The activation energy for some reaction

$$\mathrm{X}_{2}(g)+\mathrm{Y}_{2}(g) \longrightarrow 2 \mathrm{XY}(g)$$

is 167 kJ/mol, and $\Delta E$ for the reaction is 128 kJ/mol. What is the activation energy for the decomposition of XY?

Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by n = 1, by n = 2.

Draw a rough sketch of the energy profile for each of the following cases.

$$\Delta E = - 10\ \mathrm { kJ } / \mathrm { mol } , E _ { \mathrm { a } } = 50\ \mathrm { kJ } / \mathrm { mol }$$

Which reaction will have the greatest rate at 298 K? Assume the frequency factor A is the same for all three reactions.

Draw a rough sketch of the energy profile for each of the following cases.

$$\Delta E = + 10\ \mathrm { kJ } / \mathrm { mol } , E _ { \mathrm { a } } = 25\ \mathrm { kJ } / \mathrm { mol }$$

Which reaction will have the greatest rate at 298 K? Assume the frequency factor A is the same for all three reactions.

The table shows the number of aircraft midair near collisions y in year x.

Support your answer by graphing f and the data.

Solve the given differential equation by separation of variables. $d y-(y-1)^{2} d x=0$

The deconposition of ethanol $\left( \mathrm { C } _ { 2 } \mathrm { H } _ { 5 } \mathrm { OH } \right)$ on an alumina $\left( \mathrm { Al } _ { 2 } \mathrm { O } _ { 3 } \right)$ surface,

$$\mathrm { C } _ { 2 } \mathrm { H } _ { \mathrm { 5 } } \mathrm { OH } ( g ) \longrightarrow \mathrm { C } _ { 2 } \mathrm { H } _ { 4 } ( g ) + \mathrm { H } _ { 2 } \mathrm { O } ( g )$$

was studied at 600 K. Concentration versus time datawere collected for this reaction, and a plot of [A] versus time resulted in a straight line with a slope value of $- 4.00 \times 10 ^ { - 5 }\ \mathrm { mol }\ \mathrm { L } ^ { - 1 }\ \mathrm { s } ^ { - 1 }.$ Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction.

What is the premise underlying the collision model? How is the rate affected by the following?

Sketch a potential energy versus reaction progress plot for an endothermic reaction and for an exothermic reaction. Show $\Delta E$ and $E_{\mathrm{a}}$ in both plots. When concentrations and temperatures are equal, would you expect the rate of the forward reaction to be equal to, greater than, or less than the rate of the reverse reaction if the reaction is exothermic? Endothermic?

activation energy

What is the premise underlying the collision model? How is the rate affected by the following?

Sketch a potential energy versus reaction progress plot for an endothermic reaction and for an exothermic reaction. Show $\Delta E$ and $E_{\mathrm{a}}$ in both plots. When concentrations and temperatures are equal, would you expect the rate of the forward reaction to be equal to, greater than, or less than the rate of the reverse reaction if the reaction is exothermic? Endothermic?

temperature

A certain reaction has the following general form:

$$a \mathrm { A } \longrightarrow b \mathrm { B }$$

At a particular temperature and $[ \mathrm { A } ] _ { 0 } = 2.00 \times 10 ^ { - 2 }\ \mathrm { M },$ concentration versus time data were collected for this reaction, and a plot of ln[A] versus time resulted in a straight line with a slope value of $- 2.97 \times 10 ^ { - 2 }\ min^ { - 1 }.$ Calculate the half-life for this reaction.

The decomposition of hydrogen peroxide was studied at a particular temperature. The following data were obtained, where $Rate= - \frac { d \left[ \mathrm { H } _ { 2 } \mathrm { O } _ { 2 } \right] } { d t }$

$$\begin{array} { r r } { \text{Time (s)}} \quad &{ \left[ \mathrm { H } _ { 2 } \mathrm { O } _ { 2 } \right] ( \mathrm { mol } / \mathrm { L } ) } \\ \hline 0 & { 1.00 } \\ { 120 \pm 1 } & { 0.91 } \\ { 300 \pm 1 } & { 0.78 } \\ { 600 \pm 1 } & { 0.59 } \\ { 1200 \pm 1 } & { 0.37 } \\ { 1800 \pm 1 } & { 0.13 } \\ { 2400 \pm 1 } & { 0.13 } \\ { 3000 \pm 1 } & { 0.082 } \\ { 3600 \pm 1 } & { 0.050 } \end{array}$$

Determine the integrated rate law, the differential rate law, and the value of the rate constant. Calculate the $\left[ \mathrm { H } _ { 2 } \mathrm { O } _ { 2 } |\right.$ at 4000 s after the start of the reaction.

Proceed as in Example 5 and find an explicit solution of the given initial-value problem. $\frac{d y}{d x}=y e^{-x^{2}}, \quad y(4)=1$

You work 40 hours per week at a candy store and earn $7.50 per hour. You also earn$7.00 per hour babysitting and can work as many hours as you want. You want to earn $370 a week. How many hours must you babysit?

Use computer software to obtain a direction field for the given differential equation. By hand, sketch an approximate solution curve passing through each of the given points. $\frac{d y}{d x}=\frac{1}{y}$ (a) y(0) = 1 (b) y( - 2) = -l