Question

The order for the given reaction is :
\( \text{A} + 2\text{B} \rightarrow \text{Products} \)
\( \text{Rate} = k[\text{A}]^{1/2} [\text{B}]^1 \)

• A. \( 1.5 \)
• B. \( 1 \)
• C. \( 0.5 \)
• D. \( 2 \)

Hint:

Never use the coefficients from the balanced equation (like the '2' in 2B) to determine the order unless you are explicitly told the reaction is "elementary". Always use the exponents given in the Rate Law.

Answer 1

The Correct Option is A

Concept: The Order of Reaction is an empirical (experimentally determined) value that describes the dependency of the reaction rate on the concentration of the reactants.

• It is defined as the sum of the exponents of the concentration terms of the reactants in the rate law expression.

• If Rate = \( k[\text{X}]^a [\text{Y}]^b \), then the order with respect to X is \(a\), the order with respect to Y is \(b\), and the overall order is \( (a+b) \).

• Order can be an integer (0, 1, 2), a fraction, or even negative.
Step 1: Identifying the exponents from the given Rate Law.
The problem provides the specific rate equation determined by experiment: \[ \text{Rate} = k[\text{A}]^{1/2} [\text{B}]^1 \] From this expression, we can identify:

• The exponent of reactant A is \( \frac{1}{2} \) (which is \( 0.5 \)). This means the reaction is half-order with respect to A.

• The exponent of reactant B is \( 1 \). This means the reaction is first-order with respect to B.

Step 2: Mathematical calculation of the overall order.
To find the total or overall order of the chemical reaction, we simply need to calculate the arithmetic sum of these exponents: \[ \text{Overall Order} (n) = \text{Order w.r.t. A} + \text{Order w.r.t. B} \] \[ n = \frac{1}{2} + 1 \] Converting to decimals for clarity: \[ n = 0.5 + 1.0 = 1.5 \]

Step 3: Significance of the result.
The calculated overall order is 1.5. A fractional order such as 1.5 indicates that the reaction is not an elementary (single-step) reaction. Instead, it follows a complex mechanism involving multiple elementary steps, where the rate-determining step involves these specific dependencies.