molecular mass of the protein was redetermined by infusing a 5-10 pmolp.l solution of the protein in 50% aqueous acetonitrile containing 0.2% formic acid at a flow rate of 6 p,lmin into an electrospray source. The scan rate employed on the mass spectrometer was from m/z 60 to m/z 1800 in 12 s. This is a relatively slow scan speed which will lead to a more precise molecular weight determination. Scan speeds of this order may be, and indeed should be, utilized for infusion experiments if sufficient sample is available but it is unlikely to be feasible when chromatographic separations, particularly those involving capillary columns, are employed because of the restriction imposed by the chromatographic peak width (see Section 3.5.2.1 above). 

To complete our analysis, we must determine the effect of a change in temperature. According to Equation, kinetic energy is proportional to temperature, and according to Equation, kinetic energy is proportional to the square of the molecular speed. Thus, the square of the molecular speed is proportional to temperature. 

From basic statistical-thermodynamics arguments [60] the mean molecular speed in a gas can be determined approximately from the relationship between pressure and mass density as... 

C. A decrease in volume (V) occurs at constant temperature (7). Average molecular speed is determined only by temperature and will be constant. V and P are inversely related, so pressure will increase. With less wall area and at higher pressure, more collisions occur per second. 

The Mean Free Paths of Molecules. There is an interesting dependence of the rate of effusion of a gas through a small hole on the molecular weight of the gas. The speeds of motion of different molecules are inversely proportional to the square roots of their molecular weights. If a small hole is made in the wall of a gas container, the gas molecules will pass through the hole into an evacuated region outside at a rate determined by the speed at which they are moving (these speeds determine the probability that a molecule will strike the hole). 

The molecular flux models are still not closed as the mean free path I and the molecular speed quantities ([C[)m are not determined yet. A frequently used closure is examined in the next paragraph. 

FYom this formula it is seen that to calculate /i we need to determine the mean molecular speed ( ci )m- For real systems the average molecular speed is difficult to determine. Assuming that the system is sufficiently close to equilibrium the velocity distribution may be taken to be Maxwellian. For molecules in the absolute Maxwellian state the peculiar velocity equals the microscopic molecular velocity, i.e., Ci = ci, because the macroscopic velocity... 

A ballistic wavepacket motion is incompatible with a tunneling process of the proton from the enol to the keto site. The transition probability of a single attempt is much smaller than 1 and many tunnel events are necessary for an efficient population transfer leading to a gradual population rise in the product state. However, if the proton itself would move from the enol to the keto site via a barrierless path, the ESIPT would take less than 10 fs because of the small proton mass [18]. This is a first indication that slower motions of the molecular skeleton are the speed determining factors and that the proton mode is not the relevant reaction coordinate [27]. 

The quantitative laws of chemical combination provide clear pointers to the molecular theory of matter, which increases progressively in vividness and realism with the application of Newton s laws to the motions of the particles. The interpretation of phenomena such as the pressure and viscosity of gases and the Brownian motion, and the assignment of definite magnitudes to molecular speeds, masses, and diameters render it clear that a continual interchange of energies must occur between the molecules of a material system, a circumstance which lies at the basis of temperature equilibrium and determines what in ordinary experience is called the flow of heat. It is responsible indeed for far more than this, and a large part of physical chemistry follows from the conception of the chaotic motion of the molecules. This matter must now be examined more deeply. 

Paucidisperse acetylated methylated and underivatized kraft lignin fractions were selected for absolute molecular weight determinations at 8 x lO g/liter concentrations in DMF and aqueous O.lOMNaOH, respectively, using the Beckman Optima XL-A analytical ultracentrifuge. The partial specific volumes of the solute species (0.744 cm Vg), and densities p of solvent or solution were measured with a Paar 60/602 digital density meter. The sedimentation curves were scaimed at two wavelengths (280 and 320 nm) after equilibrium had been reached at more than one suitable rotor speed the effective baseline at 600 nm was subtracted from each set of sedimentation equilibrium data to correct for... 

The speed at which/(m) is maximum is called the most probable molecular speed (M)nip and can be determined by taking the derivative of /( ) with respect to u and setting this derivative to zero (see Problem 5.53) to get... 

A direct measure of molecular speed can be obtained from the process of effusion. In such an experiment a pinhole is made in the wall of a container and gas leaks into an evacuated collecting vessel. The rate of gas flow is determined from the pressure in the collection chamber. If the pinhole is sufficiently small so that leakage does not perturb the gas in the container, the effusion rate is the same as the rate at which molecules collide with a wall. In our determination of the pressure we computed this quantity. 

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