Chemistry 201 Atomic mass Avagadro’s number NC State University The mass of a proton The mass of a proton is: 1.6726231 × 10−27 kg or 1.6726231 × 10−24 grams We know this value accurately because of mass spectrometry. The number cited here has eight significant figures. We do not usually need this precision, so we often write the value as 1.67 × 10−24 grams to three significant figures. Significant figures The number of significant figures is equal to the number of digits in a measured or calculated value that contribute to its precision. Precision refers to the ability to reproducibly measure or calculate a value. If we use three significant figures, it suggests that we can reproducibly measure the value to within about 1 part in 100 or with an accuracy of 1%. This is the most common number of significant figures and this will be the default in this course (unless otherwise specified). Example The mass of the electron is reported to be: 9.1093819 × 10-31 kg Write this number to three significant figures. Example The mass of the electron is reported to be: 9.1093819 × 10-31 kg Write this number to three significant figures. Solution: The specified value should be as close as possible to the true value so we should round-off the last digit. In this case we round up to obtain 9.11 × 10-31 kg Example The mass of a neutron is approximately equal to sum of the masses of an electron and a proton. Give the neutron mass to three significant figures. Example The mass of a neutron is approximately equal to sum of the masses of an electron and a proton. Give the neutron mass to three significant figures. Solution: Start with the accurate values: 1.6726231 × 10−27 kg 9.1093819 × 10-31 kg Example The mass of a neutron is approximately equal to sum of the masses of an electron and a proton. Give the neutron mass to three significant figures. Solution: Start with the accurate values: 1.6726231 × 10−27 kg 9.1093819 × 10-31 kg Add them together 1.6735340 × 10−27 kg Example The mass of a neutron is approximately equal to sum of the masses of an electron and a proton. Give the neutron mass to three significant figures. Solution: Start with the accurate values: 1.6726231 × 10−27 kg 9.1093819 × 10-31 kg Add them together 1.6735340 × 10−27 kg Round of to give 1.67 × 10−27 kg Example The actual value of the neutron mass is: 1.6749286 × 10−27 kg Calculate the difference between the value you obtained by summing the proton and electron masses. How many significant figures are possible in your answer? Example The actual value of the neutron mass is: 1.6749286 × 10−27 kg Calculate the difference between the value you obtained by summing the proton and electron masses. How many significant figures are possible in your answer? Solution: Neutron 1.6749286 × 10−27 kg Proton + electron 1.6735340 × 10−27 kg Difference 1.3946 × 10−30 kg There are 5 significant figures in the answer. Conversion factors for atomic mass The sum of the mass of a proton and an electron is the mass of a hydrogen atom. Question: how many hydrogen atoms are there in a gram of H atoms (to 3 significant figures)? Conversion factors for atomic mass The sum of the mass of a proton and an electron is the mass of a hydrogen atom. Question: how many hydrogen atoms are there in a gram of H atoms (to 3 significant figures)? Answer: The calculated value actually has units 1.6735340 × 10−27 kg/atom Or 1.6735340 × 10−24 grams/atom Therefore, we can invert it to find, 5.97(5) × 1023 atoms/gram Atomic mass unit When we consider all of the atoms in the periodic table, the average mass of a nucleon is considered to be: 1.6605388 × 10−24 grams/nucleon We call this the atomic mass unit. We can use this value to convert atomic masses to grams or vice versa. We write the conversion as, 1.6605388 × 10−24 grams/amu To employ this value we calculate the atomic mass of an atom or molecule and then we can calculate the weight in grams using this formula. Avagadro’s number If we invert average atomic mass ___________1_____________ 1.6605388 × 10−24 grams/amu We obtained the number of particles with a given amu per gram. This number is called Avagradro’s number and is given the symbol NA. NA = 6.022141 × 1023 amu/gram This number gives the number of particles for which an atomic mass has the the same value in grams. 1 H atom = 1 amu NA H atoms = 1 gram 1 C atom = 12 amu NA C atoms = 12 grams Example How much does a molecule of pyridine weigh? (Ummm… all right, what is its mass?) Example How much does a molecule of pyridine weigh? Solution: First, we find the chemical formula for pyridine. C5H5N H H H H H N Example How much does a molecule of pyridine weigh? Solution: Second, we look up the atomic masses in the periodic table. atomic mass = 5(12) + 5 + 14 = 79 amu Third, we use the conversion factor to calculate the mass in grams (79 amu)x (1.66 × 10−24 grams/amu) = 1.31 × 10−23 grams Avogadro’s number It is a bit difficult to weigh out 10−23 grams. H H H H H N Avogadro’s number Instead, let’s ask how many molecules it takes to convert the atomic mass to its value in grams. For example, using the grams/amu conversion, let’s calculate how many hydrogen atoms have the mass of 1 gram. Avogadro’s number Instead, let’s ask how many molecules it takes to convert the atomic mass to its value in grams. For example, using the grams/amu conversion, let’s calculate how many hydrogen atoms have the mass of 1 gram. Answer: since hydrogen weighs 1 amu, its mass is 1.6605388 × 10−24 grams/atom We can invert this value to find the number of atoms per gram. 6.0221417 × 1023 atoms/gram The mole Since this number converts from atoms to gram for hydrogen, we can see that it can be used to give the number of atoms for any formula weight (i.e. molecular weight of a compound given in grams). For example, pyridine has a formula weight of 79 grams. Therefore, There are 6.0221417 × 1023 molecules in 79 grams of pyridine. Because of the importance of this number of atoms or molecules we give the name, mole. 1 mole = 6.0221417 × 1023 molecules or to 3 significant figures. 1 mole = 6.02 × 1023 molecules Avogadro’s number as a conversion factor Given the definition, 1 mole = 6.02 × 1023 molecules We can see that Avogadro’s number converts from molecules to moles. 6.02 × 1023 molecules/mole Atomic weight and molar mass The atomic weight is the numerical value tabulated for the mass of each atom in the periodic table in atomic units. The use of the word “weight” is not precise here since weight in physics represents a force (w = mg). However, the name atomic weight is so ingrained that we will not attempt to change it. We use the periodic table to calculate the molar mass as follows: for H2SO4 we find the atomic weights, H = 1, S = 32 and O = 16. Molar mass = 2(1 g/mol) + 32 g/mol + 4(16 g/mol) = 98 g/mol