For a certain reaction,the expression for half-life is $t_{1/2} \propto \frac{1}{a^{n-1}}$. What is the order of the reaction?

The rate law for the reaction $\text{Sucrose} + \text{Water} \xrightarrow{H^+} \text{Glucose} + \text{Fructose}$ is given by:

The rate of the reaction $2A + 3B \rightarrow 2C + D$ is $6 \times 10^{-4} \text{ mol dm}^{-3} \text{ s}^{-1}$, when $[A] = [B] = 0.3 \text{ mol dm}^{-3}$. If the reaction is of first order with respect to $A$ and zeroth order with respect to $B$, find the rate constant $k$.

For the reaction,$2A + B \to \text{products}$,when the concentrations of $A$ and $B$ both were doubled,the rate of the reaction increased from $0.3 \ mol \ L^{-1} \ s^{-1}$ to $2.4 \ mol \ L^{-1} \ s^{-1}$. When the concentration of $A$ alone is doubled,the rate increased from $0.3 \ mol \ L^{-1} \ s^{-1}$ to $0.6 \ mol \ L^{-1} \ s^{-1}$. Which one of the following statements is correct?

In a reaction between $A$ and $B$,the initial rate of reaction $(r_0)$ was measured for different initial concentrations of $A$ and $B$ as given below:

$A / mol \ L^{-1}$	$0.20$	$0.20$	$0.40$
$B / mol \ L^{-1}$	$0.30$	$0.10$	$0.05$
$r_0 / mol \ L^{-1} \ s^{-1}$	$5.07 \times 10^{-5}$	$5.07 \times 10^{-5}$	$1.43 \times 10^{-4}$

What is the order of the reaction with respect to $A$ and $B$?

For the reaction $XA + YB \rightarrow mp + nq$,the rate is given by $\text{Rate} = K[A]^c[B]^d$. What is the overall order of the reaction?