# An electroplating cell operates for 35 minutes with a current of 1.9 A. Calculate the amount, in...

## Question:

An electroplating cell operates for 35 minutes with a current of 1.9 A. Calculate the amount, in moles, of electrons transferred.

## Electric Current:

Electric current is needed in order to make our electrical devices work. If we don't plug our devices in to sockets or put batteries in them, no current will flow. On the atomic level, electric current is made out of moving charged particles like electrons or protons. Electric current is defined as the rate of change of the charge flowing through the circuit.

Given:

• {eq}\displaystyle t = 35\ min {/eq} is the time elapsed
• {eq}\displaystyle I = 1.9\ A {/eq} is the current

Let us first convert our time to seconds:

{eq}\displaystyle t = 35\ min \left(\frac{60\ s}{1\ min} \right) {/eq}

{eq}\displaystyle t = 35\ \require{cancel}\cancel{min} \left(\frac{60\ s}{1\ \require{cancel}\cancel{min}} \right) {/eq}

We get:

{eq}\displaystyle t = 2,100\ s {/eq}

Now for electrons, one electron carries a charge of {eq}\displaystyle q_e = 1.602\ \times\ 10^{-19}\ C {/eq}. This means that if n electrons pass through the cell by the specified time, then we can express the current as:

{eq}\displaystyle I = \frac{nq}{t} {/eq}

We isolate the electron number n:

{eq}\displaystyle n = \frac{It}{q} {/eq}

We substitute:

{eq}\displaystyle n = \frac{(1.9\ A)(2,100\ s)}{1.602\ \times\ 10^{-19}\ C} {/eq}

We get:

{eq}\displaystyle n = 2.4906\ \times\ 10^{22} {/eq}

To determine the number of moles we have, we divide our result by Avogadro's number:

{eq}\displaystyle N = \frac{2.4906\ \times\ 10^{22}}{6.022\ \times\ 10^{23}\ mol^{-1}} {/eq}

We thus get the moles of electrons:

{eq}\displaystyle \boxed{N = 0.0414\ mol} {/eq} 