The gas-phase reaction of

$$H_2$$

with

$$CO_2$$

to produce

$$H_2O$$

and CO has

$$\Delta H = 11 \mathrm { kJ }$$

and

$$\Delta S = 41 \mathrm { J } / \mathrm { K }$$

. Is the reaction spontaneous at 298.15 K? What is

$$\Delta G ?$$

Suppose that in a phase diagram, when the sample was prepared with the mole fraction of component A equal to 0.40 it was found that the compositions of the two phases in equilibrium corresponded to the mole fractions $x_{A B}=0.60$ and $x_{AB}=0.20.$ What is the ratio of amounts of the two phases?

What is the difference between a gas and a vapor? At $25^{\circ}\mathrm{C}$, which of the following substances in the gas phase should be properly called a gas and which should be called a vapor: molecular nitrogen $\left(\mathrm{N}_2\right)$, mercury?

Let's make a relatively minor change in the predator -prey equations. That is, let's assume that in the absent of predator , the prey grow according to the logistic equation. Then where all constants are assumed to be positiv number. $x^{\prime}=a x\left(1-\frac{x}{K}\right)-b x y$ $y^{\prime}=-c y+d x y$ (a) Assuming $(c / d)<K$ plot nullclines and label all equilibrium points with their coordinates. (b) Use your numerical solver to plot the solution of $x^{\prime}=0.4 x\left(1-\frac{x}{100}\right)-0.01 x y$ $y^{\prime}=-0.3 y+0.005 x y$ With initial conditions x(0)=40 and y(0)=20. What appears to be the eventual fate of both the predator and prey populations? (c) Use your numerical solver to complete a " phase portrait" for system. A phase portrait is a phase plane that show a number of solutions trajectories with different initial conditions, enough to portray the overall behavior of the system. When you compare solutions with the normal predator-prey system what are the fundamental differens?

Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assen1bled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take:

The times for each setup phase are independent.

The times for each phase follow a Normal model.

The means and standard deviations of the times (in minutes are as shown:

$$\begin{array}{l|c|c} \text { Phase } & \text { Mean } & \text { SD } \\ \hline \text { Unpacking } & 3.5 & 0.7 \\ \text { Assembly } & 21.8 & 2.4 \\ \text { Tuning } & 12.3 & 2.7 \end{array}$$

A customer decides to buy a bike like one of the display models but wants a different color. The shop has one, still in the box. The manager says they can have it ready in half an hour. Do you think the bike will be set up and ready to go as promised? Explain.

Given the system below, draw a signal-flow graph and represent the system in state space in the following forms: a. Phase-variable form b. Cascade form

$$G(s)=\frac{200}{(s+10)(s+20)(s+30)}$$

Analyze the phase plane of the differential equations for $x, y \geq 0.$ Show the nullclines and equilibrium points, and sketch the direction of the trajectories in each region.

$$\begin{align*} &\frac{dx}{dt}= x(2-x-y)\\ &\frac{dy}{dt}= y(1-x-y) \end{align*}$$

In the gas phase, nitrogen dioxide is actually a mixture of nitrogen dioxide (NO2) and dinitrogen tetroxide (N2O4). If the density of such a mixture is 2.3 g/L at 74 degree C and 1.3 atm, calculate the partial pressures of the gases and Kp for the dissociation of N2O4.

It has been shown that $\mathrm{Na}_2$ species form in the vapor phase. Describe the formation of the "disodium molecule" in terms of a molecular orbital energylevel diagram. Would you expect the alkaline earth metals to exhibit a similar property?

Find the phase relationship between the following waveforms:

$$\begin{array}{l} v=0.2 \sin \left(\omega t-60^{\circ}\right) \\ i=0.1 \sin \left(\omega t-20^{\circ}\right) \end{array}$$

Find the position function x(t) for forced mass-spring system $m=2, b=2, k=\dfrac{1}{2}, F=\dfrac{5}{2}\cos t$. Find the amplitude and phase shift for $x_{ss}$, the steady-state solution.

The main component of vinegar is acetic acid. Its formula is $\ce{CH3COOH}$. Answer the following questions:

A) Write a balanced equation of the dissociation of acetic acid in aqueous solutions, and write the phase of each of the components;

B) Write an expression for the equilibrium constant, $K_a$;

Find the phase relationship between the following waveforms:

$$\begin{array}{l} v=-4 \cos \left(\omega t+90^{\circ}\right) \\ i=-2 \sin \left(\omega t+10^{\circ}\right) \end{array}$$

A three-phase circuit has two parallel balanced $\Delta$ loads, one of 5-$\Omega$ resistors and one of 20-$\Omega$ resistors. Find the magnitude of the total line current when the line-to-line voltage is 480 V rms.