Q.(a) Write definition of half life for any chemical reaction.

Rate = (change in concentration)/(time), so its unit is mol L^-1 s^-1 (or mol dm^-3 s^-1) — the statement is correct.

Rate of a chemical reaction = -(1/stoichiometric coefficient) x d[reactant]/dt = +(1/stoichiometric coefficient) x d[product]/dt. Since concentration is expressed in mo …

Average rate is a rate measured over a finite time span; as that span shrinks to zero it becomes the instantaneous rate — so the two are equal in the limit $\Delta t \to 0$.

The average rate of a reaction over an interval $\Delta t = t_2 - t_1$ is:

$\text{Average rate} = -\dfrac{\Delta[R]}{\Delta t} = -\dfrac{[R]_2-[R]_1}{t_2-t_1}$

This is the mean rate over that whole time span and can mask how quickly the rate is actually changing within the interval.

The instantaneous rate at a specific time $t$ is the slope of the concentration-vs-time curve at that exact point:

$\text{Instantaneous rate} = -\dfrac{d[R]}{dt}$

Mathematically, the instantaneous rate is defined as the limit of the average rate as the time interval shrinks to zero:

$\text{Instantaneous rate} = \lim_{\Delta t \to 0} \left(-\dfrac{\Delta[R]}{\Delta t}\right) = -\dfrac{d[R]}{dt}$ …

The rate 'at a particular moment' (not averaged over an interval) is called the instantaneous rate.

Average rate is calculated over a finite time interval (Delta[R]/Delta t) and changes depending on which interval is chosen. To get the rate AT one specific instant, we let the time interval shrink to zero:

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Rate depends on reactant concentration; as reactants are consumed, concentration and hence rate fall with time.

For a typical reaction, Rate = k[reactant]^n. As the reaction proceeds the reactant concentration continuously decreases, so the rate also decreases with time (it is maximum at the start and appr …

For a reaction $3A \to 2B$, the rate of the reaction expressed via each species must be divided by its own stoichiometric coefficient, so rates in terms of A and B are related by the ratio of those coefficients.

Setting up the rate expression: For $3A \to 2B$, the overall rate of reaction is defined uniquely (independent of which species you track) as:

$\text{Rate}=-\frac{1}{3}\frac{d[A]}{dt}=+\frac{1}{2}\frac{d[B]}{dt}$

Solving for d[B]/dt in terms of d[A]/dt:

Given the rate of production of B is $+\dfrac{d[B]}{dt}$, equate:

$\frac12\frac{d[B]}{dt}=-\frac13\frac{d[A]}{dt}$ …

For gaseous reactions, concentration is expressed as partial pressure, so rate has units of pressure/time.

Rate of reaction = (change in concentration)/(time). For reactions involving gases, concentration is conveniently measured as partial pressure (atm) …

Average rate is measured over a finite $\Delta t$; as that interval is shrunk toward zero, the average rate converges exactly to the instantaneous rate at that moment.

The average rate of a reaction over an interval is $-\dfrac{\Delta[R]}{\Delta t}$ (or $+\dfrac{\Delta[P]}{\Delta t}$), computed using the change in concentration over a finite time interval $\Delta t$. The instantaneous rate is the rate at one particular instant, given by the derivative $-\dfrac{d[R]}{dt}$.

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Instantaneous rate is the rate at one exact moment, found as $-d[R]/dt$ — the slope of the tangent drawn to the concentration-time plot at that instant (Δt → 0).

Whereas the average rate is measured over a finite time interval, the instantaneous rate is the rate of the reaction at one particular instant of time. It is obtained mathematically by making the time interval Δt infinitesimally small (Δt → 0), turning the average-rate expression into a derivative:

$\text{Instantaneous rate} = \lim_{\Delta t \to 0} \left(-\frac{\Delta[R]}{\Delta t}\right) = -\frac{d[R]}{dt} = \frac{d[P]}{dt}$ …

Average rate = (change in concentration) / (time interval) over a finite interval $\Delta t$.

For a reaction R → P, the average rate over the time interval $t_1$ to $t_2$ is

$\text{Average rate} = -\frac{[R]_2-[R]_1}{t_2-t_1} = \frac{[P]_2-[P]_1}{t_2-t_1} = -\frac{\Delta[R]}{\Delta t} = \frac{\Delta[P]}{\Delta t}.$ …