Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

CHEM280 > CHEM280 > Flashcards

CHEM280 Flashcards

1
Q

How does SOHCAHTOA work?

When is it applied?

A

Only for right-angled triangles
sin (theta) = opposite/hypotenuse
cos (theta) = adjacent/hypotenuse
tan (theta) = opposite/adjacent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What is Pythagoras’s theorem?

A

for a right-angled triangle,
a^2 = b^2 + c^2
or
H^2 = O^2 + A^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What does sin^2(theta) + cos^2(theta) = ?

A

always = 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

How do you cancel ln and e?

A

ln and e must be directly next to each other to cancel, e.g. ln(2e^x) doesn’t cancel, you have to separate the functions for them to cancel, e.g. ln2 + ln(e^x) = ln2 +x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

rules of exponents/logs
e^x e^y = ?
ln(xy) = ?

A

= e^x+y

= lnx + lny

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

rules of exponents/logs
e^x e^y = ?
ln(xy) = ?

A

= e^x+y

= lnx + lny

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

rules of exponents/logs
(e^x)/(e^y) = ?
ln(x/y) = ?

A

= e^(x-y)
= lnx - lny

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

rules of exponents/logs
(e^x)^y = ?
ln(x^y) = ?

A

= e^xy

= ylnx

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

what does a positive derivative mean?

A

positive slope = increasing curve

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

what does a negative derivative mean?

A

negative slope = decreasing curve

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

what does x’ mean?

A

just another way of writing dx/dy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is an operator in differentiation?

A

the thing on the bottom of the differential fraction, e.g. dx/dy , y is the operator

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

how would you differentiate y = lnx?

A

= x = e^y so dx/dy = e^y,

because e is the inverse of ln, OR dy/dx = 1/x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

In terms of a graph what is an integral?

A

the area under the curve and the area between the curve and the axis - depending on which integral we’re interested in

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is a definite integral?

A

when the answer is a single number rather (e.g. the area of a shaded region), rather than a function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is a key part of your answer for integrals if not definite? why?

A

+C , it could shift the curve up or down

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

How do you differentiate?

A

The power goes to the front if a number, then MINUS one from the power

If the power is not a number (e.g. kx) you differentiate it (so will be just k) and put it in the front

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What does sin differentiate to?

A

cos

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What does cos differentiate to?

A

-sin

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

When there is already a constant in front of a variable how do you differentiate it?

A

you multiply both numbers together, e.g. y = 3q^4

-> dy/dq = 12q^3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

How do you differentiate y = 3lnq?

A

dy/dx = 3/q

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

How do you use the chain rule?

A

It’s used for a function of a function (e.g. sin(x))

  • separate the two functions into u and z and differentiate separately into du/dx * dz/du (multiplied together)
  • don’t forget to sub back in the UNDIFFERENTIATED form into the function if required (e.g. cos(u), use the undifferentiated u)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

How do you use the product rule?

A

Used for the product of two functions, (e.g. u(x) v(x) )

-Differentiate the two functions separately as u and v into du/dx(v) + dv/dx(u)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

How do you find stationary points/maxima&minima?

A
  • first differentiate the function and put the whole thing = 0
  • factorise it to find the x values
  • do the second derivative
  • substitute each x value into the eq to get two values (the stationary points)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Are maxima positive or negative?

A

NEGATIVE

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Are minima positive or negative?

A

POSITIVE

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

How do you factorise?

What if there’s a coefficient in front of the x^2?

A

-Find two numbers that have a product of the number in front of x, and a sum of the constant.

If there’s a coefficient in front of the x^2 multiply the coefficient of x^2 by the constant (the lone number) to get a new value, then instead, find two numbers which have a product of this value, and a sum of the value in front of x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

How do you do integration with an x value and power?

A

for this purpose } will be the integration symbol

don’t forget to write in the format }y dx

add one to the power and put the x value over the (power+1)
e.g. }5x^4 dx = (x^4+1)/(4+1) = 5(x^5/5) =x^5 + C

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

How do you do integrate }Ae^kx dx?

A

(1/k)Ae^kx + C

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

How do you integrate }(1/x)dx?

A

lnx + C

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

What is the integral of cos?

A

sin

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

What is the integral of sin?

A

-cos

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

How do you do definite integrals/limits?

A

Do the integral
then sub x for each limit separately
Do the upper limit-the lower limit
If the limit isn’t numerical just leave fully written out as the upper-lower
The C cancels so doesn’t remain in the final answer

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

What is the cosine rule?

A

Cos C = (a^2 + b^2 - c^2)/2ab

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

What is the cosine rule used for?

A

Finding the bond angle of C

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

How do you do partial differentiation?

A

Whatever is on the bottom of the fraction is the only thing differentiated and the other variable treated as constant (so will go to the front if a power etc)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

What is the partial derivative of (dp/dT)n,V?

A

nR/V

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

What is the partial derivative of (dp/dV)n,T?

A

-(nRT/V^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

What is the derivative of x on its own if dy/dx?

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

What is the derivative of x on its own if dx/dy?

A

0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

How do you display that something is constant in partial differentiation?

A

Write subscript outside the brackets

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

How do you do mixed partial derivatives?

when written (d^2f/dxdy

A

Differentiate with x first, then differentiate with y (or other way around)

43
Q

sinhx =?

A

1/2(e^x - e^-x)

44
Q

coshx=?

A

1/2(e^x + e^-x)

45
Q

What do you do if a term being differentiated doesn’t contain the variable being differentiated?

A

It is completely omitted from the answer

46
Q

What does infinitesimal mean?

A

when using dx instead of Dx (D being the triangle delta)

47
Q

For the thermodynamics equation, what does (ds/dV)U give as the general formula?

A

p/T

48
Q

For the thermodynamics equation, what does (dU/dS)V give as the general formula?

A

T

49
Q

For the thermodynamics equation, what does (dU/dV)S give as the general formula?

A

-p

50
Q

What is the difference between Cp and Cv?

A

in Cp the p is constant and vice versa

51
Q

What is the thermodynamics equation?

A

dH = TdS + Vdp

52
Q

In the thermodynamics equation if H (or any other variable) is constant, what is dH equal to?

A

zero, can be set to zero in the equation to help rearrange

53
Q

what does i^2 =?

A

-1

54
Q

what does (root)-1 =?

A

+/- i

55
Q

What does 1/i = ?

A

-i

56
Q

What does i^3 =?

A

i^2i = -1*i = -i

57
Q

what does (x+2i)* mean?

A

(x-2i) (* means the inverse/complex conjugate of the imaginary part)

58
Q

what does z = in terms of i?

A

z = a + ib

so z* = a - ib

59
Q

What does |z|^2 mean?

A

square modulus = (a + ib)(a - ib)

60
Q

What type of value does |z|^2 always give?

A

real and positive answer

61
Q

How do you divide z1/z2 (square modulus)?

A

write the square modulus of the denominator and write this next to the top value too so you’re multiplying and dividing by the same number, this should convert the denominator to a real number

62
Q

How do you add/subtract double brackets?

A

take everything out of the brackets, and add together, if minusing make values negative/positive as appropriate

63
Q

What is an eigenfunction?

A

When an equation has only changed by a value from the original

64
Q

What is an eigenvalue?

A

What a function was changed by overall to convert the original to the answer (when comparing the original and the answer)

65
Q

How do you write z = e^ix (x = theta) in the form z = a +ib?

A

e^ix = cosx + isinx

66
Q

How do you write z = e^-ix (x = theta) in the form z = a +ib?

A

e^-ix = cosx - isinx

67
Q

How do you normalise a function?

A

square the function, then work out the integral with the upper limit as 1 and the lower limit as -1

68
Q

How do you calculate (a + ib)^n?

A

convert to exponential = r(^n)e^inx

this is just the angle*n so in terms of a + ib = cosnx + isinnx

69
Q

what does cos(-x) = ?

A

cosx

70
Q

What does sin(-x) =?

A

-sinx

71
Q

Equation for length of a vector?

A

(root) of x^2 + y^2 = root of each of the squared components

72
Q

how do you depict a vector?

A

underlined v, bold v, or arrow across top of v

73
Q

what does the square modulus of a vector equal?

A

x^2 + y^2

74
Q

what is the format of vectors?

A

(x, y) vertically, x = across, y = up/down,

75
Q

How do you add/subtract vectors?

A

add/subtract components in the same rows, to subtract flip the signs of one of the vectors

76
Q

What is the dot product of vectors formula?

A

a.b (both underlined = vector a*vector b) = |a| |b| cosx

77
Q

How do you use the cosine rule in terms of vectors?

A

|v|^2 = |a|^2 + |b|^2 - 2|a| |b| cosx

78
Q

What does |a| represent in terms of vectors?

A

the length of a

79
Q

what is the vector cosine rule rearranged for cosx?

A

cos x = (axbx + ayby + azbz)/ |a| |b|

80
Q

How do you multiply matrices?

A

multiply each row of the first matrix, by each column of the second matrix, e.g. 1r1c = (af)+(bg), 2r1c = …

81
Q

How do you add/subtract matrices?

A

add/subtract the numbers in the same positions in each matrix

82
Q

How do you work out the determinant of a 2x2 matrix?

A

with the format a, b, c, d in a square left to right:

det = (ad) - (bc)

83
Q

How do you work out the inverse of a matrix?

A

inverse = (1/det)*matrix as follows below

top left (a) and bottom right (d) swap places, top right (b) and bottom left (c) switch signs from pos to neg etc.,

84
Q

What happens if the determinant of a matrix equals zero?

A

there is no inverse

85
Q

Does the order of multiplying matrices matter?

A

Yes, in general AB doesn’t = BA

86
Q

What is a unit/identity matrix?

A

the result of a matrix * its inverse (MM^-1) , there is a leading diagonal of 1 across the whole diagonal

87
Q

How do you prove that two matrices are the inverse of each other?

A

multiply them together and should get a unit/identity matrix if inverses of each other

88
Q

What does the term orbital refer to in maths?

A

an eigenfunction

89
Q

What does the term orbital energy refer to in maths?

A

an eigenvalue

90
Q

What do you find if asked to find the orbitals and orbital energies of a function?

A

eigenfunctions and eigenvalues

91
Q

what is the equation for kinetic energy?

A

^H = -h^2/2m * d^2/dx^2

92
Q

How do you show that something is an eigenfunction of KE?

A

differentiate it twice then multiply by -h^2/2m,

if the function is unchanged then it is an eigenfunction of the Hamiltonian ^H

93
Q

What must the value for KE always be?

A

positive

94
Q

How do you show that a vector is an eigenvector of a matrix?

A

multiply the vector by the matrix and the vector should be the same as before just multiplied by a factor, the eigenvalue can be 0 if the vector is (000)

95
Q

How do you work out eigenvalues of matrices?

A
  • the vector * the matrix (with x minused from a & d) = 0
  • solve by the formula (a-x)(d-x) - bc = 0
  • multiply out the brackets and factorise,
  • whatever number is in each bracket = the eigenvalue
96
Q

How do you work out eigenvectors of matrices?

A
  • find the eigenvalues
  • minus this from a and d
  • multiply the matrix by the vector (x, y) to get x and y values with the equations set to zero
  • solve the equations for x or y
  • sub in 1 for x
  • write as an (x, y) vector
97
Q

How do you work out the determinant of a 3x3 matrix?

A
  • choose one row of the matrix and expand along it:
  • write: first in row *|other 4 not in same row or column|
    do this for the other 2 in the row and write them in a row as if adding (don’t multiply or add!)
  • if not along the diagonals of the matrix, the row value is negative
    these are your determinants which you can calculate as normal (axd)-(bxc)
    expand along a row with simple numbers to save time
98
Q

How are i, j and k used for vectors?

A

i=x, j=y, k=z

99
Q

How is axb different to a.b?

A

axb = vector cross product,

  • write as a 3x3 matrix with i, j, k along the top,
  • write each vector along into the matrix according to i=x, j=y, k=z
  • write out the same as for a 3x3 matrix, blocking out column i write as i * |other 4| etc
  • multiply as for determinants (axd)-(bxc)
100
Q

What is a transpose matrix (M^T) ?

A

convert each row to a column and rewrite as such

101
Q

What is a complex conjugate matrix (M*)?

A

the same matrix with the complex conjugate of each value in the matrix

102
Q

What is a Hermitian conjugate matrix (M dagger)?

A

the conjugate of the transpose matrix

103
Q

How do you show a matrix is unitary?

A

the inverse = the Hermitian matrix

show by working out the Hermitian complex, multiply by the original matrix, should = the identity matrix

CHEM280 (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions