Chapter 1: Mole Balances

What You Have Learned?

1. The rate law

(a.) is a differential equation    T     F

(b.) relates reaction rate and concentration of reacting species     T     F

(c.) is only valid in the U.S.    T     F

(d.) is a function of temperature;   T     F

2. The rate of formation of species A is per unit volume is

(a.) rA    T     F

(b.) -rA    T     F

(c.) the rate of generation of species A per unit volume    T     F

(d.) r'A    T     F

(e.) none of the above    T     F

(f.) not used in Canada    T     F

3. \( \text{A} \rightarrow \text{B} \)

At a particular time t, the rate of formation of B in the reaction, rB, is 10 mole/dm3*min. Which of the following are true?

  1. The rate of disappearance of B is -10 moles/dm3*min.

  2. The rate of formation of A is -10 mole/dm3*min.

  3. The rate of disappearance of A is 10 moles/dm3*min.

  4.  rA = -10 moles/dm3*min

  5. -rA =  10 moles/dm3*min

  6. -rB = -10 moles/dm3*min

  7. Some of the above

  8. All of the above

  9. None of the above

  10. A will disappear faster if a magician is present

Solution  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Solutions

1 (a.) FALSE
F. The rate law is an algebraic equation relating the rate of reaction with the concentration of the reacting species. Example, for the elementary reaction

\[ \text{A} + \text{B} \rightarrow \text{C} \]

the rate law is:

\[ -r_A = kC_A C_B \]

Return to Problem 1
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 (b.) TRUE

-rA = function (temperature and reacting species concentration), e.g.

\[ \text{A} + 2\text{B} \leftrightarrow \text{C} \] \[ -r_A = k \left[ C_A C_B^2 - \frac{C_C}{K_C} \right] \] \[ k = A \exp \left[ \frac{-E}{RT} \right] \]

If $\Delta$Cp = 0, then

\[ K_c(T) = K_c(T_1) \exp \left[ \frac{\Delta H_{\text{rxn}}}{R} \left( \frac{1}{T_1} - \frac{1}{T} \right) \right] \]

otherwise, see p. 930 of text.

Return to Problem 1  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 (c.) FALSE It's also valid in Canada and the northern Provinces

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1 (d.) TRUE (Page 5 of Text)

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2 (a.) TRUE (Page 8 of Text)

rA=moles of A formed, per unit time, per unit volume

[rA]~[mol/dm3 s]

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2 (b.) FALSE (Pages 3 and 5 of Text)

-rA is the rate of disappearance of A, [mol/dm3 s]

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2 (c.) TRUE

rate of formation=rate of generation

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2 (d.) FALSE (Page 6 of Text)

r'A is the rate of disappearance of A per mass of catalyst, i.e. grams of catalyst [mol/kg cat s]

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2 (e.) FALSE (a & c are true)

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2 (f.) TRUE

The Toronto Maple Leafs Hockey Team has little use for rate of formation of species A.

Return to Problem 2  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\[ \text{A} \rightarrow \text{B} \]

At a particular time t, the rate of formation of B in the reaction, rB, is 10 mole/dm3*min. Which of the following are true?

  1. The rate of disappearance of B is -10 moles/dm3*min.

  2. The rate of formation of A is -10 mole/dm3*min.

  3. The rate of disappearance of A is 10 moles/dm3*min.

  4.  rA = -10 moles/dm3*min

  5. -rA =  10 moles/dm3*min

  6. -rB = -10 moles/dm3*min

  7. Some of the above

  8. All of the above

  9. None of the above

  10. A will disappear faster if a magician is present

Solution

h. (all are true)

Explanation

Consider a constant volume (V = V0) batch system \[ \text{In} - \text{Out} + \text{Generation} = \text{Accumulation} \] \[ \text{In} - \text{Out} + \text{Formation} = \text{Accumulation} \] \[ 0 - 0 + r_A V = \frac{dN_A}{dt} \]

Equivalently

\[ C_A = \frac{N_A}{V} = \frac{N_A}{V_0} \] \[ dC_A = \frac{dN_A}{V_0} \] \[ r_A V_0 = \frac{dN_A}{dt} \] \[ r_A = \frac{d\left( \frac{N_A}{V_0} \right)}{dt} \] \[ r_A = \frac{dC_A}{dt} \quad \text{(Caution: Only valid for constant volume batch system)} \]

At t = 0 then CA = 10.1 mol/dm3. A moment later at t = 0.01 sec then CA = 10.0 mol/dm3. If dCA/dt were to be positive, the concentration of A would increase with time. However, A is being consumed so the concentration of A is decreasing with time. For small times we use a different formula to find dCA/dt.

\[ \frac{dC_A}{dt} = \frac{C_{A1} - C_{A0}}{t_1 - 0} = \frac{(10.0 - 10.1) \, (\text{mol/dm}^3)}{(0.01 - 0) \, \text{s}} = -10 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \]

The rate of formation of A is

\[ r_A = \frac{dC_A}{dt} = -10 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \] \[ r_A = -10 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \] \[ -r_A = 10 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \]

B is being formed

\[ r_B = 10 \, \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}} \]

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