Calculations with moles
A fire extinguisher, a butane cylinder and a helium balloon have something in common: to make them, you need to know exactly how many moles of gas fit inside. The mole is not just a theoretical idea: it is the tool engineers use to calculate real quantities.
From mass to moles
In the laboratory, balances measure grams, but chemical reactions happen atom by atom: $18\ \text{g}$ of water contain one mole of molecules, but $18\ \text{g}$ of glucose are only a tenth of a mole. How do we convert the mass shown on the balance into the amount of substance that reacts?
You have $36\ \text{g}$ of water in a glass. Knowing that the molar mass of water is $18\ \text{g/mol}$, calculate how many moles of water the glass contains.
You have $36\ \text{g}$ of water in a glass. Knowing that the molar mass of water is $18\ \text{g/mol}$, calculate how many moles of water the glass contains.
In a laboratory, they weigh $58,5\ \text{g}$ of common salt, $\text{NaCl}$, whose molar mass is $58,5\ \text{g/mol}$. How many moles of salt have they weighed out?
In a laboratory, they weigh $58,5\ \text{g}$ of common salt, $\text{NaCl}$, whose molar mass is $58,5\ \text{g/mol}$. How many moles of salt have they weighed out?
From moles to mass
A fire extinguisher contains $3\ \text{mol}$ of carbon dioxide. If the molar mass of $\text{CO}2$ is $44\ \text{g/mol}$, what mass of gas does the fire extinguisher…
A fire extinguisher contains $3\ \text{mol}$ of carbon dioxide. If the molar mass of $\text{CO}_2$ is $44\ \text{g/mol}$, what mass of gas does the fire extinguisher contain?
In a pharmacy, they use $0,25\ \text{mol}$ of ethanol ($M = 46\ \text{g/mol}$) to prepare a disinfectant. What mass of ethanol have they used?
In a pharmacy, they use $0,25\ \text{mol}$ of ethanol ($M = 46\ \text{g/mol}$) to prepare a disinfectant. What mass of ethanol have they used?
An iron nail weighs $5,6\ \text{g}$ (molar mass of iron: $56\ \text{g/mol}$). a) How many moles of iron atoms does the nail contain? b) How many atoms is this? (Given:…
An iron nail weighs $5,6\ \text{g}$ (molar mass of iron: $56\ \text{g/mol}$).
- a) How many moles of iron atoms does the nail contain?
- b) How many atoms is this? (Given: $N_{\text{A}} = 6,022\cdot10^{23}\ \text{mol}^{-1}$)
From moles to number of particles
A single sip of water contains more than $10^{23}$ molecules, an astronomical figure that is impossible to measure directly one by one. How do we group microscopic particles into manageable packets so that we can count them?
A laboratory flask contains $0,5\ \text{mol}$ of glucose dissolved in water. How many molecules of glucose are in the flask? (Given:…
A laboratory flask contains $0,5\ \text{mol}$ of glucose dissolved in water. How many molecules of glucose are in the flask? (Given: $N_{\text{A}} = 6,022\cdot10^{23}\ \text{mol}^{-1}$)
An electrical cable contains $2\ \text{mol}$ of copper atoms. How many copper atoms is this? (Given: $N_{\text{A}} = 6,022\cdot10^{23}\ \text{mol}^{-1}$)
An electrical cable contains $2\ \text{mol}$ of copper atoms. How many copper atoms is this? (Given: $N_{\text{A}} = 6,022\cdot10^{23}\ \text{mol}^{-1}$)
When a soft drink is opened, $4,4\ \text{g}$ of $\text{CO}2$ escapes (molar mass: $44\ \text{g/mol}$). a) How many moles of gas have escaped? b) How many molecules is…
When a soft drink is opened, $4,4\ \text{g}$ of $\text{CO}_2$ escapes (molar mass: $44\ \text{g/mol}$).
- a) How many moles of gas have escaped?
- b) How many molecules is this? (Given: $N_{\text{A}} = 6,022\cdot10^{23}\ \text{mol}^{-1}$)
The volume of a mole of gas
If you measure, at standard conditions, the volume of $2\ \text{g}$ of $\text{H}_2$ ($1\ \text{mol}$), $32\ \text{g}$ of $\text{O}_2$ ($1\ \text{mol}$) and $44\ \text{g}$ of $\text{CO}_2$ ($1\ \text{mol}$), you will find that all three gases occupy exactly $22{,}4\ \text{L}$. Why do gases with such different masses and molecules occupy exactly the same space?
Under standard conditions, that is, at $0\ \celsius$ and $1\ \text{atm}$ of pressure, one mole of any gas occupies $22,4\ \text{L}$, as shown in the diagram. A balloon…
Under standard conditions, that is, at $0\ \celsius$ and $1\ \text{atm}$ of pressure, one mole of any gas occupies $22,4\ \text{L}$, as shown in the diagram.
A balloon contains $2\ \text{mol}$ of helium. What volume does the gas occupy under standard conditions?
An airtight bag contains $11,2\ \text{L}$ of air measured under standard conditions ($22,4\ \text{L/mol}$). How many moles of air are inside the bag?
An airtight bag contains $11,2\ \text{L}$ of air measured under standard conditions ($22,4\ \text{L/mol}$). How many moles of air are inside the bag?
Natural gas, which is almost entirely methane, $\text{CH}4$ ($M = 16\ \text{g/mol}$), arrives through the pipes of many homes. a) How many moles of methane are in…
Natural gas, which is almost entirely methane, $\text{CH}_4$ ($M = 16\ \text{g/mol}$), arrives through the pipes of many homes.
- a) How many moles of methane are in $16\ \text{g}$?
- b) What volume would they occupy under standard conditions ($22,4\ \text{L/mol}$)?
Chaining the three routes together
In the laboratory, a $0,25\ \text{mol}$ sample of an unknown gas weighs $11\ \text{g}$. a) Calculate the molar mass of the gas. b) Which gas could it be: methane,…
In the laboratory, a $0,25\ \text{mol}$ sample of an unknown gas weighs $11\ \text{g}$.
- a) Calculate the molar mass of the gas.
- b) Which gas could it be: methane, $\text{CH}_4$ ($M = 16\ \text{g/mol}$), or propane, $\text{C}_3\text{H}_8$ ($M = 44\ \text{g/mol}$)? Justify your answer.
In the kitchen there are two bottles: one with $100\ \text{g}$ of water ($M = 18\ \text{g/mol}$) and another with $100\ \text{g}$ of ethyl alcohol or ethanol (…
In the kitchen there are two bottles: one with $100\ \text{g}$ of water ($M = 18\ \text{g/mol}$) and another with $100\ \text{g}$ of ethyl alcohol or ethanol ($M = 46\ \text{g/mol}$).
- a) Calculate how many moles are in each bottle, to one decimal place.
- b) Which of the two contains more molecules? Justify your answer.
- c) Without doing further calculations, explain what the molar mass of a substance would need to be like for $100\ \text{g}$ of it to contain more molecules than $100\ \text{g}$ of water.
In the laboratory, a gas is collected in a container: a sample of $3,2\ \text{g}$ occupies $2,24\ \text{L}$ under standard conditions ($22,4\ \text{L/mol}$). a) How many…
In the laboratory, a gas is collected in a container: a sample of $3,2\ \text{g}$ occupies $2,24\ \text{L}$ under standard conditions ($22,4\ \text{L/mol}$).
- a) How many moles of gas are in the sample?
- b) Calculate the molar mass of the gas.
- c) Which gas is it: oxygen, $\text{O}_2$ ($M = 32\ \text{g/mol}$), or nitrogen, $\text{N}_2$ ($M = 28\ \text{g/mol}$)? Explain how you know.
Back to the beginning: To fill that helium balloon, whose gas is at a pressure close to atmospheric, you can convert its volume into moles ($n = V/22{,}4$, assuming standard conditions) and then calculate the mass in grams ($m = n \cdot M$). In the $\text{CO}_2$ extinguisher or the butane cylinder the gas is at high pressure and partly liquefied, so $22{,}4\ \text{L/mol}$ does not apply: engineers work with the mass and the molar mass ($n = m/M$) to know how many moles they inject.