Gases

The air inside a tyre 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 tyre in pascals.

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

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

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

The compressed air in a $12\ \text{L}$ diving cylinder 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 $12\ \text{L}$ cylinders could you fill at that pressure using the air in the tank?

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 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 kelvin.
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 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 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 kelvin.
2. b) Calculate the final temperature of the air in kelvin.
3. c) Express it in degrees Celsius.

In the laboratory, 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?

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 exercise book and write the name of the law applied over each arrow.

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