"Pumping" Charges — Question 3

Question 3

A chemical reaction rate fixes the steady charge-pumping rate

Use $e=1.602176634\times10^{-19}$ C, exact. Each forward reaction in an ideal source transfers two electrons through its external circuit. Reactions occur at $3.00\times10^{17}\,\mathrm{s^{-1}}$. The source has $1.20\times10^{22}$ usable reactions available.

1. Find current and ideal operating time at this rate.

2. Find the total transferable charge and verify that it equals current multiplied by operating time.

Question 3 - Solution

A chemical reaction rate fixes the steady charge-pumping rate

(a) Method and calculation

$$I=2e\dot N=0.0961306\,\mathrm A.$$$$t_{\mathrm{life}}=N_{\mathrm{avail}}/\dot N=4.00\times10^4\,\mathrm s=11.1111\,\mathrm h.$$

(b) Interpretation and further calculation

$$Q_{\mathrm{total}}=2eN_{\mathrm{avail}}=3845.22\,\mathrm C.$$$$It_{\mathrm{life}}=(2e\dot N)(N_{\mathrm{avail}}/\dot N)=2eN_{\mathrm{avail}}.$$

Physical check

The source capacity is a chemical inventory; the electrons are circulated rather than consumed by the load.