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If the molecule of $mathrm{HCl}$ was totally polar, the expected value of dipole moment was $6.12 mathrm{D}$ but the experimental value of dipole moment calculated ...

Question

If the molecule of $mathrm{HCl}$ was totally polar, the expected value of dipole moment was $6.12 mathrm{D}$ but the experimental value of dipole moment calculated was 1.03 D. Calculate the percentage ionic character.(a) 0(b) 17(c) 50(d) 90

If the molecule of $mathrm{HCl}$ was totally polar, the expected value of dipole moment was $6.12 mathrm{D}$ but the experimental value of dipole moment calculated was 1.03 D. Calculate the percentage ionic character. (a) 0 (b) 17 (c) 50 (d) 90



Answers

If the molecule of $\mathrm{HCl}$ was totally polar, the expected value of dipole moment was $6.12 \mathrm{D}$ but the experimental value of dipole moment calculated was 1.03 D. Calculate the percentage ionic character. (a) 0 (b) 17 (c) 50 (d) 90

This question is in reference to the relationship between the dipole moment of a bond, the distance or bond length between the atoms that comprise that bond and the percent Ionic character. There's an equation on page 209 in your textbook that relates the dipole moment to the charge of an electron in the distance between the positive and negative charges. There's also an equation on that same page that shows you the percent Ionic character as a ratio of the measured dipole moment of a bond to the dipole moment if the electron were completely transferred, there's also a table or a figure that shows you the percent Ionic character for various species as a function of electro negativity. It is this page where you'll find the information needed to answer this question. First, let's rewrite what was provided. We know the dipole moment of HCL was given to us as 1.8 to buy, and for HF as 1.82 to buy other information that it tells us that we need is found in figure 5.5. That shows the percent Ionic character of various species as a function of their electro negativity difference. The two species that were considering our HCL, which from the graph, if you look you could maybe estimate it is 18% ionic and H F. When you look at the graph, it appears that it might be around 43%. Ionic. The equation that you need is the dipole moment is equal to the charge of an electron multiplied by the distance between the two nuclei. Rearrangement of this equation allows you to solve for the distance between the two nuclei. Well, the dipole moment we have appear. But what about Q? Will queue corresponds to the charge of an electron if the two charges are, um, separated? If the two charges were created due to the transfer, the complete transfer of an electron? If, however, it's only a partial transfer saying 18% transfer or a 43% transfer in this Q needs to be 18% the charge of an electron, or 43% the charge of an electron. So to solve for the distance between the H and C L in HCL, we need to take the dipole moment, which was given to us is 1.0 eight by and converted into units that are found in this equation. Cool um, meters recognizing one. Dubai is three point 34 times 10 to the negative 30 kilometers. We then divide that by the charge of an electron based upon the percent Ionic character. The charge of an electron is 1.6 times 10 to the negative 19, but for HCL it's only 18% Ionic character, so 18% is 180.18 This then gives us on our value of 1.25 times 10 to the negative 10 m or 125 people meters. We then do the same thing for HF but used the 1.82 to buy and in the denominator will use the charge of an electron and the 0.43 because it's 40 Onley, 43% Ionic character and we'll get 8.34 times 10 to the negative 11 or 88 PICO meters. If we compare these calculated values to what's available in table 5.4, we'll see that they are very similar

So here we're trying to determine the charge on each hydrogen atom so we can have Let's draw the diagram here. Essentially haven't Oh, Adam here with our negative that holes. We have h at him here with her positives eyeballs and we have a die. Poor moment. Travelling like this. A typo moment travelling like this and then a resultant type all moment like this. So this will be labeled P and then this would be a piece of one and this would be peace of two. We know that this angle right here is going to be one hundred for degrees. And at this point we can write our givens. So we know that the magnitude of the resultant mo mentum rather die. Paul moment would be six point one times ten to the negative thirtieth Coolum meters. The DEA separation would be nine point six times ten to the negative ninth meters. And we have fada, which in this case would be one hundred four, divided by two. So this would be fifty two degrees s o. We know that piece of one is going to be equal to cues of acute times, dear brother and from the figure. We know that P is going to be equal to two times piece of one coastline of data. So then we can relate this and say that P equals to Q D Co sign of data, which means that Q simply equals P over to D co sign a theta and then we can solve. So Q equals. And then we have six point one times ten to the negative thirtieth and we have to. And then Dee would be again nine point six times ten to the negative ninth and then co sign of fifty two degrees. So we find that this is going to be equal to five point one seven times ten to the negative twentieth and this would be charge on each H. So this would be our final answer. Fought weather. Close your eyes five point one seven times tenth and they've twentieth cool ums. That is the end of the solution. Thank you for watching

So they're different concepts in this particular topic we have electric dye opposed, we have an electric field and we have a talk acting on that hole, electric dipole moment is essentially when you have two pairs of equal and opposite charges. So you have your cue. Are you negative? Cute? And these two charges are all separated by a distance. Ah It's a very small distance. It could be negligible but you can see it. And that typo moment is it's a vector where the magnitude is equal to the process is equal to the price of the charge. We're very distant. So we want to calculate the election typo moment in the vectors to act. There has various directions from a negative charge to a positive charge. And that's what essentially was an electric potential of a diet poses. But that's just a brief understanding of where it is. But to go to the first question um we're told to essentially to calculate what is the charge of the net charge on each atom. So the doc pol doesn't experience of course in a uniform electric field but experiences of tort in the electric field and the dia po'd experiences of force which is say charge Q. Is equal to p overact and that's for the charge of each die opposed. So queues essentially the charge and each diaper load and p is a typo moment which we briefly we briefly discussed. So p he was the charge of diet pose each type, Each typos of he is the guy opposed moment and the X. If the distance between the charges, remember the child is a small distance. So it's not that huge. So actually the distance between the two charges. And we're told to calculate the next charge on each die approach. Given that we know for each charge is equal to p overacting. We know that P is 3.4 times 10 To the -30. Cool Arms Tom's meter. So C. M. Columns meter. And the distance between two charges are given in a question As 1.0 times 10 to the negative 10 meters. As you can see the media's cancers out. So charges are basically the basically the units were charges called the colon. Um, so you eventually have a cool on. That's why the M cancers out. Put them into your calculator. We have 3.4 times 10 to the -20. Cool on. So essentially what we did here is we found the value or the magnitude of a charge on each side I oppose. So for each charge the magnitude is 3.4 Times 10 to the -20. Cool art. For part B For part B were Act two. Explain why this is not equal. Well acts to explain why this is not equal to an integral multiple of these E. In this case is our electron. So consider that considered an electric Diet code consists of a pair of equal but opposite charges but it's also separated by a small distance. We talked about the Diet code moment being a vector where the magnitude equal to the process of the charge with a distance and has a direction of either positive or negative. So if effort charge it's Qantas sized. So that means essentially has an integral multiple of a judgment electron. We know too is equal to and time. Mm And and it's just could be and the integer whether positive or negative. And he is just the charge of an electron. And We know the charging electronic constant which is 1.6 Times 10 to the -19 cool on. So the value of each charge and so to calculate the value of each charge in the diet pose we could do our oh and a few We know are the electron is 1.6. The value for the alleged huh? 1.6 times 10. The negative. My team accused the value of charging each die uphold Which is 3.4 times 10 To the -20 Koran. Now since the value of Q it's less than the charge of the electron, that means that Q. Is no longer a part of the integral multiple of the charge of an electron. So especially because the value of the charge it's less. Then what the fundamental charged electron is. We could say that because of that it is no longer integral multiple of the of that electron. So your explanation sense the value of the charge E. Of the Charles Q. My bed of the charge cube is less than and the fundamental charge of the value of E. Because decipher that we could decipher there there's that there is not an integral multiple feeds and 12 part C. For fort C. With toast to calculate the maximum church. So we asked, what is the maximum church that was in the diet pose that a diaper will experience. So for part C. Given that the maximum heart torque is this is uh a greek letter for torture. What's told that that the maximum hurt to calculate the maximum church what that the diet for would experience when it is placed in the metric field of two points 2.5 times 10 to the sport anytime slash cool art. So the electrical field is given us has given us E. And we had we know that he is 2.5 time Utah Utah black school on. Okay, so toward a torque in itself. So we have to calculate the net force acting on a dive pose given that the net force all the forces acting on each tire post is zero. And the torque the torque acting on the diet poor. They expressed as torture is expressed at Q. E. Where a few is is the charge of the dye pose. And E. Is the electric field. So Q. E. X. Science data and X. Is the distance between the two charges for max talk or max talk for the diet code to experience a max towards Data has to be 90°. So its highest point Where you have the maximum torque will be 90° data. So Q. E. X. Science data signing many degrees is one. So you left with to E. I stay enough. So Q E Q. E. You're left with cute. So we know what a cute is. Talk to people few times eight. Sorry about few times torque is given that eight times. So we know back to the original problem. We know that a diet posed moments. We know what our diet hold moment is And we have that as being 3.4 times 10 to the negative 20 To the negative 33.4 times 10 to the negative 30 mm. Cool off the meter times are electric field and we know the electric feel is is given us 2.5 times 10 to the four new times for long. Including dementia calculator. You have 8.5 times 10 to the negative 26 New times per meter. So this essentially tells us that the short acting on the dia pose is 8.5 times 10 to the negative 26 your time the media for the last one for part the for part B what's told to but told to how much energy would be needed to rotate More molecules 45° from its equivalent equilibrium position of lowest potential energy. So every time we talk about energy which is worth integration plays a part. So the energy required for the diet culture rotate. It's the work done dumped. You. You need to integrate, you need your to remember your anti grows your integration anytime your calculation work done the work required. So you have the integral and you have your lower bond and europe upon. So your initial we call that I and your final leave. All this you have towards the data, Torti data and three degrees. So the initial value Unless you're value is zero and your final value it's 45. Because we have to calculate, we're told to calculate from When the rotates from 45° from its equivalent position. So the lowest potential energy that are highest potential energy. That's what we're asking this problem. So initial value is 0° initial is zero degrees. You know, final degree. Our final position mm It's 45° mm So W equal to Gold bond for zero bob. Place five. Mhm. It was hard field electric field. Uh He by data these data right. If you look at the problems 45 degrees, that means we're dealing with the X axis. So the Y axis is negligible in this case because the rotates. So this becomes W. Is equal to E. P. Coast time. 45°- Co sign zero. Now for the potential energy of their diet pose potential energy doing this. You Think there's three points four times Hence in the Nebula 30 Times 2.5 Times 10 to the 4th. And your X axis coast on Close to 45° co sign zero. You could put this into your calculator. You have you potential energy equal to 2.49 time 10 to the -26. Use again, potential energy. The use measures the US is measured by is jules. So essentially what we found in this problem was recalculated the potential energy of the diet pose you As being equal to 2.49 times 10 to the -26. You and that's your answer for your part, A B, C and E.

So for this problem, the first thing you want to do is find the electric field from the water molecule. And so we're given the dipole moment of the water. We have the purgative ity of the vacuum, which would be just as a constant, and we have the distance between them, and that's what we're gonna need to find the electric field. It's the equation we're going to use. Is electric fields equal to die Poll moment over two pi absolute knots, Times X cubed and then playing in our values that were given that I have written on the left, you find the electric field from the Dye poll, it's going to be 4.11 times 10 to 6. Newton's over cool ums, and the direction is going to be in the positive X direction or away from the Dye poll. And so next we're going to use this electric field to find the electric force on the chlorine I on. So we know that electric force is equal to the electric field times the charge. We're given the charge of the chlorine I on. And so if we plug in that and then the electric field that we just found. You find the force is equal to 6.6 times 10 to the minus 13 Nunes and the Electric Fields movie is in the positive X direction, and the charge of the chlorine ion is negative. And so the force is going to be opposite of the electric field or in the minus X direction.


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