Question

name: abby gerald /30

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

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

Explanation:

To solve this, we use the concept of reaction stoichiometry and rate relationships in chemical reactions. For the reaction \( A + B
ightarrow C \), the stoichiometric coefficients tell us the molar ratios of reactants consumed and products formed. The rate of consumption of reactants and formation of products is related by the stoichiometry. In this reaction, the mole ratio of \( A:B:C \) is \( 1:1:1 \). So, the rate of formation of \( C \) should be equal to the rate of consumption of \( A \) and also equal to the rate of consumption of \( B \). Let's analyze each option:

• Option a: Says \( C \) forms half as fast as \( A \) and \( B \) are used. But since the stoichiometry is \( 1:1:1 \), the rate of formation of \( C \) should be equal to the rate of consumption of \( A \) and \( B \), not half. So this is incorrect.
• Option b: Says \( C \) forms twice as fast as \( A \) and \( B \) are used. But with a \( 1:1:1 \) ratio, the rate of \( C \) formation should be equal, not twice. So this is incorrect.
• Option c: Says \( C \) forms at the same rate as each of \( A \) and \( B \) are used. Since the stoichiometric coefficient for \( A \), \( B \), and \( C \) is 1, the rate of consumption of \( A \) ( \( -\frac{d[A]}{dt} \) ), consumption of \( B \) ( \( -\frac{d[B]}{dt} \) ), and formation of \( C \) ( \( \frac{d[C]}{dt} \) ) are equal. So this is correct.
• Option d: Says \( C \) forms at a rate independent of \( A \) and \( B \). But the rate of formation of \( C \) is dependent on the rate of consumption of \( A \) and \( B \) due to the stoichiometry of the reaction. So this is incorrect.
• Option e: Says \( C \) forms at a rate equal to the sum of \( A \) and \( B \) rates. But since the stoichiometry is \( 1:1:1 \), the rate of \( C \) is equal to each of \( A \) and \( B \) rates, not their sum. So this is incorrect.

Answer:

c. \( C \) forms at the same rate as each the reactants \( A \) and \( B \) are used