A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid donates a proton (H+) to a base—in other words, it is a base with a hydrogen ion added to it, as in the reverse reaction it loses a hydrogen ion. On the other hand, a conjugate base is what is left over after an acid has donated a proton during a chemical reaction. Hence, a conjugate base is a species formed by the removal of a proton from an acid, as in the reverse reaction it is able to gain a hydrogen ion. Because some acids are capable of releasing multiple protons, the conjugate base of an acid may itself be acidic.
In summary, this can be represented as the following chemical reaction:
Acid + Base ⇌ Conjugate Base + Conjugate Acid
Johannes Nicolaus Brønsted and Martin Lowry introduced the Brønsted–Lowry theory,
which proposed that any compound that can transfer a proton to any other compound is an acid, and the compound that accepts the proton is a base. A proton is a nuclear particle with a unit positive electrical charge; it is represented by the symbol H+ because it constitutes the nucleus of a hydrogen atom, that is, a hydrogen cation.
A cation can be a conjugate acid, and an anion can be a conjugate base, depending on which substance is involved and which acid–base theory is the viewpoint. The simplest anion which can be a conjugate base is the solvated electron whose conjugate acid is the atomic hydrogen.
Im doing a bit of contour integration, and a question came up with a term in it am unsure of how to do: in its simplest form it would be
\int\bar{z}dz
where z is a complex number and \bar{z} is it's conjugate. Hmm i can't get the formatting to work out properly.. :S
Hey all, I was just curious:
Why is the conjugate of a complex number (a + bi) defined as (a - bi)? If we instead change the sign of the real part (-a + bi), we still get a real number when we multiply the two. Is there a particular significance to the current definition...
I was working on some dark field filters and I was wondering if you could substitute the black spot in the centre of a dark field filter for a completely black filter with a light passing hole in the middle. Sort of an inverted dark field filter.
I seem to remember reading something like this...
multiplying by a conjugate??
Homework Statement
I am dealing with a limit, however, I am not sure how to multiply by a conjugate when there are two variables and three terms on top. For example
lim [3h + sqrt( 2x +2h) - sqrt( 2x)] / h
h->0
i don't need help solving it, i just...
pretty simple question. have to prove \hat{O} \hat{O}\dagger is a Hermitian operator.
i found that
\left( \int \int \int \psi^{\star}(\vec{r}) \hat{O} \hat{O}^{\dagger} \phi(\vec{r}) d \tau \right)^{\star} = \int \int \int \phi^{\star}(\vec{r}) \hat{O}^{\dagger} \hat{O} \phi(\vec{r}) d...
Homework Statement
I want to show that
\exp \left( i\bar{z} \right) = \overline{\exp \left( iz \right)}
if and only if
z = n\pi
for any integer n.
Homework Equations
The Attempt at a Solution
Utilizing Euler's formula, I got
\cos \bar{z} = \cos z
and...
$\lim_{x\to 1}\frac{\sqrt{x}-1}{x-1}$
Homework Statement
Calculate the limit of \lim_{x\to 1}\frac{\sqrt{x}-1}{x-1}.
Homework Equations
As above.
The Attempt at a Solution
Have tried to multiplicate with the conjugate.
Homework Statement
Consider 1L of a solution that is 0.100 M in acetic acid and 0.100 M in sodium acetate. What will the pH be, when 0.0900 mol of sodium acetate are added?
Ignore changes in volume.
acetic acid pka = 1.75 E-5
Homework Equations
HA --> H+ + A-
pH=pka +log A-/HA...
Homework Statement
Prove that z_n -> z_0 if and only if ~(z_n) -> ~(z_0) as n goes to infiinity.
~(z_n) is the conjugate of z_n.
Homework Equations
The Attempt at a Solution
|~(z_n) - ~(z_0) | = | ~(z_n) + ~(-z_0)| <=
|~(z_n)| + |~(-z_0) | = |z_n| + |z_0| <=
and I...
x''+x'+2x=0 x(0)=2 x'(0)=0
I've taken the characteristic equation and reduced the roots to
1/2 +- Sqrt(7/4)i of the form
a +- bi (i = sqrt(-1)
Then i put the homogeneous solution into the form of e^{}at*(B1cos(bt)+B2sin(bt))
for B1 i used the first i.c. and found that B1=2...
my question is what is meant by saying that A and B are similar where A and B are nxn matrices with entries in field F, also show that is A~B then A^2~b^2
first bit i have the definition for A~B is they are nxn matrices in the same field and there exists a non-singular square matrix P such...
Hi I have received PM so I would like to post this question for scientific debate
here conjugate of every variable is denoted by _.
1.define f_:R3->R3 by f_(x_)=y_, where y1=x1+(x2)2+(x3-1)2,
y2=(x1)2+x2+((x3)2-3.x3), y3=(x1)3+(x2)2+x3.prove that f_ is locally
invertible about x_=(0,0,1)...
A wave function(psi) is a mathematical quantity which gives complete information about the state of a system at a particular instant of time. But what information does the complex conjugate of a wave function(psi*) give? Does it represent the same state as psi? Or does it just have a...
I have two questions
Homework Statement
Show that the function defined by complex conjugation is not differentiable.
Homework Equations
If z = x + iy then the complex conjugate of z is x - iy
The Attempt at a Solution
f'(z) = lim z -> z1 \frac{f(z) - f(z1)}{z - z1}
So I...
Hi today I will be constructing a ratio thing for math. Our teacher asked us to survey as many people as we can. I am going to ask a simple math question and if you can answer it with 100% confidence. This is just a little survey I am not trying to trick you in doing my homework, I already know...
Homework Statement
Suppose that f(x) is a polynomial of degree n with real coefficients; that is,
f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real)
Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x)
Homework Equations...
i was thinking this over, and i'd like to know if the following statement is valid:
\oint\overline{z}dz = \oint1/zdz
over the contour \left|z\right|=1
any thoughts?
Hi,
Is there any trick to treat complex conjugate variables in polynomial equations as independent variables by adding some other constraint equation ? Say, we have polynomial equation $f(x,x^{*},y,...) = 0$. where x^{*} is the complex conjugate of variable $x$. I might think of taking $x = r...
Homework Statement
sun, I don't know why I am stuggling with a simple freakin problem. Its not even for me its for my friend who's in college algebra, but for some reaon I can't get the correct answer.
{9 - 11i \over 6i}
The Attempt at a Solution
I multiplied by the conjugate twice and...
It's very commong to use z and z* as two independent variables, differentiating with respect to one while keeping the other constant. Can you please give me some intuitive insight into this method, and why it works so well? Because every time I see this my first thought is that z and z* are NOT...
Hello All,
As I understand it, the wavefunction Psi(x) can be written as a sum of all the particle's momentum basis states (which is the Fourier transform of Psi(x)). I was woundering if the wavefunction's complex conjugate Psi*(x) can be written out in terms of momentum basis states, similar...
(a will be alpha and b will be beta)
Let y=y(x,a,b) be a general solution of Euler's equation, depending on two parameters a and b. Prove that if the ratio (subdifferential y/subdifferential a)/(subdifferential y/subdifferential b) is the same at the points, the points are conjugate.
I...
Let F:H->R bar be a function and F*:H->R bar its conjugate. Fix aEH and show that the conjugate of the new function G(u)=F(u-a) is G*(u*)=F*(u*)+<a,u>
Verify the case where F:R^2->R, F(x)=1/2(x)^2 and a = (2,-1)
I don't really know how to show this. please help
Show that the extermals of any functional of the form integ (a->b) F(x,y') dx have no conjugate points.
Not sure how to start this question, any help would be appreciated
Let A be a nxn matrix. Prove that if (A*)A=0 then A=0. What if A(A*) = 0?
A* is the conjugate transpose of A. When I write out the expansion formula, I cannot conclude that every entry of A is zero. What am I missing?
Simple question, and pretty sure I already know the answer - I just wanted confirmation,
Considering the Hermitian Conjugate of a matrix, I understand that
A^{+} = A where A^{+} = (A^{T})^{*}
Explicitly,
(A_{nm})^{*} = A_{mn}
Would this mean that for a matrix of A, where A is
a...
Homework Statement
a = x + \frac{d}{dx}
Construct the Hermitian conjugate of a. Is a Hermitian?
2. The attempt at a solution
<\phi|(x+\frac{d}{dx})\Psi>
\int\phi^{*}(x\Psi)dx + <-\frac{d}{dx}\phi|\Psi>
I figured out the second term already but need help with first term... am...
Homework Statement
Show that the helicoid and the catenoid are conjugate minimal surfaces
Homework Equations
the helicoid is given by the parameterization
X(u,v) = (asinh(v)*cosu, asinh(v)*sinu, au) = (x1, x2, x3)
the catenoid is given by the parameterization
Y(u,v) = (acoshv*cosu, a...
Homework Statement
show that det(A)=(detA)*= det(A$)
where * denotes complex conjugate and $ means transpose
Homework Equations
The Attempt at a Solution
Please help me to start the problem.I am not getting a way.
I just have a simple question about hermition conjugates of spinors. Is the hermitian conjugate of:
\epsilon \sigma^\mu \psi^\dagger
equal to:
-\psi \sigma^\mu \epsilon^\dagger
where both psi and epsilon are 2-component spinors of grassmann numbers?
I'm studying abstract algebra and never got the hang of ideas like these. Currently I am trying to grasp:
Show that the splitting field of a quadratic polynomial P(x) = Ax^x + Bx + C, with zeros \alpha and \alpha^{'} is V_\alpha = Q*1 + Q * \alpha. Q is of course the set of rationals.
I...
I am working through this algebra book and some of the problems. The chapter this comes out of is General Algebraic Systems and the section is Isomorphisms. I am new to proofs and maths higher than calculus I so I am not sure if I am following the text or not. There aren't any solutions and this...
Need Assistance w/ existence of conjugate roots in polynomial
Prove:
given that f(x) = Anx^n + An-1X^n-1+ ...A1X + A0 , and An does not = 0
=> if f(x) has a root of the form (A+Bi), then it must have a root of the form (A-iB). (complex roots)
So far I've come up with the conjugate roots...
okay, so this particular equation involves me writing conjugate of either sin or cos, but hows that possible considering they both are real in the given problem?
maybe i should convert sin and cos into their exponential form first?
but then wt would be the conjugate of this...
Please help! -Dirac delta potential-, Hermitian Conjugate
Im trying to solve problem 2.26 from Griffiths (1st. ed, Intro to Q.M.). Its about the allowed energy to double dirac potential. I came up with a final equation that is trancedental. (After I separate the even and odd solution of psi.)...
I would like to prove \mid z + \overline{z} \mid \leq 2 \mid z \mid
The first way I could think of:
\begin{multline}
RHS^2 - LHS^2\\
=4\mid z \mid^2 - \mid z + \overline{z} \mid ^ 2\\
=4z\overline{z} - (z + \overline{z})(\overline{z}+z)\\
=4z\overline{z} -...
1. Which Bronsted-Lowry acid has the strongest conjugate base?
a. HBr
b. HClO4
c. HF
d. HI
2. What is the strongest acid among the following?
a. HF
b. HCl
c. HBr
d. HI
Correct?
Thanks.
I am perplexed. My professor told me that I can conjugate:
\psi \left( x,0 \right)
However, I am confused. There is no time dependence, there is no i. It is like saying
z = a + 0i
z* = a - 0i
It is rather useless to even say that and it seems also useless to conjugate something with...
Is the the following definition correct?
Two elements a and b of a group G are said to be CONJUGATE if there exists g in G such that a=gbg^{-1}.
For instance, show that all elements in the symmetric group S5 of order 6 conjugate.
Hi everyone!
How can I find the Hermitian conjugate of the differential operator D, with
D psi = 1/i dpart/dpart(x) psi?
I know you can do this with partial integration starting from
<phi|D|psi>* = <phi|D+|psi>
but how exactly does it work?
I'm sorry for using such an ugly...
Uggh finally did all the chem problems and studied for the upcoming final but there are 2 questions left unanswered. MAybe someone can help me out with this:
If given a lists of acids, how would one know which 1 is the weakest conjugate base? For example, HF, HNO_2, H_2CO_3, H_3BO_3, HCl...
I'm doing a take home final and wanted reassurance that I'm doing the problem right. the question involves taking <Sz>of |psi>. I know it's
<psi|Sz|psi>. I've never done it for a spin 2 particle which is a 5*5 matrix.Do i just take the complex conjugate of the values without switching their...
Whats the formula for this conjugate bases? how do I get them?
a) HSO3tothe(-)
b) NH3
c) HCL
and how is the lewis acid and lewis base identified?
thanks