Recent content by DarthRoni

I'm doing the same assignment. I also got 1/3 EDIT: I'm not so sure about that answer anymore

Thank you very much, I see where I went wrong. After using your method, I arrived at a final answer of ##V = 4/3 a^3 *((3\pi - 4)/6) ## which is about 29 percent of the sphere's volume. Makes more sense. Thanks again for your help!

## V = -2/3 * \int_{0}^{2\pi} (a^2 - a^2 cos^2(\theta))^{3/2} - a^{3/2} d\theta ## ## \Rightarrow V = -2/3 * \int_{-\pi/2}^{\pi/2} a^3 (1- cos^2(\theta))^{3/2} - a^3 d\theta ## ## \Rightarrow V = -(2*a^3)/3 * \int_{-\pi/2}^{\pi/2} sin^3(\theta) - 1 d\theta ## ## \Rightarrow V = (2*a^3*\pi)/3...

Homework Statement Find the Volume of the solid that the cylinder ##r = acos\theta## cuts out of the sphere of radius a centered at the origin.Homework Equations The Attempt at a Solution I have defined the polar region as follows, $$D = \{ (r,\theta) | -\pi/2 ≤ \theta ≤ \pi/2 , 0 ≤ r...

Their plan WAS to calculate the pH. You can see why I was thrown off. Thanks again! You've once again helped me understand chemistry a little bit more. (I assume the acid dissociation constant would be applied at the end)

This is their process: 71.14ml of ##NaOH## with concentration ##2.00*10^-5 mol/L## is used to neutralize 25.00ml of ##HNO_2## solution They then state the following $$NaOH(aq) + HNO_2(aq) \rightarrow NaNO_2(aq) + H_2O$$ they then find the moles of NaOH $$n_{NaOH} = 2.00*10^-5 * 0.07114 =...

I will try to be more clear. Take a solution with a certain concentration of acetic acid (##C_2H_4O_2##). We are attempting to neutralize the solution using a another solution containing potassium hydroxide (##KOH##). My textbook suggests I use the following formula in order to find the molar...

Thanks Borek ! Always great help. However about the titration question. When we add a base (such as KOH) in an acidic solution. Is the base reacting with the acid or simply the hydrogen ions to create water ?

But hasn't the hydrogen already separated from the chlorine? I was thinking the equation should look something like this $$H_3O^+(aq) + 2Cl^-(aq) + Mg(s) \rightarrow MgCl_2(aq) + H_3O^+(aq)$$ I have one more question, when calculating the pH of a solution after neutralizing it using titration...

I am confused as to why this happens when magnesium is introduced into a hydrochloric acid solution: $$2HCl_(aq) + Mg(s) \rightarrow H_2(g) + MgCl_2(aq)$$ I understand that the magnesium will form an ionic bond with chlorine and then quickly dissolve. However, I don't understand why the hydrogen...

Thanks guys !

So let me get this straight, I can do all my operations and then only involve my significant figures at the end? Regardless if there's both addition and multiplication?

Here's an example: Disprove ##\lim_{x \rightarrow c}x+2 = c## we want to show for some ##\epsilon > 0## then ##\forall \delta>0## $$|x-c|<\delta \implies |(x+2) - c| >= \epsilon $$ We know $$|(x+2) - c| = |(x-c) + 2|$$ And let's say $$|x-c|<1$$ Because remember that we are trying to show that...

Recall the definition of ##\lim_{x\rightarrow c}f(x) = l## $$\forall \epsilon > 0\ \exists\ \delta > 0 \ such\ that\ 0<|x-c|<\delta \implies |f(x) - l| < \epsilon$$ Say that is it not true that ##lim_{x\rightarrow c}f(x) = l## this means $$\exists \epsilon > 0\ \forall\ \delta > 0\ ...

I am trying to convert a mole quantity into a mass. ##m_{CO_2}## will represent mass, ##M_{CO_2}## will represent molar mass and ##n_{CO_2}## will represent mole quantity. I have ##n_{CO_2} = 3.3## and ##M_{CO_2} = (12.01 + 2(16.00))## So, ##m_{CO_2} = 3.3(12.01 + 2(16.00))## If I compute...