Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps:

$$\mathrm { CO } ( g ) + \mathrm { Cl } _ { 2 } ( g ) \rightleftharpoons \operatorname { COCl } ( g ) + \mathrm { Cl } ( g )$$

At

$$25 ^ { \circ } \mathrm { C }$$

the rate constants for the forward and reverse reactions are

$$1.4 \times 10 ^ { - 28 } M ^ { - 1 } \mathrm { s } ^ { - 1 }$$

and

$$9.3 \times 10 ^ { 10 } \mathrm { M } ^ { - 1 } \mathrm { s } ^ { - 1 }$$

respectively. What is the value for the equilibrium constant at

$$25 ^ { \circ } \mathrm { C } ?$$

Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps:

$$\mathrm{CO}(g)+\mathrm{Cl}_2(g) \rightleftharpoons \mathrm{COCl}(g)+\mathrm{Cl}(g)$$

At $25^{\circ} \mathrm{C}$ the rate constants for the forward and reverse reactions are $1.4 \times 10^{-28} \mathrm{M}^{-1} \mathrm{~s}^{-1}$ and $9.3 \times 10^{10} \mathrm{M}^{-1} \mathrm{~s}^{-1}$, respectively. What additional information would you need in order to decide whether the reaction as written is endothermic or exothermic?

The formation of SO3 from SO2 and O2 is an intermediate step in the manufacture of sulfuric acid, and it is also responsible for the acid rain phenomenon. The equilibrium constant KP for the reaction 2 SO2 (g) + O2 (g) <=> 2 SO3 (g) is 0.13 at 830 degree C. In one experiment 2.00 mol SO2 and 2.00 mol O2 were initially present in a flask. What must the total pressure at equilibrium be in order to have an 80.0 percent yield of SO3?

For the equilibrium $\mathrm { PH } _ { 3 } \mathrm { BCl } _ { 3 } ( s ) \rightleftharpoons \mathrm { PH } _ { 3 } ( g ) + \mathrm { BCl } _ { 3 } ( g )$ $K _ { p } = 0.052$ at $60 ^ { \circ } \mathrm { C }$ After 3.00 g of solid $PH_3BCl_{3}$ is added to a closed 1.500-L vessel at $60 ^ { \circ } \mathrm { C }$ the vessel is charged with 0.0500 g of $BCl_3(g).$ What is the equilibrium concentration of $PH_3?$

The following reaction $\ce{2H2S(g) ⇌ 2H2(g) + S2(g)}$, $K_c=1.67\times10^{-7}$

is carried out at $\ce{800\degree C}$ with the following initial concentrations: $\ce{[H2S] = 0.100M}$, $\ce{[H2] = 0.100M}$, and $\ce{[S2] = 0.00 M}$. Find the equilibrium concentration of $\ce{S2}$. Express the molarity to three significant figures.

A rocket's mass decreases as it burns fuel. The equation of motion for a rocket in vertical ight can be obtained from Newton's law, and it is

$$m ( t ) \frac { d v } { d t } = T - m ( t ) g$$

where $T$ is the rocket's thrust and its mass as a function of time is given by $m ( t ) = m _ { 0 } ( 1 - r t / b ) .$ The rocket's initial mass is $m _ { 0 } ,$ the burn time is $b$ , and $r$ is the fraction of the total mass accounted for by the fuel. Use the values $T = 48,000 \mathrm { N } , m _ { 0 } = 2200 \mathrm { kg } , r = 0.8 , g = 9.81 \mathrm { m } / \mathrm { s } ^ { 2 } ,$ and $b = 40 \mathrm { s } .$ Determine the rocket's velocity at burnout.

At

$$1285 ^ { \circ } \mathrm { C }$$

the equilibrium constant for the reaction

$$\mathrm { Br } _ { 2 } ( g ) \rightleftharpoons 2 \mathrm { Br } ( g ) \text { is } K _ { c } = 1.04 \times 10 ^ { - 3 }$$

A 0.200-L vessel containing an equilibrium mixture of the gases has 0.245 g

$$\mathrm { Br } _ { 2 } ( g )$$

in it. What is the mass of Br(g) in the vessel?

The equilibrium constant Kc for the reaction I2(g) <=> 2I(g) is 3.8×10^-5 at 727 °C. Calculate Kc and Kp for the equilibrium 2I(g) <=> I2(g)

At $\ce{850 K}$ the equilibrium constant for the reaction:

$\ce{2SO2(g) + O2(g) ⇌ 2SO3(g)}$

is $K_c=15$. If the given concentrations of the three gases are mixed, predict in which direction the net reaction will proceed toward equilibrium:

a. $\ce{[SO2] = 0.60 M, [O2] = 0.70 M, [SO3] = 0.16 M}$

b. $\ce{[SO2] = 0.20 M, [O2] = 0.60 M, [SO3] = 0.60 M}$

c. $\ce{[SO2] = 0.10 M, [O2] = 0.20 M, [SO3] = 0.40 M}$

At 800 K, the equilibrium constant for

$$\mathrm { I } _ { 2 } ( g ) \rightleftharpoons 2 \mathrm { I } ( g )$$

is

$$K _ { c } = 3.1 \times 10 ^ { - 5 }$$

If an equilibrium mixture in a 10.0-L vessel contains

$$2.67 \times 10 ^ { - 2 }$$

of I(g), how many grams of

$$I_2$$

are in the mixture?

A sample of nitrosyl bromide (NO Br) decomposes according to the equation

$$2 \mathrm { NOBr } ( g ) \rightleftharpoons 2 \mathrm { NO } ( g ) + \mathrm { Br } _ { 2 } ( g )$$

An equilibrium mixture in a 5.00-L vessel at

$$100 ^ { \circ } \mathrm { C }$$

contains 3.22 g of NOBr, 3.08 g of NO, and 4.19 g of

$$Br_2$$

What was the mass of the original sample of NOBr?

According to a model developed by economists E. Heady and J. Pesek, if fertilizer made from N pounds of nitrogen and P pounds of phosphate is used on an acre of farmland, then the yield of corn (in bushels per acre) is

$$Y = 7.5 + 0.6 N + 0.7 P - 0.001 N ^ { 2 } - 0.002 P ^ { 2 } + 0.001 N P$$

A farmer intends to spend $30/acre on fertilizer. If nitrogen costs 25 cents/lb and phosphate costs 20 cents/lb, which combination of N and P produces the highest yield of corn?

draw a scatter diagram

$$\begin{array}{ccccccc}{X} & {0} & {1.2} & {1.8} & {2.3} & {3.5} & {4.1} \\ \hline Y & {2} & {6.4} & {7} & {7.3} & {4.5} & {2.4} \\ \hline\end{array}$$

Find the value of k that would make the left side of each equation a perfect square trinomial. $25 x^{2}-k x+1=0$