How is phenol converted to acetophenone?

How are the following conversion carried out?

Ethanol to methanol

Give the structure and the IUPAC name of the major product obtained in the following reaction

Write the mechanism of the reaction of acid (${\mathrm{H}}_2{\mathrm{SO}}_4$) with ethene.

Identify A and B in the following reactions :

Identify A and B in the following reactions :

Give the structure and IUPAC name of the major product obtained in the following reaction.
 

Consider a first order gas phase decomposition reaction given below: $\mathrm{X}\left(\mathrm{g}\right)\to \mathrm{Y}\left(\mathrm{g}\right)+\mathrm{Z}\left(\mathrm{g}\right)$. The initial pressure of the system before decomposition of $\mathrm{X}$ was ${\mathrm{p}}_{\mathrm{i}}$. After lapse of time t, total pressure of the system increased by $\mathrm{a}$ units and became ${\mathrm{p}}_{\mathrm{x}}$.  What will be the rate constant $\left(\mathrm{k}\right)$ for the reaction?

In a reaction between $\mathrm{X}$ and $\mathrm{Y}$, the initial rate of reaction $\left({\mathrm{r}}_{\circ }\right)$ was measured for different initial concentrations of $\mathrm{X}$ and $\mathrm{Y}$ as given below:

What is the order of reaction with $\mathrm{X}$ and $\mathrm{Y}$ ?