Question

1. for the reaction a + b → c, which statement is correct concerning the formula of product c?

a. c forms twice as fast as the reactants a and b are used
b. c forms half as fast as a is used
c. c forms at the same rate as a and b are used up
d. c forms at a rate independent of the rate of change in concentration of a and b
e. c forms at a rate equal to the sum of the rate at which reactants a and b are used

Explanation:

To solve this problem, we analyze each option based on chemical reaction kinetics and stoichiometry principles:

Option a:

In a reaction \( A + B
ightarrow C \), the stoichiometric coefficients don’t directly determine reaction rates (rate depends on rate laws, not just coefficients). So C’s formation rate isn’t necessarily half of A/B consumption. Eliminate a.

Option b:

The statement “C forms twice as fast as the reactants A and B are used” is incorrect. From \( A + B
ightarrow C \), the molar ratio is 1:1:1. If 1 mol of A and 1 mol of B react, 1 mol of C forms. So the rate of C formation should match the rate of A/B consumption (considering stoichiometry), not twice as fast. Eliminate b.

Option c:

“C forms at a rate independent of A and B” is wrong. Reaction rates depend on reactant concentrations (via rate laws), so C’s formation rate is dependent on A and B. Eliminate c.

Option d:

For \( A + B
ightarrow C \), the stoichiometric ratio is 1:1:1. Thus, the rate of C formation (\( \frac{\Delta[C]}{\Delta t} \)) equals the rate of A consumption (\( -\frac{\Delta[A]}{\Delta t} \)) and the rate of B consumption (\( -\frac{\Delta[B]}{\Delta t} \)). This matches the statement “C forms at the same rate as each of A and B are used up.” Keep d.

Option e:

The sum of A and B consumption rates is \( -\frac{\Delta[A]}{\Delta t} + (-\frac{\Delta[B]}{\Delta t}) \). From \( A + B
ightarrow C \), \( -\frac{\Delta[A]}{\Delta t} = -\frac{\Delta[B]}{\Delta t} = \frac{\Delta[C]}{\Delta t} \). So the sum of A and B consumption rates is \( 2 \times \frac{\Delta[C]}{\Delta t} \), meaning C forms at half the sum of A/B consumption rates. Thus, e is incorrect.

Answer:

d. C forms at the same rate as each of A and B are used up