# Chapter 1: Mole Balances

## Self Test - The Convention for Rates of Reaction

Consider the reaction

in which the rate of disappearance of A is 5 moles of A per
dm^{3} per second at the start of the
reaction.

At the start of the reaction

(a) What is -r_{A}?

(b) What is the rate of formation of B?

(c) What is the rate of formation of C?

(a) +15 (b) -15 (c) -7.5 (d) +7.5

(d) What is the rate of disappearance of C?

(a) +15 (b) -15 (c) -7.5 (d) +7.5

(e) What is the rate of formation of A,
r_{A}?

(f) What is -r_{B}?

## Answers

(a) -r_{A} is the rate of disappearance of A is

_{A}= 5 mol/dm

^{3}/s

(b) For every one mole of A that disappears, two moles of B disappear. Reactant B is a is disappearing twice as fast as reactant. I.e., A.

-r_{B} = 2 x -r_{A} = 10 moles/dm^{3}/s

Multiplying by minus one (-1) we get the rate of formation of B

_{B}= -10 mol/dm

^{3}/s

B is being used up therefore its rate of formation is a negative number.

(c) C is a product that is being formed three times as fast as A is disappearing

_{C}= 3 x (-r

_{A}) = 15 mol/dm

^{3}/s

Because C is a product is being formed, its rate of formation is positive.

(d) The rate of disappearance of C is
-r_{C}. Therefore we multiply the rate of
formation of C, r_{C}, by minus one (-1) to
get

_{C}= -15 mol/dm

^{3}/s

Because C is a product, its
rate of disappearance, -r_{C}, is a negative
number.

(e) A is a reactant that is being used up therefore its rate of formation is negative

_{A}= -5 mol/dm

^{3}/s

(f) -r_{B} is the rate of disappearance of B

_{B}= 2 x (-r

_{A}) = 10 mol/dm

^{3}/s

## Summary

Rate
of disappearance of A = -r_{A} = 5
mole/dm^{3}/s

Rate
of disappearance of B = -r_{B} = 10
mole/dm^{3}/s

Rate
of disappearance of C = -r_{C} = -15
mole/dm^{3}/s

Rate
of formation of A = r_{A} = -5
mole/dm^{3}/s

Rate
of formation of B = r_{B} = -10
mole/dm^{3}/s

Rate
of formation of C = r_{C} = 15
mole/dm^{3}/s

For *reactants* the rate of *disappearance* is a
positive (+) number.

For *products* the rate of *disappearance* is a
negative (-) number because they are being formed and not disappearing.

For *reactants* the rate of *formation* is a negative
(-) number because they are disappearing and not being formed.

For *products* the rate of *formation* is a positive (+)
number.

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