Chapter 16, Problem 62P

An expression for the root mean square velocity, vrms, of a gas was derived. Using Maxwell’s velocity distribution, one can also calculate the mean velocity and the most probable velocity (mp) of a collection of molecules. The equations used for these two quantities are vmean=(8RT/πM)1/2 and vmp=(2RT/M)1/2 These values ​​have a fixed relationship to each other.(a) Arrange these three quantities in order of increasing magnitude.(b) Show that the relative magnitudes are independent of the molar mass of the gas.(c) Use the smallest velocity as a reference for establishing the order of magnitude and determine the relationship between the larger and smaller values.

The reaction of solid dimethylhydrazine, (CH3)2N2H2, and liquefied dinitrogen tetroxide, N2O4, has been investigated for use as rocket fuel. The reaction produces the gases carbon dioxide (CO2), nitrogen (N2), and water vapor (H2O), which are ejected in the exhaust gases. In a controlled experiment, solid dimethylhydrazine was reacted with excess dinitrogen tetroxide, and the gases were collected in a closed balloon until a pressure of 2.50 atm and a temperature of 400.0 K were reached.(a) What are the partial pressures of CO2, N2, and H2O?(b) When the CO2 is removed by chemical reaction, what are the partial pressures of the remaining gases?

One liter of chlorine gas at 1 atm and 298 K reacts completely with 1.00 L of nitrogen gas and 2.00 L of oxygen gas at the same temperature and pressure. A single gaseous product is formed, which fills a 2.00 L flask at 1.00 atm and 298 K. Use this information to determine the following characteristics of the product:(a) its empirical formula;(b) its molecular formula;(c) the most favorable Lewis formula based on formal charge arguments (the central atom is N);(d) the shape of the molecule.