# engineering

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Answer the problems in the file attached with explanation and show steps . Answer the problems in the file attached with explanation and show steps . Answer the problems in the file attached with explanation and show steps .

CHMY 373 2019 – Problem Set 1 Due: Friday Jan. 18 Reminder: Problem sets are due on Fridays at 5:00 pm. All work should be stapled, written on only one side of each page, solved in order and boxed, and deposited in the CHMY 373 mailbox at CBB 103 the front office . Late problem sets will not be accepted. The lowest problem set score of the semester will be dropped, and the remaining sets will be graded and normalized to a total of 100 points. Working with others and using outside resources is encouraged, but the work you submit must be self‐written and reflect your understanding. Reading: Chapter 16, Simon & McQuarrie 1. Just how close is too close? The ideal gas law is only valid in the “dilute limit,” where the particles are far enough apart that the simplifying assumptions built into the law remain relevant: no interactions occur and the volume of the particles themselves is negligible. a. Estimate the distance in Å between molecules of nitrogen N at 25 °C and 1.0 bar centre to centre . Now, compare this to the functional diameter of a nitrogen molecule ~3.6 Å . What fraction of the total distance between molecules at these conditions is the molecular diameter? b. Nitrogen is significantly non‐ideal at 30 MPa 300 bar and 25 °C. What is the distance between molecules of nitrogen assuming ideal gas behavior under these conditions, and what fraction of this distance is the molecular diameter of nitrogen? c. Now estimate the distance in Å between water H O molecules at 100° C and 1.0 bar assuming ideal gas behavior . Repeat the calculation for liquid water at 100 °C and 1.0 bar given that the density of liquid water at this temperature is 0.96 g mL . Comment on your results the diameter of a water molecule is also ~3 Å . 2. The Redlich‐Kwong equation of state is a slightly more complex model than the van der Waals equation that we have already discussed, but it works in a similar way. Every gas has a unique set of characteristic parameters used to describe its deviation from ideality, both in finite volume and in interactions. In general, the R‐K model is closer to reality than the vdW model at above the critical temperature. a. Plot the compressibility factor, , as a function of pressure for methane CH using the Redlich‐Kwong equation of state at 223 K the critical temperature of methane is ~191 K . Use the R‐K equation parameters given in Chapter 16. The limits on your plot must be: 0‐1000 bar x‐axis and 0‐2 dimensionless, y‐axis . Be sure to indicate units or lack thereof on your graph. Use a computer program or plot the points on graph paper by hand, but use at least 10 points to plot the “isotherm” line of constant 223 K . b. Plot the compressibility factor, , as a function of pressure for hydrogen H2 using the Redlich‐Kwong equation of state at 223 K the critical temperature of hydrogen is ~33 K . Use the R‐K equation parameters given in Chapter 16. The limits on your plot must be the same as above: 0‐1000 bar x‐axis and 0‐2 dimensionless, y‐axis . Be sure to indicate units or lack thereof on your graph. Use a computer program or plot the points on graph paper by hand, but use at least 10 points to plot the “isotherm” line of constant 223 K . c. Identify the difference between the two plots above and give a reason for the different behavior of methane and hydrogen at intermediate pressures. 3. Show by using the critical point conditions where the subscript “ ” indicates the critical value that, for a van der Waals gas with coefficients and : 3 8 27 and thus: 27 3 8 4. Liquid CO is an excellent solvent and is employed as such in numerous industrial processes, namely in extraction and drying applications. The critical point of CO is conveniently close to room temperature and pressure, allowing CO to be either supercritical above its critical temperature or subcritical below its critical temperature by gently heating or cooling as the process demands. a. Determine the critical temperature in K , critical pressure in bar , and critical density in g/mL of CO using the van der Waals equation of state. b. How do these values compare to the actual critical temperature, actual critical pressure, actual critical density, and actual densities of CO in both the saturated liquid at the normal boiling point 236 K, 1 bar and the free gas in the “standard state” 273 K, 1 bar . c. Calculate the experimental “actual” value of the following quotient for CO using reference data from a table , and determine the error of the van der Waals universal prediction of this quotient for CO : d. Determine a routine by describing the temperature/pressure pathway by which to extract liquid CO solvent consider it pure for simplicity from a vessel held at 273 K and 35 bar starting condition so that the final condition is a gas at 10 mbar at any final temperature without crossing any phase transitions along the way. Plot it on a P‐T diagram and use the “actual” critical point values to plot that point. Hint: the shortest path requires three distinct steps. 5. The isothermal compressibility of a substance, expansion, , are universally defined as: , and the coefficient of thermal 1 , 1 , of an ideal gas? What are the dimensions of a. What is the expression for the and suggest appropriate units ? b. Is the isothermal compressibility an extensive or intensive property? c. What is the expression for the of an ideal gas? What are the dimensions of and suggest appropriate units ? d. Is the coefficient of thermal expansion an extensive or intensive property?

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