The root-mean-square distance travelled by a molecule undergoing a one-dimensional random walk in a liquid or gas in a time interval is . The diffusion coefficient for the diffusion of sucrose through water at a temperature of 20°C is 4.59 * 10^-10 m² s^-1. Calculate the distance through which a sucrose molecule moves in 1.00 ms.

Question

Quizplus · Accepted Answer

The root-mean-square distance $d$ travelled by a molecule in a one-dimensional random walk can be calculated using the formula $d = \sqrt{2Dt}$, where $D$ is the diffusion coefficient and $t$ is the time. Given $D = 4.59 \times 10^{-10} \, \text{m}^2/\text{s}$ and $t = 1.00 \times 10^{-3} \, \text{s}$, substituting these values into the formula gives $d = \sqrt{2 \times 4.59 \times 10^{-10} \times 1.00 \times 10^{-3}} \approx 3.03 \times 10^{-6} \, \text{m}$ or $3.03 \, \mu\text{m}$.

The Root-Mean-Square Distance Travelled by a Molecule Undergoing a One-Dimensional μ\muμ

The Root-Mean-Square Distance Travelled by a Molecule Undergoing a One-Dimensional $\mu$