Calculating Avogadro's Number



Avogadro's number isn't a mathematically derived unit. The number of particles in a mole of a material is determined experimentally. This method uses electrochemistry to make the determination. You may wish to review the working of

Start by calculating the volume of one mole of solid Al =(26.98 g/mol)/(2.70 g/mL)= 9.99 mL/mol. According to the packing density, only 0.74 og this is atoms (the rest is empty space), so the volume of the atoms alone is (9.99 mL/mol)x0.74 = 7.39.

Determining avogadroLaw
  • Key Points The mole allows scientists to calculate the number of elementary entities (usually atoms or molecules) in a certain mass of a given substance. Avogadro’s number is an absolute number: there are 6.022×10 23 elementary entities in 1 mole. This can also be written as 6.022×10 23 mol -1.
  • Calculating Avogadro’s number Number of stearic acid molecules / Moles of stearic acid A number = N molecules / M A number = (1.76 x 10 16 molecules) / (.000000320 moles) A number = 5.50 x 10 22 molecules Trial 2 calculations Calculating length of thread used C = (l Circle) x 2 So, C = (11.2 cm) x 2 C = 22.4 cm Calculating radius.
  • However, in its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro number as the exact value N = 6.022 140 76 × 1023, and redefined the mole as the amount of a substance under consideration that contains N constituent particles of the substance.
  • The number of units in one mole of any substance is called Avogadro’s number or Avogadro’s constant. It is equal to 6.022140857×10 23. The units may be electrons, ions, atoms, or molecules, depending on the character of the reaction and the nature of the substance.
electrochemical cells before attempting this experiment.
The objective is to make an experimental measurement of Avogadro's number.
A mole can be defined as the gram formula mass of a substance or the atomic mass of an element in grams. In this experiment, electron flow (amperage or current) and time are measured in order to obtain the number of electrons passing through the electrochemical cell. The number of atoms in a weighed sample is related to electron flow to calculate Avogadro's number.
In this electrolytic cell both electrodes are copper and the electrolyte is 0.5 M H2SO4. During electrolysis, the copper electrode (anode) connected to the positive pin of the power supply loses mass as the copper atoms are converted to copper ions. The loss of mass may be visible as pitting of the surface of the metal electrode. Also, the copper ions pass into the water solution and tint it blue. At the other electrode (cathode), hydrogen gas is liberated at the surface through the reduction of hydrogen ions in the aqueous sulfuric acid solution. The reaction is:
2 H+(aq) + 2 electrons -> H2(g)
This experiment is based on the mass loss of the copper anode, but it is also possible to collect the hydrogen gas that is evolved and use it to calculate Avogadro's number.
  • Direct current source (battery or power supply)
  • Insulated wires and possibly alligator clips to connect the cells
  • 2 Electrodes (e.g., strips of copper, nickel, zinc, or iron)
  • 250-ml beaker of 0.5 M H2SO4 (sulfuric acid)
  • Water
  • Alcohol (e.g., methanol or isopropyl alcohol)
  • Small beaker of 6 M HNO3 (nitric acid)
  • Ammeter or multimeter
  • Stopwatch
  • Analytical balance capable of measuring to nearest 0.0001 gram
Obtain two copper electrodes. Clean the electrode to be used as the anode by immersing it in 6 M HNO3in a fume hood for 2-3 seconds. Remove the electrode promptly or the acid will destroy it. Do not touch the electrode with your fingers. Rinse the electrode with clean tap water. Next, dip the electrode into a beaker of alcohol. Place the electrode onto a paper towel. When the electrode is dry, weigh it on an analytical balance to the nearest 0.0001 gram.
The apparatus looks superficially like this diagram of an electrolytic cell except that you are using two beakers connected by an ammeter rather than having the electrodes together in a solution. Take beaker with 0.5 M H2SO4 (corrosive!) and place an electrode in each beaker. Before making any connections be sure the power supply is off and unplugged (or connect the battery last). The power supply is connected to the ammeter in series with the electrodes. The positive pole of the power supply is connected to the anode. The negative pin of the ammeter is connected to the anode (or place the pin in the solution if you are concerned about the change in mass from an alligator clip scratching the copper). The cathode is connected to the positive pin of the ammeter. Finally, the cathode of the electrolytic cell is connected to the negative post of the battery or power supply. Remember, the mass of the anode will begin to change as soon as you turn the power on, so have your stopwatch ready!
You need accurate current and time measurements. The amperage should be recorded at one minute (60 sec) intervals. Be aware that the amperage may vary over the course of the experiment due to changes in the electrolyte solution, temperature, and position of the electrodes. The amperage used in the calculation should be an average of all readings. Allow the current to flow for a minimum of 1020 seconds (17.00 minutes). Measure the time to the nearest second or fraction of a second. After 1020 seconds (or longer) turn off the power supply record the last amperage value and the time.
Now you retrieve the anode from the cell, dry it as before by immersing it in alcohol and allowing it to dry on a paper towel, and weigh it. If you wipe the anode you will remove copper from the surface and invalidate your work!
If you can, repeat the experiment using the same electrodes.
Anode mass lost: 0.3554 grams (g)
Current(average): 0.601 amperes (amp)
Time of electrolysis: 1802 seconds (s)
Remember:
one ampere = 1 coulomb/second or one amp.s = 1 coul
charge of one electron is 1.602 x 10-19 coulomb
  1. Find the total charge passed through the circuit.
    (0.601 amp)(1 coul/1amp-s)(1802 s) = 1083 coul
  2. Calculate the number of electrons in the electrolysis.
    (1083 coul)(1 electron/1.6022 x 1019coul) = 6.759 x 1021 electrons
  3. Determine the number of copper atoms lost from the anode.
    The electrolysis process consumes two electrons per copper ion formed. Thus, the number of copper (II) ions formed is half the number of electrons.
    Number of Cu2+ ions = ½ number of electrons measured
    Number of Cu2+ ions = (6.752 x 1021 electrons)(1 Cu2+ / 2 electrons)
    Number of Cu2+ ions = 3.380 x 1021 Cu2+ ions
  4. Calculate the number of copper ions per gram of copper from the number of copper ions above and the mass of copper ions produced.
    The mass of the copper ions produced is equal to the mass loss of the anode. (The mass of the electrons is so small as to be negligible, so the mass of the copper (II) ions is the same as the mass of copper atoms.)
    mass loss of electrode = mass of Cu2+ ions = 0.3554 g
    3.380 x 1021 Cu2+ ions / 0.3544g = 9.510 x 1021 Cu2+ ions/g = 9.510 x 1021 Cu atoms/g
  5. Calculate the number of copper atoms in a mole of copper, 63.546 grams.
    Cu atoms/mole of Cu = (9.510 x 1021 copper atoms/g copper)(63.546 g/mole copper)
    Cu atoms/mole of Cu = 6.040 x 1023 copper atoms/mole of copper
    This is the student's measured value of Avogaro's number!
  6. Calculate percent error.
    Absolute error: |6.02 x 1023 - 6.04 x 1023 | = 2 x 1021
    Percent error: (2 x 10 21 / 6.02 x 10 23)(100) = 0.3 %

Estimating Avogadro's Number Lab Answers

Determining avogadro

Contrary to the beliefs of generations of chemistry students, Avogadro’s number—the number of particles in a unit known as a mole—was not discovered by Amadeo Avogadro (1776-1856). Avogadro was a lawyer who became interested in mathematics and physics, and in 1820 he became the first professor of physics in Italy. Avogadro is most famous for his hypothesis that equal volumes of different gases at the same temperature and pressure contain the same number of particles.

Determining Avogadro's Number Lab Report

The first person to estimate the actual number of particles in a given amount of a substance was Josef Loschmidt, an Austrian high school teacher who later became a professor at the University of Vienna. In 1865 Loschmidt used kinetic molecular theory to estimate the number of particles in one cubic centimeter of gas at standard conditions. This quantity is now known as the Loschmidt constant, and the accepted value of this constant is 2.6867773 x 1025 m-3.

Calculating Avogadro's Number

The term “Avogadro’s number” was first used by French physicist Jean Baptiste Perrin. In 1909 Perrin reported an estimate of Avogadro’s number based on his work on Brownian motion—the random movement of microscopic particles suspended in a liquid or gas. In the years since then, a variety of techniques have been used to estimate the magnitude of this fundamental constant.

Estimating Avogadro's Number Lab

Accurate determinations of Avogadro’s number require the measurement of a single quantity on both the atomic and macroscopic scales using the same unit of measurement. This became possible for the first time when American physicist Robert Millikan measured the charge on an electron. The charge on a mole of electrons had been known for some time and is the constant called the Faraday. The best estimate of the value of a Faraday, according to the National Institute of Standards and Technology (NIST), is 96,485.3383 coulombs per mole of electrons. The best estimate of the charge on an electron based on modern experiments is 1.60217653 x 10-19 coulombs per electron. If you divide the charge on a mole of electrons by the charge on a single electron you obtain a value of Avogadro’s number of 6.02214154 x 1023 particles per mole.

Calculating Avogadro's Number Calculator

Another approach to determining Avogadro’s number starts with careful measurements of the density of an ultrapure sample of a material on the macroscopic scale. The density of this material on the atomic scale is then measured by using x-ray diffraction techniques to determine the number of atoms per unit cell in the crystal and the distance between the equivalent points that define the unit cell (see Physical Review Letters, 1974, 33, 464).