Exercises: Calculations with moles

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.

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 laboratory, they weigh $58.5\ \text{g}$ of table salt, $\text{NaCl}$, whose molar mass is $58.5\ \text{g/mol}$. How many moles of salt have they weighed out?

A laboratory flask contains $0.5\ \text{mol}$ of glucose dissolved in water. How many molecules of glucose are in the flask? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

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?

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 electrical cable contains $2\ \text{mol}$ of copper atoms. How many copper atoms is this? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

When a soft drink is opened, $4.4\ \text{g}$ of $\text{CO}_2$ escapes (molar mass: $44\ \text{g/mol}$).

1. a) How many moles of gas have escaped?
2. b) How many molecules is this? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

An iron nail weighs $5.6\ \text{g}$ (molar mass of iron: $56\ \text{g/mol}$).

1. a) How many moles of iron atoms does the nail contain?
2. b) How many atoms is this? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

In the lab, a $0.25\ \text{mol}$ sample of an unknown gas weighs $11\ \text{g}$.

1. a) Calculate the molar mass of the gas.
2. 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.

Natural gas, which is almost entirely methane, $\text{CH}_4$ ($M = 16\ \text{g/mol}$), arrives through the pipes of many homes.

1. a) How many moles of methane are in $16\ \text{g}$?
2. b) What volume would they occupy under standard conditions ($22.4\ \text{L/mol}$)?

A small weather balloon contains $11.2\ \text{L}$ of nitrogen, $\text{N}_2$, measured under standard conditions ($22.4\ \text{L/mol}$).

1. a) How many moles of $\text{N}_2$ does it contain?
2. b) How many molecules is this? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

A gold ingot contains $1.2044\times10^{24}$ gold atoms (molar mass of gold: $197\ \text{g/mol}$).

1. a) How many moles of gold is this? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)
2. b) What is the mass of the ingot?

A car emits $44\ \text{g}$ of $\text{CO}_2$ (molar mass: $44\ \text{g/mol}$) on a short trip.

1. a) How many moles of $\text{CO}_2$ has it emitted?
2. b) Considering the formula $\text{CO}_2$, how many moles of oxygen atoms does this emission contain?
3. c) How many molecules of $\text{CO}_2$ has it emitted? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

Before a race, a runner takes an energy gel containing $9\ \text{g}$ of glucose (molar mass: $180\ \text{g/mol}$).

1. a) How many moles of glucose is this?
2. b) How many molecules of glucose will she take? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

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 ($M = 46\ \text{g/mol}$).

1. a) Calculate how many moles are in each bottle, to one decimal place.
2. b) Which of the two contains more molecules? Justify your answer.
3. 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.

A drop of water falling from a faucet weighs $0.09\ \text{g}$ ($M(\text{H}_2\text{O}) = 18\ \text{g/mol}$).

1. a) How many moles of water are in the drop?
2. b) How many molecules does it contain? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)
3. c) Each water molecule has $2$ hydrogen atoms: how many hydrogen atoms are in the drop?
4. d) Comment on the results: do you think it is possible to count these molecules one by one?

When you play sports, your cells "burn" glucose with oxygen according to the reaction:

$\text{C}_6\text{H}_{12}\text{O}_6 + 6\ \text{O}_2 \rightarrow 6\ \text{CO}_2 + 6\ \text{H}_2\text{O}$

The diagram shows the particles involved in the reaction:

The equation is read as follows: for every mole of glucose, $6\ \text{mol}$ of $\text{O}_2$ are consumed and $6\ \text{mol}$ of $\text{CO}_2$ are formed. An athlete burns $90\ \text{g}$ of glucose ($M = 180\ \text{g/mol}$) during a training session.

1. a) How many moles of glucose has he burned?
2. b) How many moles of oxygen has he consumed?
3. c) What volume does this oxygen occupy at standard temperature and pressure ($22.4\ \text{L/mol}$)?

A camping gas cylinder contains $5.8\ \text{kg}$ of butane, $\text{C}_4\text{H}_{10}$ ($M = 58\ \text{g/mol}$).

1. a) Express the mass in grams and calculate how many moles of butane are in the cylinder.
2. b) What volume would that gas occupy under standard conditions ($22.4\ \text{L/mol}$)? Express it also in $\text{m}^3$ ($1\ \text{m}^3 = 1000\ \text{L}$).
3. c) The cylinder has a capacity of only $12\ \text{L}$. Explain how it is possible for so much gas to fit inside it, considering the state of the butane inside the cylinder.

In the lab, a gas is collected in a container: a sample of $3.2\ \text{g}$ occupies $2.24\ \text{L}$ under standard conditions ($22.4\ \text{L/mol}$).

1. a) How many moles of gas are in the sample?
2. b) Calculate the molar mass of the gas.
3. 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.

Avogadro discovered that equal volumes of different gases, under the same conditions, contain the same number of molecules. We have two $22.4\ \text{L}$ containers under standard conditions: one with propane, $\text{C}_3\text{H}_8$ ($M = 44\ \text{g/mol}$), and another with carbon dioxide, $\text{CO}_2$ ($M = 44\ \text{g/mol}$). Observe the diagram in the figure.

1. a) How many moles are in each container? Which one contains more molecules?
2. b) What is the mass of the gas in each container? Does the result surprise you? Explain why.
3. c) Which of the two containers contains more atoms in total? Justify your answer by counting the atoms in each molecule.

A teaspoon of table salt, $\text{NaCl}$ ($M = 58.5\ \text{g/mol}$), contains $5.85\ \text{g}$ of salt.

1. a) How many moles of $\text{NaCl}$ are in the teaspoon?
2. b) Salt is an ionic compound: instead of molecules, it contains equal numbers of $\text{Na}^+$ ions and $\text{Cl}^-$ ions. How many moles of $\text{Na}^+$ ions and how many of $\text{Cl}^-$ ions are in the teaspoon?
3. c) How many ions are there in total in the teaspoon? (Given: $N_{\text{A}} = 6.022\times10^{23}\ \text{mol}^{-1}$)

A delivery van emits $220\ \text{g}$ of $\text{CO}_2$ ($M = 44\ \text{g/mol}$) for every kilometer it travels. On a working day, it covers $100\ \text{km}$.

1. a) What mass of $\text{CO}_2$ does it emit in one day? Express it in grams and in kilograms.
2. b) How many moles of $\text{CO}_2$ is this?
3. c) What volume would that gas occupy under standard conditions ($22.4\ \text{L/mol}$)? Express the result in $\text{m}^3$ ($1\ \text{m}^3 = 1000\ \text{L}$).
4. d) The cargo area of a van has a volume of about $10\ \text{m}^3$. Compare that volume with that of the gas emitted and comment on why efforts are made to reduce vehicle emissions.

Unit challenge. How much gas does a reaction emit in your kitchen? Investigate the reaction between baking soda ($\text{NaHCO}_3$, $M = 84.0\text{ g/mol}$) and the acetic acid in store-bought vinegar ($5\,\%$ acetic acid by mass, $M = 60.0\text{ g/mol}$; density $\approx 1.0\text{ g/mL}$).

1. Home measurement: On a kitchen scale (sensitivity $\pm 1\text{ g}$), weigh a glass with $50\text{ mL}$ of vinegar together with a sample of baking soda. Carefully mix them, wait for the bubbling to stop, and weigh the resulting setup. The mass lost corresponds to the released $\text{CO}_2$. Repeat the test for three different masses: $2\text{ g}$, $4\text{ g}$, and $6\text{ g}$ of baking soda.

2. Data processing: Construct a data table with the initial masses, final masses, and the net mass of $\text{CO}_2$ with its propagated uncertainty ($\pm 2\text{ g}$). Plot a scatter plot representing the mass of $\text{CO}_2$ versus the mass of $\text{NaHCO}_3$.

3. Calculations and report: Write and balance the chemical equation. Calculate the amount of substance in moles of baking soda used and identify the limiting reactant in each test and determine the expected theoretical mass of $\text{CO}_2$. Write a brief lab report comparing the theoretical results with the experimental ones and calculating the percent yield.

Evaluation criteria:

• Rigor in taking home measurements and explicit expression of uncertainties.

• Quality and clarity in the representation of the data table and graph.

• Accuracy in calculating molar masses, converting to moles, and stoichiometry.

• Critical interpretation of the obtained yield and sources of experimental error.