Nitrogen molecular speed

FIG U R E 9.14 The Maxwell-Boltzmann distribution of molecular speeds in nitrogen at three temperatures. The peak in each curve gives the most probable speed, u p, which is slightly smaller than the root-mean-square speed, Urms The average speed Uav (obtained simply by adding the speeds and dividing by the number of molecules in the sample) lies in between. All three measures give comparable estimates of typical molecular speeds and show how these speeds increase with temperature. 

Since the molecules of a gas are in constant motion, they all possess kinetic energy. The greater the kinetic energy of a gas molecule, the greater is its speed. Experiments show that molecules in a sample of gas are not all travelling at the same speed. Figure 10.9 shows the spread of molecular speeds of nitrogen at 300 K and 3000 K, and of chlorine gas at 300 K. 

Hg. 10.9 The spread of molecular speeds In chlorine and nitrogen gases. 

FIGURE 10.17 DisIrBiuljon of molecular speeds for nitrogen gas. (a) The effect of tempeiatuie on molecular speed. The relative area under the curve for a range of speeds gives the relative traction of molecules that have those speed. 

A Figure 10.13 Distribution of molecular speeds for nitrogen gas. (a) The effect of temperature on molecular speed. The relative area under the curve for a range of speeds gives the relative fraction of molecules that have those speeds, (b) Position of most probable (Ump), average (Uav), and root-mean-square (u,rns) speeds of gas molecules. The data shown here are for nitrogen gas at 0°C. 

M Figure 10.18 Distribution of molecular speeds for nitrogen at 0°C (blue line) and 100°C (red line). 

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

The NMR experiment can be conducted in a temperature range from liquid nitrogen (-209°C) to + 150°C. This gives the experimenter the ability to slow down rapid molecular motions to observable rates or to speed up very slow or viscous motions to measurable rates. 

Knowing the factors that affect chemical equilibrium has great practical value for industrial applications, such as the synthesis of ammonia. The Haber process for synthesizing ammonia from molecular hydrogen and nitrogen uses a heterogeneous catalyst to speed up the reaction (see p. 540). Let us look at the equilibrium reaction for ammonia synthesis to determine whether there are factors that could be manipulated to enhance the yield. 

---