Calculating the acquisition time of a sample and hold circuit?
The worst-case distance from the final solution in terms of voltage on C1 is (from the step response of an RC-filter):

$$
V(t)=V_{max}\exp(-t/(R_1C_1))
$$

Where \$V_{max}\$ is the maximum input swing (change per sample). 
Now you might want to settle a bit more than LSB. In terms of a relative deviation of (an arbitrary) 1/4th of LSB you can write:

$$
 LSB/4 = \exp(-t/(R_1C_1)) \\
 \log(LSB/4) = -t/(R_1C_1) \\
 t = - (R_1C_1)\log(LSB/4) 
$$

Since you have 8 bits, LSB relative to 1 is \$2^{-8}\$. Then the above formula yields about 0.301 ms.