Gases

The air inside a tire can be described using three variables: pressure, volume, and temperature.

1. a) Explain in your own words what each of them indicates.
2. b) State the SI unit used to measure each one.
3. c) Knowing that $1\ \text{atm}=101325\ \text{Pa}$, express the pressure of $2\ \text{atm}$ of a bicycle tire in pascals.

To study gases, temperature must always be expressed in kelvin: $T(\text{K})=T(\celsius)+273$.

1. a) A lab is at $22\ \celsius$: how many kelvin is that equivalent to?
2. b) Liquid nitrogen is at $-196\ \celsius$: what is this in kelvin?

The Kelvin scale starts at absolute zero, the lowest temperature that can exist: $-273\ \celsius$.

1. a) How many kelvins is $-273\ \celsius$?
2. b) Explain why nothing can exist at $-300\ \celsius$.
3. c) What happens to the particles of a gas when its temperature approaches absolute zero?

According to the kinetic model, a gas is made up of tiny particles that move continuously and collide with the walls of the container. Observe the model in the figure.

1. a) Explain in your own words what the pressure of a gas is according to this model.
2. b) If you put more particles into the same container, what happens to the collisions and to the pressure?
3. c) And if you heat the gas without changing the number of particles, what changes in the collisions?

You cover the tip of a syringe containing $10\ \text{mL}$ of air at ambient pressure $1\ \text{atm}$ and push the plunger down to $5\ \text{mL}$, without changing the temperature. The pressure-volume graph shows both situations.

1. a) State Boyle's law: what is the relationship between the pressure and volume of a gas at constant temperature?
2. b) Calculate the pressure of the air inside the syringe.

A bicycle pump contains $300\ \text{cm}^3$ of air at $1\ \text{atm}$. Pushing the plunger with the nozzle connected to the tire, the air inside reaches $4\ \text{atm}$ without changing temperature. Apply Boyle's law, $p_1\times V_1=p_2\times V_2$, and calculate what volume the air in the pump occupies then.

The compressed air in a $12\ \text{L}$ diving tank is at $200\ \text{atm}$. All of this air is allowed to enter a $240\ \text{L}$ tank at the same temperature.

1. a) Calculate the pressure reached by the air in the tank.
2. b) How many $12\ \text{L}$ diving tanks could you fill at that pressure using the air in the tank?

A diver releases a $2\ \text{cm}^3$ bubble at a depth of $40\ \text{m}$, where the total pressure is $5\ \text{atm}$. The water temperature barely changes during the ascent. The figure shows the ascent of the bubble.

1. a) What volume will the bubble have when it reaches the surface, at $1\ \text{atm}$?
2. b) Calculate its volume as well when passing through a depth of $10\ \text{m}$, where the pressure is $2\ \text{atm}$.
3. c) Use the results to explain the first rule of scuba diving: why you must never hold your breath during ascent.

A workshop compressor takes $40\ \text{L}$ of outdoor air, at $1\ \text{atm}$, and forces it into a $8\ \text{L}$ tank without changing the temperature.

1. a) What is the resulting pressure of the air in the tank?
2. b) Afterwards, the compressor forces another $40\ \text{L}$ of outdoor air into the same tank. What pressure does it reach now?
3. c) If we kept adding air continuously, would the pressure increase indefinitely? Explain what would happen in reality with the particles so close together and with the tank itself.

You want to test Boyle's law using a sealed syringe containing air and weights placed on the plunger.

1. a) What quantities would you measure and using which instruments?
2. b) Which quantity must you keep constant for the experiment to be valid? How would you ensure this?
3. c) What numerical result should be repeated across all measurements if the law holds true?
4. d) Sketch the pressure-volume graph you expect to obtain in your notebook and describe its shape: is it a straight line?

You can do it on paper and send a photo with your answer.

A cylinder with a freely moving plunger, such that the internal pressure does not change, contains $600\ \text{mL}$ of air at $300\ \text{K}$. It is heated to $400\ \text{K}$. The V–T graph shows the process.

1. a) State Charles's law.
2. b) Calculate the final volume of the air.

A scientific team in the Arctic fills a balloon with $400\ \text{mL}$ of air at $-23\ \celsius$. They bring it into a warm tent at $27\ \celsius$, where the balloon can expand freely at constant pressure.

1. a) Express both temperatures in kelvins.
2. b) Apply Charles's law, $\frac{V_1}{T_1}=\frac{V_2}{T_2}$, and calculate the volume of the balloon inside the tent.

A balloon contains $2\ \text{L}$ of air at $27\ \celsius$. It is left in the sun and, expanding at constant pressure, reaches a volume of $2.2\ \text{L}$.

1. a) Express the initial temperature in kelvins.
2. b) Calculate the final temperature of the air in kelvins.
3. c) Express it in degrees Celsius.

In the lab, air is heated at constant pressure and the following measurements are obtained: at $300\ \text{K}$ the volume is $600\ \text{mL}$; at $350\ \text{K}$, $700\ \text{mL}$; at $400\ \text{K}$, $800\ \text{mL}$. The graph shows the three measurements.

1. a) Calculate the quotient $\frac{V}{T}$ for each measurement: what do you observe?
2. b) Which law is being tested?
3. c) Predict the volume you would measure at $450\ \text{K}$.
4. d) If you extend the data backwards, at what temperature would the volume be zero? What is this temperature called, and why do you think a real gas never reaches it?

Aerosol cans carry this warning: "Do not puncture or burn, even after use."

1. a) What happens to the pressure of the gas inside when the temperature rises significantly, if the volume of the can does not change?
2. b) What is the name of the law that describes this behavior?
3. c) Explain why the can could explode even if there is no product left inside.

You rinse a plastic bottle with hot water, seal it immediately and leave it to cool down: after a while, it collapses inward.

1. a) What has happened to the temperature of the air trapped inside?
2. b) And to its pressure?
3. c) Explain why the bottle collapses inward, comparing the internal pressure with the atmospheric pressure outside.

Car manufacturers recommend measuring tire pressure when "cold", before making a trip.

1. a) After an hour on the highway, the tires are hot: what has happened to the temperature of the air inside and to its pressure, if the volume barely changes?
2. b) What is the name of the law that explains this behavior?
3. c) Reason why measuring them when hot is misleading: does the pressure appear higher or lower than it ideally should be?

Two identical closed containers contain the same amount of air. One is at $300\ \text{K}$ and the other at $600\ \text{K}$. Look at the diagram.

1. a) Which one has higher pressure? If the pressure in the cold container is $2\ \text{atm}$, calculate its value in the hot container.
2. b) Explain the result using the kinetic model: what do the particles in the hot gas do differently?

A spray can contains its gas at $3\ \text{atm}$ when at $27\ \celsius$. Assume that the pressure increases in proportion to the temperature measured in kelvins. The p-T graph shows the situation.

1. a) Express $27\ \celsius$ in kelvins.
2. b) If the can can withstand a maximum of $6\ \text{atm}$, at what temperature, in kelvins and in degrees Celsius, would the pressure reach the limit?
3. c) A car parked in the sun reaches $54\ \celsius$ inside, "double" that of $27\ \celsius$. Calculate the actual pressure of the gas at $54\ \celsius$ and explain why it is not double what it was at the start: where is the catch?

A plunger compresses air at constant temperature and the pressure rises. Explain this using the kinetic model:

1. a) If the temperature does not change, does the speed of the particles change when compressed?
2. b) If the speed is the same, why does the pressure rise? Think about how many times the particles collide with the walls when the container becomes smaller.

A gas occupies $4\ \text{L}$ at $27\ \celsius$ and $1\ \text{atm}$. First, it is compressed at constant temperature to $2\ \text{L}$ and then heated at constant pressure to $177\ \celsius$.

1. a) What is the pressure of the gas after compression?
2. b) Express the temperatures of the second step in kelvins.
3. c) What volume does the gas occupy at the end?
4. d) Draw a diagram showing the three states in your notebook and write the name of the law applied over each arrow.

You can do it on paper and send a photo with your answer.

Two identical balloons contain $1\ \text{L}$ of air at $27\ \celsius$ and $1\ \text{atm}$. Balloon A is left in the sun and its air heats up to $57\ \celsius$, being able to expand at constant pressure. Balloon B is submerged $10\ \text{m}$ into a swimming pool, where the pressure is $2\ \text{atm}$ and the temperature does not change. The diagram summarizes the two cases.

1. a) Calculate the final volume of each balloon.
2. b) Which one ends up with a larger volume?
3. c) Explain, naming the law used in each case, why one inflates and the other shrinks.

The pressure of a gas depends on how many times the particles collide with the walls and how strong each collision is. Use only this idea to explain the three gas laws:

1. a) Boyle's law: when reducing the volume without changing the temperature, why does the pressure increase?
2. b) Charles's law: when heating a gas that can expand, why does the volume increase until the internal pressure equals the external pressure?
3. c) Gay-Lussac's law: when heating a gas sealed in a rigid container, why does the pressure increase?