Chapter 5 - Gases and the Kinetic-Molecular Theory

How do we calculate pressure?

It is the force divided by the area.

Think of atmospheric pressure!!!

What would happen if the pressure outside didn’t match the pressure on the inside of something? Let’s say the pressure on the outside is greater than that of the inside; what happens?

The object could either implode or explode.

If the pressure on the outside is grear than that of the inside, the object could implode!

Look at image

Ask whether we need to convert units of Pressure.

If we do, save this flashcard. Otherwise, delete it:

Fill out the values of this table from top to bottom:

101.325 kPa
1 atm
760 mmHg
760 torr
14.696 lb/in²
1.01325 bar

What does an “ideal gas” even mean?

It means that the relationships between volume, pressure, temperature, and the amount are linear.

Note: this doesn’t actually exist, but gases (like noble ones) behave nearly identical to this.

What does Boyle’s law state?

At a constant tempearture, the volume occupied by a gas is inversely proportional to the pressure

PV = constant

So as pressure increases, volume decreases; as volume increases, pressure decreases.

What does Charles’s law state?

At a constant pressure, the volume occupied by a gas is directly proportional to its absolute (kelvin) temperature.

V/T = constant or V = constant * T

TLDR: as temperature increases, volume increases; as temperature decreases, volume decreases.

What happens with temperature and pressure? if you increase one, what happens to the other?

They are directly proportional! As one increases, the other increases!

What is avogadro’s law?

This states that at a fixed temperature and pressure, the volume occupied by a gas is directly proportional to the amount of mols of gas.

V is proportional to n (mols)

What is standard temperature and prssure (STP)? Actually give these conditions is what I mean!

Also, what is standard molar volume?

STP: 0^oC (273.15 K) and 1 atm (760 torr).

SMV (standard molar volume) is 22.4 L but only when STP is met.

What does the ideal gas law tell us? What is this constant’s value AND UNIT?

It tell us that PV = nRT

R = 0.0821 (atm * L)/(mol * K)

The ideal gas law is great because it allows us to compare two different gases to each other using the equation:

P₂V₂ / n₂T₂ = P₂V₂ / n₂T₂

It also means that if things are kept the same for each one, like n and T, then we can just do PV = PV!!!

A 3.50-L sample of neon gas has a pressure of 924 torr. What pressure (in atm) is required to compress the gas into a tank with a volume of 1350 cm³ at constant temperature?

1. Write out everything we have

   1. V₁ = 3.50-L

   2. P₁ = 924 torr (we’ll need atm soon)

   3. P₂ is unknown (what we’re solving for)

   4. V₂ = 1350 cm³ (we’ll need L soon)

2. Convert Everything We need to

   1. P₁ = 924. 924 / 760 = 1.22 atm.

   2. V₂ = 1350 cm³ = 1350 mL or 1.35 L

3. Use ideal gas law:

   1. PV = PV

      1. (3.50)(1.22) = P(1.35)

         1. P = 3.16 atm

Answer question: Revisit 5.3 for more practice problems like these because they’re difficult!!!!

Recognize that the only thing changing here is temperature. The important part here is that VOLUME stays the same. The problem says that pressure is constant too.

The only thing left is n. If n were constant, V would have to double when T doubles. This isn’t the case, so n IS NOT constant.

We also know from Avogadro’s law (V/n = V/n) that if volume were to stay the same here, with P constant and T doubling, n would have to be halved. (write out ideal gas law to better visualize this).

We see that in equation 3, n decreases from 2 to 1. Boom. Equation 3 is our answer

How does density work if all ideal gases occupy the same volume at STP? Is it all the same? What is another formula for density then?

Density is still different but because the volume is the same, the only differences come from molar mass (since D = M/V)

Another formula that you can use is D = (P * M) / RT

Where P = pressure, M = molar mass, R = constant, T = temperature

Find the density in g/L of CO₂ and the number of molecules per liter at STP and at room conditions (20^o C and 1.00 atm).

AMU of CO₂ = 44.01

There should be four answers here!

First Part (density)

• D = m/v or PM/RT

  • 1.00 × 44.01 / 0.0821 × 273 K = 1.96 g/L

Second Part (molecules at STP)

• 1.96 g / 1 L * (1 mol CO₂ / 44.01 g CO₂) * (6.022 × 10²³ molecules CO₂ / 1 mol CO₂) = 2.68 × 10²² molecules CO₂ / L

Third Part (density @ room conditoins)

• Use density formula

  • 1.00 × 44.01 / 0.0821 × 293.15 (cuz 273 + 20) = 1.83 g/L (somewhere close to this is right since the book uses 273 instead of 273.15!)

Fourth Part (molecules @ room conditions)

• 1.83 g / 1 L * (1 mol CO₂ / 44.01 g CO₂) * (6.022 × 10²³ molecules CO₂ / 1 mol CO₂) = 2.50 × 10²² molecules CO₂ / L

The alkali metals (group 1) react with halogens (group 17), forming ionic metal halides. What mass of potassium chloride forms when 5.25 L of chlorine gas at 0.950 atm and 293 K reacts with 17.0 g of potassium?

potassium = 39.10 amu
KCl = 74.55 amu

1. Write balanced equation

   1. 2K (s) + Cl₂ (g) —> 2KCl (s)

2. Write out variables for chlorine

   1. P = 0.950 atm, T = 293 K, V = 5.25 L, n = unknown.

      1. Solve for n very easily:

         1. PV/RT = (0.950 × 5.25) / (0.0821 × 293) = 0.207 mol

3. Turn mass of K into mol

   1. 17.0 / 39.10 = 0.435 mol K

4. Find the limiting reactant by throginw in the mols of chlorine and potassium into balanced equation

   1. 0.207 × 2/1 = 0.414 mol KCL

   2. 0.435 × 2/2 = 0.435 mol KCl

      1. Cl₂ is the limiting reactant!

5. Use mol of Cl₂ to find grams of KCl

   1. 0.414 KCl * 74.55 = 30.9 g KCl

What does Dalton’s law state?

It says that in a mixture of gases that DONT react, the total pressure is the sum of all partial presures:

P_total = P₁ + P₂ + … + P_n

How do you find mole fraction? How does this help in Dalton’s law?

You take the moles of one substance and divide it by the total amount of mols.

This helps in Dalton’s law because we can just use the mole fraction of (substance A) and multiply it by the total pressure to get that (substance A) pressure.

Look at picture (formula):

A chemical engineer puts noble gases consisting of 5.50 g He, 15.0 g Ne, and 35.0 g Kr in a piston cyclinder at 298 K and 0.885 atm. Find the partial pressure of each gas.

Start by finding the moles of each gas, which I’m giving you since it’s EZ:

He: 1.37 mol
Ne: 0.743 mol
Kr: 0.418 mol

1. Find the moles of each gas

2. Find the total amount of moles for the equation P_A = X_A + P_total

   1. 1.37 + 0.743 + 0.418 = 2.53 mol

3. Find the mole fraction for each substance

   1. 1.37 / 2.53 (He)

   2. 0.743 / 2.53 (Ne)

   3. 0.418 / 2.53 (Kr)

4. Then multiply each value (so the 1, 2, 3, above) by 0.885 atm and you should get:

   1. 0.479 atm (He)

   2. 0.260 atm (Ne)

   3. 0.146 atm (Kr)

5. A great way to check if you’re right is by adding up all three answers to see if it gets to 0.885—the total pressure!

C₂H₂ is produced in a laboratory when CaC₂ reacts with water:

CaC₂ (s) + 2H₂O (l) —> C₂H₂ (g) + Ca(OH)₂ (aq)

The total gas pressure of C₂H₂ collected is 738 torr and the volume is 523 mL. At 296K, the vapor pressure of water is 21 torr. How many grams of C₂H₂ are collected?

C₂H₂ = 26.04 amu

1. We need to obviously get the grams of C₂H₂, and to do that, we should write out everything we have:

   1. P = (738 - 21) = 717 torr, V_{in liters} = 0.523 L, T_{in kelvin} = 296 K

      1. We can now easily solve for n. (717/760)*0.523 = n*0.0821×296

         1. n = 0.0203 mol

2. Turn the n value into grams

   1. 0.0203 mol * 26.04 = 0.529 g C₂H₂

There’s this idea called KMT (kinetic-molecular theory) and it has four prerequisites, otherwise it cannot be used. What are they?

1. Since the volume of each gas molecule is so small compared to the total volume, we can assume the volume of gas is zero

2. Gas particles are in constant, random, straight-line motion except when they collide with the container walls or with each other.

3. The particle collisions do not lose any kinetic energy through friction.

4. The average kinetic energy of the gas particles is proportional to the absolute temperature.

Which line has the highest temperature acting on it? What observation can you make about temperature?

It’s the third graph (green). We can obseve that as temperature increases, so does the variability with the individual gas particles.

Why don’t O₂ molecules (which hit the container wall at a higher force) have more pressure and therefore more volume than ligher H₂ molecules?

It’s because of KMT, whose fourth condition states that all gases have the same average kinetic energy at a particular temperature.

It actually shows that particles with a lower molar mass have a higher most probable speed, but the area under the graph shoes they have the same average kinetic energy

Look at image

What is mean free path? How is it obtained?

Mean free path is the average distance a particle travels between collisions at a given temperature and pressure. We can obtain this by considering the density and diameter of the particle. (wont need to know how to calculate)

For example, the N₂ molecule which is 3.7 × 10^-10 m in diameter has a mean free path of 6.6 × 10^-8 m, which means it travels an average of 180 molecular diamteres before smashing into a fellow traveler.

This is great for figuring out the rate of diffusion and heat flow!

What is collision frequency (i really wonder)?

This is the average number of collisions per second that each particle undergoes (either with another particle or with the container its in).

What is effusion? What is Graham’s law of effusion (two parts)?

This is the rate at which a gas escapes through a tiny hole in the container into an evacuated space.

Graham’s law of effusion states that effusion is inversely proportional to the square root of its molar mass: rate = 1 / sqrt(M)

It also states that time is proportional to the sqare root of molar mass.

If it takes 1.25 min for 0.010 mol of He to effuse, how long will it takes for the same amount (0.010 mol) of ethane (C₂H₆) to effuse?

He = 4.003 g / mol
C₂H₆ = 30.068 g /mol

1. Since we are comparing the times here, we need to do Time1 / Time2 = Sqrt(M₁/M₂)

2. In this case, we’ll do x/1.25 = sqrt(30.068/4.003)

   1. x = 3.43 min