Data from a self$-$catalyzed step growth polymerization are expected to follow the rate equation

$p=1-\frac{1}{\sqrt[\phantom{2}]{u_0+kt}}$

where $t$ is the time, $u_0$ and $k$ are constants, and $p$ is the dimensionless "fractional conversion" of reactive

chemical groups. $p$ is defined by $[A]=[A{]}_0(1-p),$ so $p=0$ when no A groups have reacted and $p$ equals

$1$ when all of the groups have reacted $($so none are left, $[A]=0).$ A parameter $u_0$ in equation $1$ that differs

from $1$ corresponds to a nonzero fractional conversion $p$ at $t=0.$ This way of analyzing reactions will arise in

chemical kinetics.

Rearrange the formula in equation $1$ to a form appropriate for linear least squares. Then check by plotting these

data points to confirm that your graph shows a linear dependence.

Hint: you may find it convenient to work with $(1-p),$ instead of $p$ itself.

Comment: You do not need to determine parameters $u_0$ and $k.$