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QUESTION 87According to the Stokes-Einstein equation, if the radius of one particle is twice the radius of a second particle r1 = 2 r2 ) , then the relative value o...

Question

QUESTION 87According to the Stokes-Einstein equation, if the radius of one particle is twice the radius of a second particle r1 = 2 r2 ) , then the relative value of their diffusion coefficients should be a.D1 = Dz / 8 b. Di = Dz/ 2 Dz = Dz / 4 d.D1 = 2 DzQUESTION 88The Stokes-Einstein equation is valid only if the diffusing particles are a. At equilibrium (there is no concentration gradient) b. Cold Warm d.Spheres

QUESTION 87 According to the Stokes-Einstein equation, if the radius of one particle is twice the radius of a second particle r1 = 2 r2 ) , then the relative value of their diffusion coefficients should be a.D1 = Dz / 8 b. Di = Dz/ 2 Dz = Dz / 4 d.D1 = 2 Dz QUESTION 88 The Stokes-Einstein equation is valid only if the diffusing particles are a. At equilibrium (there is no concentration gradient) b. Cold Warm d.Spheres



Answers

The $ \textit{diffusion equation} $ $$ \dfrac{\partial c}{\partial t} = D \dfrac{\partial ^2c}{\partial x^2} $$ where $ D $ is a positive constant, describes the diffusion of heat through a solid, or the concentration of a pollutant at time $ t $ at a distance $ x $ from the source of the pollution, or the invasion of alien species into a new habitat. Verify that the function $$ c(x, t) = \dfrac{1}{\sqrt{4 \pi Dt}} e^{-x^2/(4Dt)} $$ is a solution of the diffusion equation.

In the given problem, the Caribbean Billy Beane di ignited in the outside on that night. Didn't I actually see one? The concentration of benefit concentrations are doing where this is already the reactions until equilibrium. So you re brand concentrations have given here. Now the warning will be reacting. Trees on the home We have to fight. What is in your people in concentration? Open door for on, you know, and also by nobody big politics. But they, uh, actually become more bone or no, because nitrogen dioxide is brown in color and ovaries colorless. Well, it's so unlike because we will get late. The big living in Constant you put in sequence unconditional, you know, to you. Anyway, one conditional into over equals the little boy. 010475 zero full seven was Well, do you wanna wait? You don't hold seven point, you know, blood 4321 No, you got to get the value 4.63 They do, then both minus you. And here you want to know Is this No. Suppose we increase a a big reason According to her, the decrease of warding Johar the concentration go incineration beverage's that is the initial conservation All the extent recover. You should want in effect, Mr Www. And do that is he want hope the trained in Morning, If you will release awarding to hop, record these injuries rifle using please now in this reaction, even see can't do it for one more of into a border is giving two months of age an increase in business on this year, we drive the reaction you would be left inside, since the reactionary they would do. The direction in which less number of Moore's off Morse is present in the reactions is forming reactions. So and in Greece, off pressure here, the neighborhood reaction back do they starting with you. So the contribution all in new into a horrible, big, increased Well, I mean, that would be illegal. That would let us see what had been in Cleveland concentration again. We will get blade. They compared the grill. Keep in constant will remain the same. So Casey equals the new constitutional and no do square by indoor book. This is what we have to find out. But that was we have to go right? And I see Gaber were we compared the initial constitutional concentration on the Caribbean concentration, indoor war and your to the emissions. I do the initial I knew. When the world is reduced, he's going to be a little bored for 87 into two. And she had the value is, you know, board 47 by you Didn't? No. Once it's happened when you reach a secret, Graham support six is the most bidding would change in the concentration Will be Will do. Zero born. No, William. It's so when we fix zoomed in consciousness, we have already seen that very arsonist going backward direction. So they have been increasingly considers. Well, that is We're gonna bay it would be outed less x. I'm here this minus two weeks. But each more often do over a bomb. Two more up in your toe, you know, do is getting into. As for the given the question can dojo given doing you? Is it a You should. So let us substitute these values here in the Caribbean. Constantly expression, you know, board, you know? Well, someone fire. Thank you too. Minus two x Boisclair Already wanted by zero born 0 47 aboard for good. Seven going to do less things equals. If you can't read this, this will be equal. Does over equivalent Constant for 463 in September minus which we have only got grated here. No, we have the final. Great. If you do a calculation off this X my political competition are using a graphic of my thermometer will give you the value of X secrets. Zero born 0137 will be two values. Of course, For a theoretical question, that second debate is negative. So we're not considered that value. So once the new agreements established the wants and there's been to before maybe Equador zero point 487 in the door plus x video board you don't want equals I want my in Dublin. What I and that if we know, do equals one you know, for so in for you. You need to minus Do you do terrible 0137 equals little point 067 What? No can t heal the guns in their concentration. Assange's from 0.4 seven play to you know, born 06 7.4. So you want you can see from this man who this right under four reaction will Mr will be done darker

Here the value U. C. is equal to one. Multiplication, one x 1, multiplication one which is equal to one. So you see is greater than Casey reaction will proceed backwards direction. So I'm just writing it A to G plus P two. G is in equilibrium with C to G Plus The two D. So here concentration at equilibrium age one plus X by 10, one plus X by 10. one -X by 10. one -XY. 10. These are the concentration, add equilibrium position. So I can write the Christian at 0.25 physical too, one -X by 10 squared by one plus X. Bye then square. Which I'm solving I get the value of X is equal to 0.333. Now it A to G is equal to one plus X by 10 Which is equal to 1.333 By 10, which is equal to 0.133. So the option C. Is correct.

In this given chemical reaction, three molecules of a reacts with one molecule, er B to produce two molecule of C and one molecule of D. One thing we cannot hear that is in gaseous state. B is in pure solid estate, while C and D are inadequate state. Now, after the, after this reaction has achieved equilibrium, their concentrations in terms of mood or more clarity is given in the problem. So is 2.48 mol B is 2.41 mole C has the concentration 1.13 Mueller, and D has the concentration 2.27 Golden. So these are the datas are the equilibrium values Now in the problem, it is also mentioned that volume of the flask in which the a gas has filled. The volume is 1.87 liter. And we have to find equilibrium constant for this lee Jackson. So first of all, we will we will convert all the concentrations in a single unit, since C. And they are already in Mueller units. Therefore we will convert the concentration of a also in Mueller unit. So how Mueller unity is achieved for that. We divide the moral values with the uh most by volume. So here for a the mole is 2.48 moles divided by volume is 1.87 later. So this will be the modularity of I guess now the question is how we will write expression for Casey or equilibrium constants. We know that while we write the expression for equilibrium constants, we neglect the pure solids and pure liquids here. Pure solid is present and that is at um be therefore we will neglect its concentration since its concentration will not change with time, it will be always unity. Now, first we enumerated, we write the product concentration 1st. So what is the water? The products that are C&D. Now the power of these concentrations will be their corresponding coefficient. Now, coefficient of CS two, Therefore, concentration of C will be squired and coefficient of D is one. Therefore there will be one in the power of fish, in the power of the concentration of D. So this will be divided by the concentration of reactant and there is only one reactant since we are neglecting the concentration of be it, since it's a pure solid. Therefore, concentration of A. And its coefficient is three. Therefore it will go into the power of A. So this is equal to now we can put the data's of their concentration values at the equilibrium. So C. Is one point 13 Mueller police square and two D. Has the concentration 2.27 Mueller Divided by concentration of a. That is 2.48 divided by 1.87 whole cube. So from here we get the value of Casey that is equals two, one point 242 So the correct option is option E. That is one point 24 so this will be the answer for this problem.

For party. We can first right out the equilibrium expression K equals concentration of age to Waas Square over a concentration of age to square times concentration of us too. And since we're given a set of concentration, we can calculate the reaction quotient at this point. So we plug in the concentration for the product age to us and the reactant h two N s, too. So voyage to us. We have 0.5 mol and then square H two concentration. We have 0.25 Mol Square and as to concentration, we have its 3.15 small and this would give us 26.67 And we know that the equilibrium constant in this case it's 1.1 times 10 to the seventh. And we know that this is last NK, which means the reaction hasn't reached equilibrium yet. And since this is smaller than K, that means the product is less than the re less than the concentration and equilibrium and the reacting concentration is more than the concentration at equilibrium. So from this point on, the equilibrium would shift to the right so would have an increase of product and decrease of reacting and finally to reach the equilibrium constant. And for part C, assuming died the reacting to remain the same concentration. What would the product concentration needs to be to reach the equilibrium constant And so so from the equilibrium expression we have the product concentration H two s square you goes K the constant times concentration of H two square times as two square. So the concentration of us to so the concentration off age two s would equal the brute square of K times age to cause sensations square times us too. And if we're plucking a number, Okay, we have 1.1 times 10 to the seven and then we have concentration of H two, which is 0.25 Moles square. And as to we have 0.15 MOL and the result here would be 0.32 times tend to the third mall which is 320 more. And this would be the concentration needed for H two s if the reactions remain in the same equilibrium and we want to establish an equilibrium


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