Question

What is the meaning of a positive sign in the average rate of the reaction?

Answer 1

Explain the definition of rate, average rate of reaction. In average rate of reaction, write the formula and its meaning. The formula of average rate is $\dfrac{{{\left[ \text{P} \right]}_{2}}-{{\left[ \text{P} \right]}_{1}}}{{{\text{t}}_{2}}-{{\text{t}}_{1}}}$ and $-\dfrac{{{\left[ \text{R} \right]}_{2}}-{{\left[ \text{R} \right]}_{1}}}{{{\text{t}}_{2}}-{{\text{t}}_{1}}}$. $\dfrac{{{\text{y}}_{2}}-{{\text{y}}_{1}}}{{{\text{x}}_{2}}-{{\text{x}}_{1}}}$ of concentration of reactants or products v/s time graph gives the average rate. As time increases the concentration of reactants decreases and that of products increases.

Complete step by step solution:
Let us first discuss what is rate, then, we will move to the average rate.
Rate of reaction is actually the speed of reaction or how quickly any reaction proceeds in forward direction.
Let us now understand what is average rate and understand it by writing its expression:
Consider a reaction, $\text{R}\to \text{P}$ where volume remains constant. R is the reactant and P is the product of the reaction. Let ${{\left[ \text{R} \right]}_{1}}$ and ${{\left[ \text{P} \right]}_{1}}$ are the concentrations of reactants and products at time ${{\text{t}}_{1}}$ and ${{\left[ \text{R} \right]}_{2}}$ and ${{\left[ \text{P} \right]}_{2}}$ are the concentrations of reactants and products at time ${{\text{t}}_{2}}$. So, the difference in time, concentration of reactant and concentration of product will be $\vartriangle \text{t = }{{\text{t}}_{2}}-{{\text{t}}_{1}}$, $\vartriangle \left[ \text{R} \right]={{\left[ \text{R} \right]}_{2}}-{{\left[ \text{R} \right]}_{1}}$ and $\vartriangle \left[ \text{P} \right]={{\left[ \text{P} \right]}_{2}}-{{\left[ \text{P} \right]}_{1}}$ respectively.
The rate of appearance of P is equal to increase in concentration of P in the time duration. Its expression is $+\dfrac{\vartriangle \left[ \text{P} \right]}{\vartriangle \text{t}}$. Positive sign indicates increment in the concentration of P.
The rate of disappearance of R is equal to decrease in concentration of R in the time duration. Its expression is $-\dfrac{\vartriangle \left[ \text{R} \right]}{\vartriangle \text{t}}$. Negative sign indicates decrease in the concentration of R.
Additional Information: The unit of the average rate of reaction is the same as the unit of rate of reaction. The average rate is the change in concentration per unit time. Concentration is molarity or moles of particles per unit volume.
The unit of concentration is $\dfrac{\text{moles}}{\text{litre}}$ or M. The unit of time is seconds. The unit of average rate of reaction will be $\dfrac{\text{M}}{\text{t}}$ or $\text{M}\text{.se}{{\text{c}}^{-1}}$ or $\text{mol}\text{. }{{\text{L}}^{-1}}\text{. }{{\text{s}}^{-1}}$.

Note: Other than average rate, there is instantaneous rate also. Sometimes, students consider it to be the same as the definition of the two terms almost matches with each other. But there is a difference. Let us see that.
Average rate = $\dfrac{{{\left[ \text{P} \right]}_{2}}-{{\left[ \text{P} \right]}_{1}}}{{{\text{t}}_{2}}-{{\text{t}}_{1}}}$ and $-\dfrac{{{\left[ \text{R} \right]}_{2}}-{{\left[ \text{R} \right]}_{1}}}{{{\text{t}}_{2}}-{{\text{t}}_{1}}}$.
Instantaneous rate = When $\vartriangle \text{t}\to \text{0}$, then, ${{\text{r}}_{\text{inst}}}=-\dfrac{\text{d}\left[ \text{R} \right]}{\text{dt}}=\dfrac{\text{d}\left[ \text{P} \right]}{\text{dt}}$. It is the limiting point of difference in the concentration per unit of time. The slope of tangent drawn at any time ‘t’ on the C vs t graph will give instantaneous rate.