REACTIONS INVOLVING A LIMITING REAGENT
When given a problem and information on all of the reactants (the amounts present), you have to determine the limiting reagent by calculating which reactant gives the least amount of product.
It will be the reactant that is totally consumed in the reaction.
The limiting reagent limits or determines the product formed and all stoichiometric calculations are based on the consumption of the limiting reagent.
To solve a limiting quantities problem you need to follow these steps:
(1)Calculate the number of moles of one reactant required to react with all other reactant(s) present.
(2)Compare the number of moles of that one reactant with the number of moles required. This comparison will help you to identify which reactant is present in excess and which reactant is in a limiting quantity.
(3)Calculate the quantity of reactants used up and products produced on the basis of the quantity of reactant in limiting quantity.
EXAMPLE #1
How many moles of NaCl can be produced by the reaction of 2.0 moles of NaOH with 3.0 Moles of HCl?
(1)Write a balanced equation.
NaOH + HCl ------ NaCl + H2O
(2)Determine the number of moles of NaOH required to react completely with 3.0 moles of HCl.
This means that HCl is in excess and NaOH is the limiting reagent. Once the 2 moles of NaOH react with 2 moles of HCl, one mole of HCl will remain and there can be no further reaction due to an absence of NaOH.
(3)Show the number of moles of NaCl that can be produced based on the 2.0 moles of NaOH present.
EXAMPLE # 2
How many grams of Ca(ClO4)2 can be prepared by the treatment of 12.5 g CaO with 75.0 g HClO4?
We only have 0.223 moles of CaO present, so CaO is the limiting reagent. HClO4 is in excess!
ATOMIC STRUCTURE
Everything that is visible to us is a result of changes in the atomic structure of matter.
James Maxwell developed the mathematical theory assuming light is a wave. He described all forms of radiation in terms of oscillating or wave-like electric and magnetic fields in space.
The range of frequencies or wavelengths of electromagnetic radiation is the electromagnetic spectrum.
Wavelength (λ – “lamda”) is the distance between corresponding points in two successive waves. Wavelength is measured in nanometers (nm).
Waves can also be defined by their amplitude or height. Zero amplitude is a node.
Frequency (ν – “nu”) is the number of waves passing a point (your eye) per unit time. The unit for frequency is s-1 (1/sec) or hertz (Hz).
The velocity of a wave can be calculated from :
v = λ x ν (m/s =m x s-1)
Velocity is a physical constant in a vacuum.
ν = c x 1/λ c = 2.9979245 x 108 m/s
The unique set of wavelengths absorbed by a substance is called the spectrum of that substance.
In spectroscopy the wavelength of light absorbed is a characteristic of the substance being excited.
EXAMPLE #1
Orange light has a wavelength of 620 nm. What is the wavelength in meters? What is the frequency?
Max Planck discovered that a minimum of energy can be gained (absorption of E) or lost (emission of E) by an atom. Energy was not given off continuously, but instead in little packets or quanta.
Planck said that this energy change must have an integral value and must be related to the frequency.
E = hν ( ν = frequency, h = Planck’s constant or 6.6260755 x 10-34 J ∙ s)
E = n(hν)
EXAMPLE #2
If the frequency of orange light is 4.8 x 1014 Hz, what is the energy of one quantum of orange light?
In 1913, Niels Bohr explained the stability of the hydrogen atom and the line spectrum of hydrogen by 2 postulates:
(1)ENERGY LEVEL POSTULATE
An electron can only have specific energy values in an atom. Bohr pointed out that the absorption of light by hydrogen at definite wavelengths means definite changes in the energy of electrons. Bohr said electrons could only occupy certain energy levels.
(2)TRANSITIONS BETWEEN ENERGY LEVELS
An electron in an atom can change energy only by going from one energy level to another (a transition).
When an electron drops from a larger orbit to a smaller one energy is emitted. The frequency of light emitted depends on the amount of energy in the quantum.
If the atom absorbs energy, the electron may jump to a higher energy level or orbit. The size of the smallest orbit which an electron can occupy (the one closest to the nucleus) is called the ground state of an electron.
Electrons absorb or emit only whole numbers (3 not 3 ½ quanta) of quanta.
The emission of a particular frequency of light is the emission spectrum.
The light emitted by a heated solid, such as W (used in incandescent bulbs), is a continuous spectrum.
The light emitted by a heated gas, such as Ne, is a line spectrum, with dark areas of no light.
The spectrum is viewed with a spectrascope.
In 1905, Albert Einstein tackled the theoretical explanation of the photoelectric effect, where light hits a metal surface and knocks an electron off. Einstein used Planck’s ideas to explain the photoelectric effect.
(1)Light has particle properties. Einstein called the particles photons.
(2)Each photon has a characteristic energy (E = hν).
(3)If the energy of the photon hitting the metal is not enough, nothing happens. If it is just enough then the entire energy of the photon is absorbed and converted into the energy of the electron.
(4)The more energetic the photon, the more energetic the electron. The greater the intensity of the light, the greater the number of photons and the greater the number of electrons ejected.
In 1910, Ernest Rutherford tested J.J. Thomson’s model of the atom with the gold foil experiment.
Thomson supposed the atom was a uniform sphere of positively charged matter within which thousands of electrons circulated in coplanar rings.
In his experiment, Rutherford passed a beam of alpha particles (He+2 ions) through a piece of gold foil (10-4 cm thick). A ZnS fluorescent screen surrounding the foil detects alpha particles that pass through the foil or are deflected.
Rutherford concluded that the atom is mostly empty space with a dense nucleus containing most of the atom’s mass and charge. Most of the alpha particles were undeflected as they passed through the foil. Those that hit the nucleus were deflected through large angles.
In 1923, French physicist Louis DeBroglie proposed a hypothesis which led the way to the present atomic theory of matter.
DeBroglie studied Planck’s and Einstein’s work and concluded that if light can have particle-wave duality so can electrons and other moving particles.
He stated that if a particle is moving it has a wavelength but if its velocity is too small, its wavelength cannot be measured. But due to the fact that an electron is a small particle that moves fast it should have a measureable wavelength, calculable by the DeBroglie equation :
λelectron = h/mv
wavelength (of an electron) = Planck’s constant/mass x velocity
E = mc2
E = hν
therefore,
hν = mc2
A wave has only one possible wavelength (given by λ = c/ν) and only one possible amount of energy (E = hν). So, if λ, ν, or E are known we can calculate the other two.
EXAMPLE # 3
A red light has a wavelength of 600 nm. What is the frequency? What is the energycontent of one photon of this light?
In the 19th century, Johann Balmer worked out a mathematical relation that accounted for the three lines of longest wavelength in the visible emission spectrum of hydrogen atoms (the red, green, and blue lines).
Johannes Rydberg determined that the wavelengths of the lines (in the visible emission spectrum of hydrogen) can be predicted with the following equation:
1/λ = R(1/4 – 1/n2)
(where n is greater than 2)
λ = wavelength
R =Rydberg constant(1.09737 x 10-7 m-1)
n= an integer associated with each spectral line
If n = 3, the λ red line can be calculated.
If n =4, the λ green line can be calculated.
If n = 5, the λ blue line can be calculated.
These groups of visible lines are now called the Balmer series of lines.
An electron with n =1 has the most negative energy and is most strongly attracted to the nucleus.
An electron with n = 2 is less strongly attracted to the nucleus.
If an electron with n = 1 is excited (absorbs E) it is said to be in its excited state. To return to ground state it must emit energy.
Δ E = Efinal state – Einital state
Δ E = -Rhc(1/n2final – 1/n2inital)
If an electron moves from a high energy state to a low one, a photon is emitted and the emission line is observed. If a photon is absorbed an absorption line is seen.
Bohr showed that the energy possessed by a single electron of the H atom, in the nth stationary state, is given by the equation:
E = - Rhc/n2
h= Planck’s constant
c = velocity of light
R = Rydberg constant
Eample #4
What are the energies of the n =1 and n = 2 states of the hydrogen atom in J/atom and in kJ/mole?
Example #5
An electron in a hydrogen atom moves from a higher state to the n = 3 state. Give the ninitial for the transition that would account for the least energetic line of the series. What is the energy involved in this transition? What are the ν and λ for the light emitted?