Chapter 1, Problem 1.4Q

What does a negative number for the rate of formation of species (e.g., species A), r_A = −3 mol/dm³  s, signify? What does a positive number signify? Explain.

Interpretation Introduction

Interpretation:

The significance of a given negative number for the rate of formation of species A with explanation is to be stated. The significance of a positive number for the rate of formation of species A with explanation is to be stated.

Concept introduction:

The rate of formation of any species is the total number of moles of the species, $j$ that are produced per unit volume and per unit time. The rate of formation of a species is denoted by $r_j$. The unit of rate of formation is ${\text{mol/m}}^{\text{3}}\text{s}$.

Answer to Problem 1.4Q

The negative number for the rate of formation of species A signifies that it is present at the reactant side. The positive number for the rate of formation of species A signifies that it is present at the product side.

Explanation of Solution

The given rate of formation of a species A is,

    $r_{\text{A}}=-3{\text{mol/dm}}^{\text{3}}\cdot \text{s}$

The above mentioned negative number of rate of formation of a species A, $r_{\text{A}}$, signifies that species A is present at the side of the reactant. It also describes that species A is converting itself into a product by disappearing through decomposition or combination reactions. The expression for the stoichiometric equation for species A which is converted into a product, P is shown as,

    $\text{A}\to \text{P}$

According to the stoichiometry of the reaction, one mole of product, P is formed by the disappearance of one mole of A. As, species A is disappearing to produce the species P, thus, the numerical value of rate of formation of A possess the negative sign. Hence, negative number of rate of formation of a species A signifies that species A is present at the side of the reactant.

The positive number for rate of formation of a species A is,

    $r_{\text{A}}=3{\text{mol/dm}}^{\text{3}}\cdot \text{s}$

The above mentioned positive number of rate of formation of a species A, $r_{\text{A}}$, signifies that species A is present at the side of the product. The expression for the stoichiometric equation for species A which is forming by the disappearance of species B is shown as,

    $\text{B}\to \text{A}$

According to the stoichiometry of the reaction, one mole of product, A is formed by the disappearance of one mole of B. As, species B is disappearing to produce the species A, thus, the numerical value of rate of formation of A possess the positive sign. Hence, positive number of rate of formation of a species A signifies that species A is present at the side of the product.

Conclusion

The negative number for the rate of formation of species A signifies that it is present at the reactant side. The positive number for the rate of formation of species A signifies that it is present at the product side.