Chemistry · Chapter 13

The Small-x Shortcut and Its Limits

Set a constant and a starting amount, and this bench solves the problem twice. Once with the shortcut, once in full, so you can see exactly when dropping the x stops being honest.

Shortcut against full answer the gap is the price of the shortcut

The shortcut value of x against the full value

Move the sliders to see how the two answers compare.

Why both gates say the same thing everything here depends only on c ÷ K

Percent dissociated and percent error against the ratio

Both gates are the same gate. A large ratio of c0 to K means little breaks apart, and when little breaks apart the dropped x hardly mattered. The marker is your current problem.

Set the problem

K = 2.0 × 10-10
0.100 M

Both answers

0.0% error in x shortcut holds
Ratio c0 ÷ K = 4.5 × 108
Shortcut x = 4.69e-6 M
Full x = 4.69e-6 M
Share that broke apart = 0.0047%
This shape passes 5% at a ratio of about 380

The working

The verdict
Keep the shortcut
x came out far under five percent of the start, so dropping it changed almost nothing.