A magnesium ion, Mg²⁺, with a charge of 3.2⨉10^-19 C and an oxide ion, O2-, with a charge of -3.2⨉10^-19 C, are separated by a distance of 0.35 nm. How much work would be required to increase the separation of the two ions to an infinite distance?

Video transcript

Welcome back everyone in this example, we're told that the distance between a magnesium two plus ion with a charge of 3.2 times 10 to the 19th power columns and a chloride ion with a charge of 1.6 times 10 to the 19 columns is 2.53 PK meters. What is the amount of work needed to make the distance between the two ions an infinite distance. So what we need to recognize is that to calculate the work needed to make the distance between our ions infinite. We're going to need to calculate electrostatic energy presented by E sub E L. We should recognize that because we are going to be increasing the distance between our ions. We're going to be doing work on the ions where we're going to be moving against the direction of the electro electric field of our ions. And so we're going to recall that. Our equation for electrostatic potential energy can be calculated by taking columns constant, multiplied by the quotient where we have Q one for our first charge of our caddy on Q two and I'll write that in a different color which represents the charge of our an ion. And then in the denominator we have our term D. As diameter or the distance between our charges. We can use the same interpretation to calculate for the amount of work that's going to be being done on the electric field between our charged ions in order to increase their distance. And so we would say that work can be calculated by taking again, columns constant, multiplied by the quotient Where we have the charge of Arkady on, multiplied by the charge of our an ion divided by the radius squared or the diameter of our charged ions between our charged ions. So let's calculate using either one of these formulas and in this case let's just go ahead with this first equation where plugging in what we know, we can say that our electrostatic potential energy is equal to columns constant, which we should recall represents the value 8.99 times 10 to the ninth power in units of jewels. Times meters divided by columns squared. So let's make these parentheses bigger. This is our columns constant, which we're multiplying by our quotient where we have in our numerator, the charge of Arkady on given in the prompt as 3.2 times 10 to the 92. The negative 19th power units of columns, which is then multiplied by the charge of our an ion Which is given in the prompt as 1.6 times 10 to the negative 19th power units of columns. In our denominator, we plug in the distance between our charged particles which is given in the prompt as 2.53 PK meters. But because we recognize that we have units of meters. In our numerator from our columns constant, we're going to convert from PICO meters, two m in the denominator. So by recalling upon the fact that are prefixed PICO means that we have 10 to the negative 12 power of our base unit meter for one m. This allows us to cancel out units of PICO meters, leaving us with meters in the denominator, which we can now cancel out with meters in the numerator continuing to cancel out our units because we're calculating for electrostatic potential energy, we want to be left with jewels. So we're going to cancel out our units of columns squared with columns squared here in the numerator, leaving us with jewels as our final unit for energy and what this will calculate to in our calculators is a value of 1.82 times 10 to the negative 16th power jewels. And so this would be our electrostatic potential energy or the amount of work that is going to be needed to act upon our electric field between our charged ions to increase the distance between them. So we're acting against that electric field. So what's highlighted in yellow here is our final answer. But we actually need to correct this so that it's only two sig figs because that is the least amount of sig figs in our prompt. So let's erase this. And for 26 figs we would just have 1.8 times 10 to the negative 16th power jewels as our final answer here for two sick fix. So I hope that everything I reviewed was clear. If you have any questions, please leave them down below and I'll see everyone in the next practice video.