Root mean square, speed of gas

EXAMPLE 4.9 Sample exercise Calculating the root mean square speed of gas molecules... 

How does the root mean square speed of gas molecules vary with temperature Illustrate this relationship by plotting the root mean square speed of N, as a function of temperature from T = 100 I< to T = 300 K. ... 

We can now do something remarkable we can use the ideal gas law to calculate the root mean square speed of the molecules of a gas. We know that PV = nRT for an ideal gas therefore, we can set the right-hand side of Eq. 19 equal to nRT and rearrange the resulting expression ( nMv2ms = nRT) into... 

This important result is used to find the root mean square speeds of the gas-phase molecules at any temperature (Fig. 4.25). We can rewrite this equation to emphasize that, for a gas, the temperature is a measure of mean molecular speed. From... 

The kinetic model of gases is consistent with the ideal gas law and provides an expression for the root mean square speed of the molecules vnns = (3RT/M)l/2. The molar kinetic energy of a gas is proportional to the temperature. 

In an experiment on gases, you are studying a L.00-L sample of hydrogen gas at 20°C and 2.40 atm. You heat the gas until the root mean square speed of the molecules of the sample has been doubled. What will be the final pressure of the gas ... 

C05-0075. Determine the root-mean-square speed of SFg molecules under the conditions of Problem 5.31. C05-0076. Determine the root-mean-square speed of H2 molecules under the conditions of Problem 5.32. C05-0077. If a gas line springs a leak, which will diffuse faster through the atmosphere and why, CH4 or... 

The average kinetic energy, e, is related to the root-mean-square (rms) speed u through the equation e = /i mi/ Because the MM of CH4 (16) is slightly less than that of NH3 (17), the root-mean-square speed of CH4 is slightly higher than that of NH3. Root-mean-square speed is inversely proportional to the square root of the molar mass of the gas. 1 point for correct answer and explanation. 

Researchers recently reported the first optical atomic trap. In this device, beams of laser light replace the physical walls of conventional containers. The laser beams are tightly focused. They briefly (for 0.5 s) exert enough pressure to confine 500 sodium atoms in a volume of 1.0 X 10 m. The temperature of this gas is 0.00024 K, the lowest temperature ever reached for a gas. Compute the root-mean-square speed of the atoms in this confinement. 

The escape velocity necessary for objects to leave the gravitational field of the Earth is 11.2 km Calculate the ratio of the escape velocity to the root-mean-square speed of helium, argon, and xenon atoms at 2000 K. Does your result help explain the low abundance of the light gas helium in the atmosphere Explain. 

Equation (5.12) shows that the root-mean-square speed of a gas increases with the square root of its temperature (in kelvins). Because appears in the denominator, it follows that the heavier the gas, the more slowly its molecules move. If we substitute 8.314 J/K mol for R (see Appendix 2) and convert the molar mass to kg/mol, then will be calculated in meters per second (m/s). This procedure is illustrated in Example 5.17. 

The temperature of a 5.00-L container of N2 gas is increased from 20 °C to 250 °C. If the volume is held constant, predict qualitatively how this change affects the following (a) the average kinetic energy of the molecules (b) the root-mean-square speed of the molecules (c) the strength of the impact of an average molecule with the container waHs (d) the total number of collisions of molecules with walls per second. 

Equation (5.16) shows that the root-mean-square speed of a gas increases with the square root of its temperature (in kelvins). Because Ji appears in the denominator, it... 

A root-mean-square speed for gas particles is easy to define but should not obscure a key point Gas particles do not all move at the same speed. Also, as implied at the beginning of this section, not all possible speeds are equally probable. Rather, there is a particular distribution of different gas speeds in any sample. What is the mathematical expression that gives us the distribution of gas speeds ... 

Example 15.12. Find a formula for the mean of the square of the speed and the root-mean-square speed of molecules in a gas ... 

The square root of this value, (s ), is the root-mean-squared speed of the non-interacting gas particles. The root-mean-squared speed increases as the square root of temperature. A manifestation of this is that as air warms, the speed at which sound may be transmitted increases because of the greater average speed of the particles. 

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