# Search results for query: *

1. ### Carts gaining and losing mass: What happens to velocity?

Homework Statement There are 2 versions of the problem that I've heard: A bucket on wheels is moving at a constant velocity on a frictionless surface. It's raining out so the bucket is gaining mass. Will it slow down, speed up, or remain at that velocity as it gains mass? A cart loaded...
2. ### Point groups and symmetry: Adding and subtracting operations

Homework Statement I haven't been assigned these questions, but I'm trying to trudge through them to better understand symmetry. This is for my inorganic class. It's just a series of short questions like: C3 – S56 = ? S4 + i = ? C3 + i = ? Stuff like this. And just looking at the...
3. ### Thermodynamics: 3-chambered system

Actually, the two methods don't give me the same answer. If I use wC = -(wA + wB), I get wC = 458.027 kJ, and q = ΔU - w = -227.683 kJ. If I take ΔU of the entire system to be qC, then I get -1143.737 kJ. I'm not sure, but why would w = 0 for the entire system? EDIT: I just re-calculated it...
4. ### Thermodynamics: 3-chambered system

Ah, sorry, for the first one I meant q = ΔU - wC = ΔU - [- (wA + wB)]. For the second, his rationale is that you can take the process stepwise, and calculate the q for first the isothermal, reversible expansion (q = nRT ln (Vf/Vi), where T = 300 K), and then calculate q for the isochoric...
5. ### PChem: Calculating pH

Because of the autoprotolysis of water? So we'd use Kw = 1 x 10–14 to get OH- in terms of H3O+, correct? But this doesn't change the pH by an appreciable amount does it? One thing I was struggling with was how to factor the 0.1 M contribution of the OH- into the charge balance. Does the right...
6. ### Thermodynamics: 3-chambered system

So, it wouldn't be correct to use q = nRT ln (Vf/Vi) + n \int_{700}^{300} \bar{C_{v}}dT? That's what my friend thinks is correct; essentially it's the same way we found ΔS, but we aren't dividing by T, because ΔS = q/T. Wouldn't there be expansion work against volume in chamber B and A that...
7. ### PChem: Calculating pH

Yes, you're correct of course. I noticed that later on but forgot to edit it in. Also, I believe my mass balance neglected [H3PO4]. But the pH of 7.3 was after correcting for these. Oddly enough, I got around 10 after adding NaOH, however my friend got 12; not particularly sure why. Also...
8. ### Thermodynamics: 3-chambered system

Homework Statement In a 3-chambered system, separated by 2 pistons, all of the walls are adiabatic, except for the wall on the outside of chamber C (the wall marked }). [A | B | C} The pistons are frictionless, the gas fills all 3 chambers and is ideal, and \bar{} = R. Total volume = 12...
9. ### PChem: Calculating pH

Yeah, I know there's going to be very little [PO43-], but our prof wants us to calculate it as if there will be. And yeah, he does want it done the long way. It's a terrible equation, but wolfram alpha helped me get the final answer, which, if I did everything right, should be about 7.351.
10. ### PChem: Calculating pH

Homework Statement 8.9985 g of Na2HPO4 and 4.0211 g of NaH2PO4 * 7 H2O are added to 1 L of 0.20 M KCl in water. KCl does not participate in any way but to maintain ionic strength, at 0.20 M. H3PO4 (aq) + H2O → H2PO4- (aq) + H3O+, Ka1 = 7.11 x 10-3 Ka2 = 6.32 x 10-8 Ka3 = 7.1 x 10-13 (a)...
11. ### Estimate the standard reaction Gibbs energy of the following reaction:

That was the equation that I ended up using when I revised my answer. In the end, I got that at 100 K, ΔG = –68.6 kJ. Our professor also had us approximate the value using the Gibbs-Helmholtz equation, which gave me –72.6 kJ. It makes sense for the two values to be off, because I know the...
12. ### Estimate the standard reaction Gibbs energy of the following reaction:

Homework Statement "Estimate the standard reaction Gibbs energy of the following reaction: N2 + 3 H2 ‒‒> 2 NH3 at 100K and at 1000K." Homework Equations ΔS(T2) = S°(T1) + ∫ n Cp dT/T ΔG = ΔH ‒ TΔS Given data: http://imgur.com/MBakUEB (may need to right-click and select...
13. ### Find all critical points, and identify them as minima, maxima, or

So I've been slowly plodding through this problem, and so far this is what I've done: Took partial of ##x##, factored out the ##e## term and canceled it, because it can never equal ##0##. So ##x^2+4y^2-1 = 0## Same with the partial of ##y##: ##x^2+4y^2 = 4## Now, these are ellipses...
14. ### Find all critical points, and identify them as minima, maxima, or

Homework Statement Consider the function f(x,y) = (x2 + 4y2)e(1-x2-y2) Find all critical points, and identify them as maxima, minima, or saddle points. The Attempt at a Solution I took the partial of x and the partial of y, and set them equal to 0. This is what I got: fx(x,y) =...
15. ### Predict the product of the following reactions:

Homework Statement Predict the major organic product of the following reactions: The Attempt at a Solution For 1, I got: And for 2, I got: If anyone can help confirm, I'd be much obliged! Our professor is crazy and gives these types of problems for practice...
16. ### Quick question about Ampere's Law and how to use it?

Hmm. I'm guessing since they're orthogonal, ##\int {\vec B \cdot d\vec s} = 0##, right? Okay. That makes perfect sense, thank you! Actually, on the subject, I was wondering about something that I saw on a website somewhere. Apparently, the graph of B vs radius of a solid, cylindrical...
17. ### Quick question about Ampere's Law and how to use it?

I just have a quick question about how to use Ampere's Law. It says that ∫B ds = u0(i_enc), which I suppose is easy enough to understand. But I'm having trouble reconciling it with the notion of, say, the magnetic field at the center of a loop of wire. The magnetic field at the center of a...
18. ### Find the current through the 100 Ohm resistor:

Homework Statement Find the current through the 100 Ohm resistor: http://imgur.com/sohdpyE The Attempt at a Solution So I was able to simplify the 100 and 500 resistors, as well as the 20, 20 and 10 series resistors, but I can't seem to discern at all whether any of the remaining ones...
19. ### Multivariable derivatives problem?

Homework Statement Let f(x,y,z)=u(t), where t=xyz. Show that f_{xyz} = F(t) and find F(t). The Attempt at a Solution I'm a little confused about the presentation of the variables in this problem. What does F(t) refer to? This isn't a chain rule question, because it's presented before chain...
20. ### Given the partial derivatives, find the function or show it does not exist.

I realized that a few minutes after I posted it, my bad! So we've got f_{x_k}=kx_x. The function f described by this set of partial derivatives should be in the form f(x_1, x_2, ... , x_n), right? So I run into a bit of a snag when we integrate that partial. If f_{x_1} = x_1, then...
21. ### Given the partial derivatives, find the function or show it does not exist.

Homework Statement f'_x = kx_k, k = 1, 2, ..., n The Attempt at a Solution The partial should be f(sub)x(sub)k, as in, the partial derivative of f with respect to x_k. I wasn't sure how to represent that using TeX. I'm honestly at a complete loss here, because I'm not entirely sure what...
22. ### Two questions on vectors, regarding dot and cross product?

That was brilliant! Splendid hint, it was all I needed to get the answer, thank you! Just to confirm, dotting ##\vec v_1## into both sides left me with c1|##\vec v_1##|2 = 0, which of course implies that c1 = 0. I repeated by dotting ##\vec v_2## into the original, and by the same process...
23. ### Two questions on vectors, regarding dot and cross product?

Homework Statement 1. Suppose that u + v + w = 0. Show that u x v = v x w = w x u. What is the geometric interpretation of this result? (Note: The interpretation should explain both the length and the direction). 2. Let v1, v2, and v be three mutually orthogonal vectors in space. Use the...
24. ### Solving an Algebraic Proof for Vector Equation

You were right, there was a mistake in my signs. c2 = (w2 – w1)/2 c1 = (w2 + w1)/2 That should be right. And in fact, when I plug in these values for c1 and c2 in the c1<1, 1> + c2<-1, 1> expression, after simplification I am left with <w1, w2>. So, the expressions for c1 and c2 we...
25. ### Solving an Algebraic Proof for Vector Equation

Okay... So: <w1, w2> = <c1 – c2, c1 + c2> w1 = c1 – c2 and w2 = c1 + c2 c1 = w1 – c2 and c1 = w2 – c2 So: w1 + c2 = w2 – c2 w1 = w2 – 2c2 c2 = (w2 – w1)/2 Plugging this back into c1 = w2 – c2: c1 = w2 – (w2 – w1)/2 c1 = (2w2 – w2 – w1)/2 c1 = (w2 – w1)/2 And hence c1 = c2...
26. ### Solving an Algebraic Proof for Vector Equation

Okay, I think I might have it. So say w = v1 + v2, in which case w = <0, 2>. Hence, w1 = 0 and w2 = 2. So: c1 – c2 = 0, so c1 = c2 and c1 + c2 = 2 But c1 = c2, so c1 + c1 = 2 2c1 = 2 c1 = 1 Hence c2 = 1. But the problem I have is that we calculated c1 and c2 to be 1, but...
27. ### Solving an Algebraic Proof for Vector Equation

I'm sorry, I'm not entirely sure I understand what you're saying here. When you say we're given ##w_1## and ##w_2##, do you mean what we have just found, i.e. ##w_1## = <##c_1## – ##c_2##>? Or do you mean ##w_1## was something that was given to us earlier in the problem? And I'm not sure I...
28. ### Solving an Algebraic Proof for Vector Equation

Hmm. I suppose that makes sense, I might have overlooked that fact. So then, <w1, w2> = <c1 – c2, c1 + c2> w1 = c1 – c2 w2 = c1 + c2 So the horizontal component of our vector w was shown to be c1 – c2, and the vertical component was shown to be c1 + c2. Alright, that's cool. Is that then the...
29. ### Solving an Algebraic Proof for Vector Equation

Homework Statement Let v1 = <1, 1> and v2 = <-1, 1>. Show that for any vector w in the plane one can find constants c1 and c2 so that w = c1v1 + c2v2. (Hint: Express w in component form and obtain two linear equations for the unknowns c1 and c2. Homework Equations The Attempt at a...