# Given that a battery produces a current of 2.5 A that passes through molten zinc chloride for 3...

## Question:

Given that a battery produces a current of 2.5 A that passes through molten zinc chloride for 3 minutes, what charge would be dissipated through the electrolyte?

## Electric Current:

Electric current can be defined as the rate of change per unit time of the charge that flows in a circuit. We can write this concept out in equation form as:

{eq}\displaystyle I = \frac{\Delta q}{\Delta t} {/eq}

We can relate the electric current to other relevant electronic parameters like electric power, potential difference, and resistance.

Given:

• {eq}\displaystyle I = 2.5\ A {/eq} is the current
• {eq}\displaystyle \Delta t = 3\ min {/eq} is the time

Let us first convert our time to seconds:

{eq}\displaystyle \Delta t = 3\ min \left(\frac{60\ s}{1\ min} \right) {/eq}

We cancel like units:

{eq}\displaystyle \Delta t = 3\ \require{cancel}\cancel{min} \left(\frac{60\ s}{1\ \require{cancel}\cancel{min}} \right) {/eq}

We get:

{eq}\displaystyle \Delta t = 180\ s {/eq}

Now electric current can be defined as:

{eq}\displaystyle I = \frac{\Delta q}{\Delta t} {/eq}

We isolate the charge dissipated:

{eq}\displaystyle \Delta q = I\Delta t {/eq}

We substitute:

{eq}\displaystyle \Delta q = (2.5\ A)(180\ s) {/eq}

We thus get:

{eq}\displaystyle \boxed{\Delta q = 450\ C} {/eq}