Atomic Mass and Molecular Mass
An atom weighs far less than you might imagine: it takes billions upon billions of them for a scale at the corner store to notice. So how do you compare what a water molecule weighs with a salt molecule or an oxygen molecule? In this section you will learn to "weigh" atoms and molecules with a unit made to their size.
Atomic mass: how much an atom weighs
If you put a speck of dust on a scale, it reads zero because it is too light. But if you compare two atoms with each other, you can tell which one weighs twice or three times as much. That is why scientists picked a reference and said how many times heavier each atom is than it.
Look at the bars: the height of each one is proportional to the element's atomic mass (10 px for each u). The oxygen bar is 16 times taller than the hydrogen bar. (Careful: the bar represents mass, not the size of the atom; size does not follow this proportion.)
The lightest atom, hydrogen, weighs $1\ \text{u}$. Carbon weighs $12\ \text{u}$, that is, $12$ times more than hydrogen; nitrogen weighs $14\ \text{u}$ and oxygen $16\ \text{u}$. To find how many times heavier one atom is than another, you divide their atomic masses.
What is the atomic mass of an element and in which unit is it measured? Look up the atomic mass of carbon and oxygen in the periodic table, and state which of the two…
What is the atomic mass of an element and in which unit is it measured? Look up the atomic mass of carbon and oxygen in the periodic table, and state which of the two atoms weighs more.
These are the atomic masses of four elements: $\text{H} = 1\ \text{u}$, $\text{C} = 12\ \text{u}$, $\text{N} = 14\ \text{u}$ and $\text{O} = 16\ \text{u}$. a) How many…
These are the atomic masses of four elements: $\text{H} = 1\ \text{u}$, $\text{C} = 12\ \text{u}$, $\text{N} = 14\ \text{u}$ and $\text{O} = 16\ \text{u}$.
- a) How many times heavier is a carbon atom than a hydrogen atom?
- b) And a nitrogen atom than a hydrogen atom?
Molecular mass: adding up atoms
If you snap together three pieces of a building set, the block weighs the same as the sum of the three pieces. The same happens with molecules: they are atoms joined together, and their mass is the sum of the masses of their atoms.
Notice that there are substances made of a single element, like the $\text{O}_2$ in the air or the $\text{N}_2$ used to fill bags of chips: their molecular mass is the atomic mass times the number of atoms. And there are substances like $\text{NaCl}$ (salt): you add up the masses of each element in the formula.
The oxygen we breathe travels through the air forming molecules of $\text{O}2$. If the atomic mass of oxygen is $16\ \text{u}$, calculate the molecular mass of…
The oxygen we breathe travels through the air forming molecules of $\text{O}_2$. If the atomic mass of oxygen is $16\ \text{u}$, calculate the molecular mass of $\text{O}_2$.
The figure shows the model of a water molecule. Calculate the molecular mass of water, $\text{H}2\text{O}$ (atomic masses: $\text{H} = 1\ \text{u}$;…
The figure shows the model of a water molecule.
Calculate the molecular mass of water, $\text{H}_2\text{O}$ (atomic masses: $\text{H} = 1\ \text{u}$; $\text{O} = 16\ \text{u}$).
The gas that forms bubbles in soft drinks is carbon dioxide, $\text{CO}2$. The figure shows its molecule. Calculate its molecular mass (atomic masses:…
The gas that forms bubbles in soft drinks is carbon dioxide, $\text{CO}_2$. The figure shows its molecule.
Calculate its molecular mass (atomic masses: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
The salt we add to food is $\text{NaCl}$. Calculate its molecular mass (atomic masses: $\text{Na} = 23\ \text{u}$; $\text{Cl} = 35.5\ \text{u}$).
The salt we add to food is $\text{NaCl}$. Calculate its molecular mass (atomic masses: $\text{Na} = 23\ \text{u}$; $\text{Cl} = 35.5\ \text{u}$).
Nitrogen gas, $\text{N}2$, is used to fill bags of chips to keep them crunchy. Calculate its molecular mass (atomic mass: $\text{N} = 14\ \text{u}$).
Nitrogen gas, $\text{N}_2$, is used to fill bags of chips to keep them crunchy. Calculate its molecular mass (atomic mass: $\text{N} = 14\ \text{u}$).
Explain in your own words the difference between atomic mass and molecular mass, and give an example of each.
Explain in your own words the difference between atomic mass and molecular mass, and give an example of each.
Calculating with subscripts and parentheses
An element's subscript tells you how many atoms of that element there are. When there is a set of parentheses with a subscript outside, that number multiplies everything inside.
Mollusc shells and school chalk are made of calcium carbonate, $\text{CaCO}3$. The figure shows the atoms that form it. Calculate its molecular mass (atomic masses:…
Mollusc shells and school chalk are made of calcium carbonate, $\text{CaCO}_3$. The figure shows the atoms that form it.
Calculate its molecular mass (atomic masses: $\text{Ca} = 40\ \text{u}$; $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
Glucose, $\text{C}6\text{H}{12}\text{O}6$, is the sugar that your muscles use when you do sport. Calculate its molecular mass (atomic masses: $\text{H} = 1\ \text{u}$;…
Glucose, $\text{C}_6\text{H}_{12}\text{O}_6$, is the sugar that your muscles use when you do sport. Calculate its molecular mass (atomic masses: $\text{H} = 1\ \text{u}$; $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
Sulphuric acid, $\text{H}2\text{SO}4$, is used in car batteries. Calculate its molecular mass (atomic masses: $\text{H} = 1\ \text{u}$; $\text{S} = 32\ \text{u}$;…
Sulphuric acid, $\text{H}_2\text{SO}_4$, is used in car batteries. Calculate its molecular mass (atomic masses: $\text{H} = 1\ \text{u}$; $\text{S} = 32\ \text{u}$; $\text{O} = 16\ \text{u}$).
Slaked lime, which is used in building work and vegetable gardens, has the formula $\text{Ca(OH)}2$. The figure shows its structure. Calculate its molecular mass…
Slaked lime, which is used in building work and vegetable gardens, has the formula $\text{Ca(OH)}_2$. The figure shows its structure.
Calculate its molecular mass carefully: the subscript $2$ outside the bracket multiplies everything inside it (atomic masses: $\text{Ca} = 40\ \text{u}$; $\text{O} = 16\ \text{u}$; $\text{H} = 1\ \text{u}$).
Comparing masses
With molecular masses you can compare substances: how many times heavier one is than another, which is the lightest, or what mass a group of molecules has.
To compare groups of molecules, multiply the mass of one by the number of molecules. For example, $3$ molecules of $\text{N}_2$ weigh $3 \times 28 = 84\ \text{u}$. And if $100$ molecules of a gas weigh $100$ times the mass of one, the ratio between two bags with the same number of molecules is the same as the ratio between their molecular masses.
If you are given the molecular mass and one atom is missing, subtract: take the total, remove what you already know, and divide by the number of missing atoms.
The natural gas used in cookers is methane, $\text{CH}4$, and the ammonia in some cleaning products is $\text{NH}3$. The figure shows their molecules. a) Calculate the…
The natural gas used in cookers is methane, $\text{CH}_4$, and the ammonia in some cleaning products is $\text{NH}_3$. The figure shows their molecules.
- a) Calculate the molecular mass of each one.
- b) Which of the two molecules weighs more?
(Atomic masses: $\text{H} = 1\ \text{u}$; $\text{C} = 12\ \text{u}$; $\text{N} = 14\ \text{u}$.)
The molecular mass of $\text{CO}2$ is $44\ \text{u}$ and the atomic mass of oxygen is $16\ \text{u}$. Look at the model in the figure. Without looking at the periodic…
The molecular mass of $\text{CO}_2$ is $44\ \text{u}$ and the atomic mass of oxygen is $16\ \text{u}$. Look at the model in the figure.
Without looking at the periodic table, deduce the atomic mass of carbon and explain how you worked it out.
An oxygen molecule, $\text{O}2$, weighs $32\ \text{u}$ and a nitrogen molecule, $\text{N}2$, weighs $28\ \text{u}$. A hydrogen molecule, $\text{H}2$, weighs only…
An oxygen molecule, $\text{O}_2$, weighs $32\ \text{u}$ and a nitrogen molecule, $\text{N}_2$, weighs $28\ \text{u}$. A hydrogen molecule, $\text{H}_2$, weighs only $2\ \text{u}$.
- a) How many hydrogen molecules are needed together to weigh the same as one oxygen molecule?
- b) And to weigh the same as one nitrogen molecule?
Order these molecules from lowest to highest molecular mass, calculating the mass of each one first: $\text{SO}2$, $\text{O}2$, $\text{CO}2$ and $\text{CH}4$ (atomic…
Order these molecules from lowest to highest molecular mass, calculating the mass of each one first: $\text{SO}_2$, $\text{O}_2$, $\text{CO}_2$ and $\text{CH}_4$ (atomic masses: $\text{H} = 1\ \text{u}$; $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$; $\text{S} = 32\ \text{u}$).
A salt formed by a metal and chlorine has the formula $\text{XCl}2$ and a molecular mass of $111\ \text{u}$. The figure shows its model. a) Knowing that…
A salt formed by a metal and chlorine has the formula $\text{XCl}_2$ and a molecular mass of $111\ \text{u}$. The figure shows its model.
- a) Knowing that $\text{Cl} = 35.5\ \text{u}$, calculate the atomic mass of element $\text{X}$.
- b) Look it up in the periodic table and identify the element.
- c) Write the full name of the salt.
A glucose molecule, $\text{C}6\text{H}{12}\text{O}6$, has a molecular mass of $180\ \text{u}$. a) How many water molecules ($18\ \text{u}$) weigh the same as one glucose…
A glucose molecule, $\text{C}_6\text{H}_{12}\text{O}_6$, has a molecular mass of $180\ \text{u}$.
- a) How many water molecules ($18\ \text{u}$) weigh the same as one glucose molecule?
- b) How many hydrogen molecules ($2\ \text{u}$)?
- c) Do the same calculation for oxygen ($32\ \text{u}$). Do you get an integer? Explain what it means if it does not come out exact.
Compare without a balance, using only calculations: a) Which weighs more: two water molecules ($18\ \text{u}$ each) or one oxygen molecule ($32\ \text{u}$)? b) What…
Compare without a balance, using only calculations:
- a) Which weighs more: two water molecules ($18\ \text{u}$ each) or one oxygen molecule ($32\ \text{u}$)?
- b) What about three nitrogen molecules ($28\ \text{u}$ each) or two of carbon dioxide ($44\ \text{u}$ each)?
- c) Explain the procedure you followed to compare them.
Two closed bags each contain $100$ molecules: the first contains methane, $\text{CH}4$, and the second sulfur dioxide, $\text{SO}2$ (atomic masses:…
Two closed bags each contain $100$ molecules: the first contains methane, $\text{CH}_4$, and the second sulfur dioxide, $\text{SO}_2$ (atomic masses: $\text{H} = 1\ \text{u}$; $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$; $\text{S} = 32\ \text{u}$).
- a) Calculate the molecular mass of each gas.
- b) How much does the contents of each bag weigh, in $\text{u}$?
- c) How many times more does one bag weigh than the other? Justify your answer.
Mass percentage and average masses
Sometimes you want to know what part of a molecule belongs to each element. It is calculated as a fraction:
$$\%\ \text{del elemento} = \frac{\text{masa del elemento en la fórmula}}{\text{masa molecular}} \times 100$$Why do they add up to 100%? Because the parts from each element together make up the whole molecule.
Weighted average mass. When a mixture has several kinds of molecules, its "average" mass is calculated by multiplying each mass by its percentage (as a fraction) and adding. It is the same thing you do to calculate a grade average when the grades have different weights.
The atomic mass on the table is an average. Atoms of the same element can have different masses (isotopes). The mass you see on the table is the weighted average based on the abundance of each isotope. That is why chlorine appears with $35.5\ \text{u}$: some atoms weigh $35\ \text{u}$ and others $37\ \text{u}$, and since there are more of the $35\ \text{u}$ kind, the average ends up closer to $35$ than to $37$.
The molecular mass of calcium carbonate, $\text{CaCO}3$, is $100\ \text{u}$. The bar in the figure shows how that mass is divided. a) Calculate what percentage of the…
The molecular mass of calcium carbonate, $\text{CaCO}_3$, is $100\ \text{u}$. The bar in the figure shows how that mass is divided.
- a) Calculate what percentage of the mass corresponds to calcium ($40\ \text{u}$).
- b) Do the same for carbon ($12\ \text{u}$) and for oxygen (three atoms of $16\ \text{u}$ in total).
- c) Check that the three percentages add up to $100\ \%$.
Sulfur dioxide, $\text{SO}2$, is released by volcanoes and is also used as a preservative in dried fruit. a) Calculate its molecular mass ($\text{S} = 32\ \text{u}$;…
Sulfur dioxide, $\text{SO}_2$, is released by volcanoes and is also used as a preservative in dried fruit.
- a) Calculate its molecular mass ($\text{S} = 32\ \text{u}$; $\text{O} = 16\ \text{u}$).
- b) What percentage of the mass of the molecule is sulfur? And oxygen?
- c) Explain why the two percentages must add up to exactly $100\ \%$.
The atomic mass of chlorine shown in the periodic table is $35.5\ \text{u}$, but no chlorine atom weighs exactly that: some chlorine atoms weigh $35\ \text{u}$ and…
The atomic mass of chlorine shown in the periodic table is $35.5\ \text{u}$, but no chlorine atom weighs exactly that: some chlorine atoms weigh $35\ \text{u}$ and others weigh $37\ \text{u}$ (these are called isotopes). The figure represents the two types of atoms.
- a) Explain in your own words how it is possible for the atomic mass in the periodic table to be $35.5\ \text{u}$.
- b) Reason which of the two types of chlorine atoms will be more abundant in nature.
Air is approximately $80\ \%$ nitrogen $\text{N}2$ ($28\ \text{u}$) and $20\ \%$ oxygen $\text{O}2$ ($32\ \text{u}$). The figure represents a sample of air. a) Calculate…
Air is approximately $80\ \%$ nitrogen $\text{N}_2$ ($28\ \text{u}$) and $20\ \%$ oxygen $\text{O}_2$ ($32\ \text{u}$). The figure represents a sample of air.
- a) Calculate the average molecular mass of air. Hint: weight each mass according to its percentage.
- b) Does a molecule of $\text{CO}_2$ ($44\ \text{u}$) weigh more or less than an "average" molecule of air?
- c) Use the result to reason why, in a closed room without draughts where $\text{CO}_2$ is being released (for example, a cellar where grape must is fermenting), this gas tends to accumulate near the floor.
Back to the beginning: atoms are not weighed in grams but in $\text{u}$, and a molecule weighs what its atoms add up to; that is how we compare water, salt, or oxygen without a scale.