The correct option is Between 1 and 2.

Let's understand the concept of van't Hoff factor, denoted by $i$, and why it lies between 1 and 2 for a solution of acetic acid (${\mathrm{CH}}_3\mathrm{COOH}$) in water.

The van't Hoff factor is a measure of the effect of a solute on colligative properties, and is defined as the ratio of the actual concentration of particles produced when the substance is dissolved to the concentration of a substance as calculated from its mass.
For solutes that dissociate in solution, the value of $i$ is greater than 1.

Acetic acid (${\mathrm{CH}}_3\mathrm{COOH}$) is a weak electrolyte. When dissolved in water, it undergoes partial dissociation (ionization) to form acetate ions (${\mathrm{CH}}_3{\mathrm{COO}}^{-}$) and hydrogen ions ($H^{+}$) or hydronium ions ($H_3{O}^{+}$) according to the following equilibrium reaction:

${\mathrm{CH}}_3\mathrm{COOH}\rightleftharpoons {\mathrm{CH}}_3{\mathrm{COO}}^{-}+H^{+}$

If we assume the initial concentration of acetic acid is 1 and its degree of dissociation is $\alpha$ (where $0<\alpha <1$), we can represent the equilibrium states as follows:
- At initial state (before dissociation):
Moles of ${\mathrm{CH}}_3\mathrm{COOH}=1$, Moles of ${\mathrm{CH}}_3{\mathrm{COO}}^{-}=0$, Moles of $H^{+}=0$.
- At equilibrium state:
Moles of ${\mathrm{CH}}_3\mathrm{COOH}=1-\alpha$, Moles of ${\mathrm{CH}}_3{\mathrm{COO}}^{-}=\alpha$, Moles of $H^{+}=\alpha$.

The total number of moles of solute particles at equilibrium is:
$n_{\mathrm{total}}=(1-\alpha )+\alpha +\alpha =1+\alpha$

The van't Hoff factor $i$ is calculated as:
$i=\frac{\text{Total moles of particles at equilibrium}}{\text{Initial moles of particles}}=\frac{1+\alpha }{1}=1+\alpha$

Since acetic acid is a weak acid, it does not dissociate completely. This means that its degree of dissociation ($\alpha$) is greater than 0 but strictly less than 1:
$0<\alpha <1$

Substituting this range of $\alpha$ into the expression for $i$ gives:
$1<i<2$

Thus, the value of the van't Hoff factor $i$ for a ${\mathrm{CH}}_3\mathrm{COOH}$ solution in water is between 1 and 2.