A\(_{(g)}\) + 2B\(_{(g)}\) \(\rightarrow\) C\(_{(g)}\) In the reaction represented by the equation above, the rate...
A\(_{(g)}\) + 2B\(_{(g)}\) \(\rightarrow\) C\(_{(g)}\)
In the reaction represented by the equation above, the rate of appearance of C is found experimentally to be independent of the concentration of A and to increase four folds when the concentration of B is doubled. The rate law for the reaction is
- A)Rate = \(K[A]^0[B]^4\)
- B)Rate = \(K[A]^0[B]^2\)
- C)Rate = \(K[A][B]^2\)
- D)Rate = \(K[A]^2[B]^0\)
Correct Answer: B)Rate = \(K[A]^0[B]^2\)
Explanation
The question is asking about a chemical reaction between gases A and B that produces gas C. The rate of appearance of gas C has been found to be independent of the concentration of gas A, but to increase fourfold when the concentration of gas B is doubled. The question wants us to determine the rate law for the reaction.
The rate law describes the relationship between the concentration of the reactants and the rate of the reaction. From the experimental data, we know that the rate of the reaction depends only on the concentration of gas B, and not on the concentration of gas A. This means that the rate law must contain [B] raised to some power, but [A] raised to the power of zero.
The options given are different possible rate laws for the reaction. Option A has [A] raised to the power of zero, but also has [B] raised to the power of 4, which is inconsistent with the experimental data. Option B has [A] raised to the power of zero and [B] raised to the power of 2, which agrees with the experimental data. Option C has [A] raised to the power of 1, which is inconsistent with the experimental data. Option D has [A] raised to the power of 2, which is also inconsistent with the experimental data.
Therefore, the correct answer is Option B: Rate = \(K[A]^0[B]^2\). This means that the rate of the reaction is proportional to the square of the concentration of gas B, and is independent of the concentration of gas A. This question relates to the study of chemical kinetics, which is the study of the rates of chemical reactions and the factors that affect them. The rate law is an important concept in chemical kinetics, and it is used to describe how the rate of a reaction depends on the concentrations of the reactants.