The Rate Law and Rate Constant

Consider a reaction $a\text{G}+\text{bH}\to \text{products}$.  When concentration of both the reactants $\mathrm{G}$ and $\mathrm{H}$ is doubled, the rate increases by eight times. However, when the concentration of $\mathrm{G}$ is doubled, keeping the concentration of $\mathrm{H}$ constant, the rate is doubled. The overall order of the reaction is:

Consider the chemical reaction:

${\text{N}}_2\left(\text{g}\right)+3{\text{H}}_2\left(\text{g}\right)⟶2{\text{NH}}_3\left(\text{g}\right)$

The rate of this reaction can be expressed in terms of time derivatives of concentration of  $N_2\left(\text{g}\right)\text{ , }{\text{H}}_2\left(\text{g}\right)\text{ and }{\text{NH}}_3\left(\text{g}\right)$ Identify the correct relationship amongst the rate expressions:

What is meant by specific reaction rate?

Give the general expression for a balanced chemical equation by applying the law of mass action.

For a certain reaction, the rate $=\mathrm{k} [\mathrm{A}{]}^2 [\mathrm{B}]$, when the initial concentration of A is tripled keeping concentration of B constant, the initial rate would 

In an enzyme solution, sucrose undergoes fermentation. If $0.10 \mathrm{mol}/\mathrm{L}$ solution of sucrose is reduced to $0.05 \mathrm{mol}/\mathrm{L}$ in $10$ hours and to $0.025 \mathrm{mol}/\mathrm{L}$ in $20$ hours, then the rate constant of the reaction will be?

If concentrations of $\mathrm{A}\&\mathrm{B}$ are expressed in terms of $\mathrm{mol}/{\mathrm{dm}}^3$, and time in minutes calculate the units for the rate constant for the following reaction:

$\mathrm{A}+\mathrm{B}\to \mathrm{AB}, \mathrm{R}=\mathrm{K}{\left[\mathrm{A}\right]}^{\mathrm{x}}{\left[\mathrm{B}\right]}^{\mathrm{y}}$

The rate of the reaction : ${\mathrm{CH}}_3{\mathrm{COOC}}_2{\mathrm{H}}_5+\mathrm{NaOH}\to {\mathrm{CH}}_3\mathrm{COONa}+{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}$ is given by the equation,

Rate $=\mathrm{K}\left[{\mathrm{CH}}_3{\mathrm{COOC}}_2{\mathrm{H}}_5\right]\left[\mathrm{NaOH}\right]$. If concentration is expressed in mol ${\mathrm{L}}^{-1}$, the unit of $\mathrm{K}$ is

The initial concentration of the reactant is $0.1$ mole ${\mathrm{L}}^{-1}$. The rate constant for this reaction is $1\times {10}^{-2}$ mole ${\mathrm{L}}^{-1}{\mathrm{S}}^{-1}$. When the concentration of the reactants is increased to $0.2$ mole ${\mathrm{L}}^{-1}$, the value of the rate constant [assume constant $\mathrm{T}$]

For a reaction $\mathrm{A}+\mathrm{B}\to$ products, the rate of reaction was doubled when the concentration of $\mathrm{A}$ was doubled. When concentration of $\mathrm{A}$ and $\mathrm{B}$ both was doubled, the rate was again doubled, order of reaction with respect to $\mathrm{A}$ and $\mathrm{B}$ are

How is rate constant of a reaction affected by temperature? Write the name of this relation. How will you calculate activation energy of a reaction with the help of this relation?

For the reaction ${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}+{\mathrm{H}}_2\mathrm{O}\stackrel{ {\mathrm{H}}^{+} }{\to }{\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6+{\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$, write the rate law equation.

What is rate constant? Write 'two applications' of rate law.

Show that for the reactions of first order, the unit of rate constant does not depend upon the units of concentration.

The gas phase decomposition of acetaldehyde, ${\mathrm{CH}}_3\mathrm{CHO}\left(\mathrm{g}\right)\stackrel{ }{\to }{\mathrm{CH}}_4\left(\mathrm{g}\right)+\mathrm{CO}\left(\mathrm{g}\right)$, at $680 \mathrm{K}$ is observed to follow the rate expression, $\mathrm{rate}=\frac{-\mathrm{d}\left[{\mathrm{CH}}_3\mathrm{CHO}\right]}{\mathrm{dt}}=\mathrm{k}{\left[{\mathrm{CH}}_3\mathrm{CHO}\right]}^{\frac{3}{2}}$. If the rate of decomposition is followed by monitoring the partial pressure of acetaldehyde, we can express the rate as $\frac{-\mathrm{d}\left[{\mathrm{CH}}_3\mathrm{CHO}\right]}{\mathrm{dt}}=\mathrm{k}{\left[{\mathrm{CH}}_3\mathrm{CHO}\right]}^{\frac{3}{2}}$. 

If the pressure is measured in atmospheres and the time in minutes, then what is the unit of rate constant $\mathrm{k}$?

What is meant by 'rate constant, $\mathrm{k}$ ' of a reaction ? If the concentration be expressed in $\mathrm{mol} {\mathrm{L}}^{-1}$ units and time in seconds, what would be the unit for a first order reaction? 

What is meant by 'rate constant, $\mathrm{k}$ ' of a reaction ? If the concentration be expressed in $\mathrm{mol} {\mathrm{L}}^{-1}$ units and time in seconds, what would be the unit for a zero order reaction? 

Define the following:
 Rate law