Dinitrogen pentoxide decomposes into nitrogen dioxide and oxygen. If 5.00 L of

$$\mathrm { N } _ { 2 } \mathrm { O } _ { 5 }$$

reacts at STP, what volume of

$$\mathrm { NO } _ { 2 }$$

is produced when measured at

$$64.5 ^ { \circ } C$$

and 1.76 atm?

Let y(t) be a solution of

$$( \cos y + 1 ) \frac { d y } { d t } = 2 t$$

such that y(2) = 0. Show that

$$\sin y + y = t ^ { 2 } + C.$$

We cannot solve for y as a function of t, but assuming that y(2) = 0, find the values of t at which

$$y ( t ) = \pi.$$

Use reduction potentials to determine whether the reactions in the following problems are spontaneous.

$$\mathrm { Cl } _ { 2 } + \mathrm { Sn } \rightarrow 2 \mathrm { Cl } ^ { - } + \mathrm { Sn } ^ { 2 + }$$

Complete the sentences using the preview words. They-coordinate of the point where a graph of a line crosses the y-axis is the _.

$2 t ^ { 3 } s v ^ { 5 } , 6 v ^ { 3 } t ^ { 4 } ,$ and $10 v ^ { 8 } s ^ { 4 }$

Assume that Rayleigh's criterion gives the limit of resolution of an astronaut's eye looking down on Earth's surface from a typical space shuttle altitude of 420 km. (a) Under that idealized assumption, estimate the smallest linear width on Earth's surface that the astronaut can resolve. Take the astronaut's pupil diameter to be 5 mm and the wavelength of visible light to be 550 nm. (b) Can the astronaut resolve the Great Wall of China, which is more than 3000 km long, 5 to 10 m thick at its base, 4 m thick at its top, and 8 m in height? (c) Would the astronaut be able to resolve any unmistakable sign of intelligent life on Earth's surface?

Solve the equation.

$$\ln ( 4 x - 7 ) = \ln ( x + 11 )$$

Fluorine gas reacts violently with water to produce hydrogen fluoride and ozone according to the following equation:

$$3 \mathrm { F } _ { 2 } ( g ) + 3 \mathrm { H } _ { 2 } \mathrm { O } ( l ) \longrightarrow 6 \mathrm { HF } ( g ) + \mathrm { O } _ { 3 } ( \mathrm { g } )$$

What volumes of

$$O_3$$

and HF gas would be produced by the complete reaction of

$$3.60 \times 10 ^ { 4 } \mathrm { mL }$$

of fluorine gas? All gases are measured under the same conditions.

A sample of ethanol burns in

$$O_2$$

to form

$$CO_2$$

and

$$H_2O$$

according to the following equation:

$$\mathrm { C } _ { 2 } \mathrm { H } _ { 5 } \mathrm { OH } + 3 \mathrm { O } _ { 2 } \rightarrow 2 \mathrm { CO } _ { 2 } + 3 \mathrm { H } _ { 2 } \mathrm { O }$$

If the combustion uses 55.8 mL of oxygen measured at 2.26 atm and

$$40 . ^ { \circ } \mathrm { C }$$

, what volume of

$$CO_2$$

is produced when measured at STP?

In one method of manufacturing nitric acid, ammonia is oxidized to nitrogen monoxide and water:

$$4 \mathrm { NH } _ { 3 } ( \mathrm { g } ) + 5 \mathrm { O } _ { 2 } ( g ) \longrightarrow 4 \mathrm { NO } ( g ) + 6 \mathrm { H } _ { 2 } \mathrm { O } ( l )$$

What volume of oxygen will be used in a reaction of 2800 L of

$$NH_3$$

? What volume of NO will be produced? All volumes are measured under the same conditions.

Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $\int _ { 0 } ^ { 1 } \ln x d x$

Dinitrogen pentoxide decomposes to produce nitrogen dioxide and oxygen:

$$2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightarrow \mathrm{O}_2(\mathrm{~g})+4 \mathrm{NO}_2(\mathrm{~g})$$

Copy and complete each of the following sentences in your notebook and fill in the blanks.$\mathrm{cm}$

(a) $0.50 \mathrm{~mol}$ of dinitrogen pentoxide will produce mol of oxygen and. mol of nitrogen dioxide.

(b) mol of dinitrogen pentoxide will produce mol of oxygen and $1.60 \mathrm{~mol}$ of nitrogen dioxide.

Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution.

$$x ^ { 2 } - 9 = 0$$

What pressure in atmospheres will 1.36 kg of

$$N_2O$$

gas exert when it is compressed in a 25.0 L cylinder and is stored in an outdoor shed where the temperature can reach

$$59 ^ { \circ } \mathrm { C }$$

during the summer?