C15 Ideal Gases

Question 1

What is 1 Pa equal to?

Answer 1

1Pa = 1Nm^-2

Question 2

How does a Gas Exert a Pressure?

Answer 2

-Gas consists of molecules in constant random motion.

-When a molecule collides with surface it undergoes a momentum change as it reverses direction.

-By Newton’s 2nd and 3rd laws, the surface therefore experiences a force from the colliding molecule.

-Pressure exerted by gas is equal to total force exerted by the molecules on a unit area of the surface

-P = F / A (where F is the force perpendicular to the surface area).

Question 3

Assumptions about Ideal Gases and Kinetic Theory: (6)

Answer 3

1) Molecules are points- the vol of molecules is insignificant compared to vol of the ideal gas.

2) Molecules don’t attract each other- if they did then pressure exerted by the gas on its container would reduce.

3) All collisions between gas molecules and their container are elastic- no loss in KE.

4) Time taken for a collision is much shorter than the time between collisions.

5) Any sample of an ideal gas contains a very large no. of molecules.

6) The molecules in a gas have constant random motion.

Question 4

How can the amount of a substance be measured?

Answer 4

Amount of a substance, can be measured in the SI base unit of the mole.

Question 5

What’s one mole?

Answer 5

One mole is the amount of substance containing 6.02×10^23 particles (atoms or molecules).

Question 6

What is Avogadro’s Constant (Na)?

Answer 6

Avogadro’s constant (Na), is equal to no. of atoms in exactly 12g of the isotope carbon 12.

Question 7

What’s the equation for calculating the number of molecules in a substance?

Answer 7

The no. of particles (molecules) in a substance, determined by multiplying no. of moles of the substance by Avogadro’s constant:

N = n x Na

Question 8

What is the Molar Mass of a substance?

Answer 8

Molar mass of a substance = mass of one mole of the substance.

Question 9

Equation used for Molar Mass?

Answer 9

M= m / n

-m is the mass of the substance,
-M is the molar mass (in grams, which is the same as the nucleon number for the atom/molecule) of the particles that make up the substance.
-n, the no. of moles.

Question 10

What does the experimental gas laws state?

Answer 10

These state how the pressure (p), vol (V) and the absolute temp (T) of an ideal gas relate to each other.

Question 11

Real gases at relatively low pressures and well above their condensation temp behave like…

Answer 11

an ideal gas.

Question 12

Boyle’s Law states:

Answer 12

Boyle’s law states that the pressure exerted by a fixed amount of gas is inversely proportional to its volume at a constant temperature.

Question 13

What is the equation, For a fixed mass of gas at a constant temp:

Answer 13

pV = constant

Question 14

Ideal Gas

Answer 14

Ideal gas, defined as gas that obeys Boyle’s law at all pressures.

Question 15

Equation for when a gas changes pressure from p1 to p2 while undergoing a vol change from V1 to V2:

Answer 15

p1 x V1 = p2 x V2

Question 16

Why is it Real Gases do not obey Boyle’s Law at very high pressures?

Answer 16

Because as pressure increase the vol decreases exponentially resulting gas to condense and molecules eventually attract each other, breaking the ideal gas assumptions.

Question 17

-By plotting p vs 1/V we get straight line graphs for each temp. A change in temp would effect what?

Answer 17

The gradient (represents the constant), as increase in temp = increase in pressure.

Question 18

For pressure laws temperature must always be in what units?

Answer 18

Kelvin

Question 19

Pressure Law:

Answer 19

For a fixed mass of gas at a constant volume:
P / T = constant

When a gas changes pressure from p1 to p2 while undergoing a temp change from T1 to T2:
p1 / T1 = p2 / T2

Question 20

Charles’ Law:

Answer 20

For a fixed mass of gas at a constant pressure,

V / T = constant

When a gas changes volume from V1 to V2 while undergoing a temp change T1 to T2:

V1 / T1 = V2 / T2

-Temperature must always be in Kelvin

Question 21

The Ideal Gas Equation:

Answer 21

Combining all three gas laws for a constant mass of gas gives,

pV / T = constant

constant = n x R (n, no. of mols and R, molar gas constant, 8.31)

Therefore pV = nRT

p1V1 / T1 = p2V2 / T2
(Temp in Kelvin)

We know N = n x Na

Therefore pV = (N / Na) x RT
Rearrange to get pV = (R / Na) x NT
Boltzmann constant, k = R / Na
Where k is another constant, 1.38 x 10^-23
And so ideal gas equation can be written as pV = kNT (N, the no. of molecules).

Question 22

What does the Kinetic Theory of Gases state:

Answer 22

Kinetic Theory of gases- states a gas consists of point molecules moving about in random motion.

Question 23

How does the pressure of a gas alter with if the volume in the container decreases?

Answer 23

Volume: if vol container decreases, greater no. molecules hitting inside container per sec.
Greater force exerted, pressure increases.

Question 24

How does the pressure of a gas alter with if the temperature in the container increases?

Answer 24

Temperature: if temp of container increases, molecules moving greater speeds, more hitting inside container per sec and will each exert greater force (Newton’s 2nd Law).

Question 25

What’s Brownian Motion, evidence?

Answer 25

-First observed 1827 with pollen grains in water.

-Idea that very small objects have random motion in a liquid or gas due to random bombardment by the molecules in this substance.

Question 26

Molecular speed variation:

Answer 26

The molecules inside ideal gas, have continuous spread of speeds.

The speed of individual molecules may change when it collides with another molecule but the distribution of speeds remains the same provided the gas temp doesn’t change.

Question 27

What is the KE of a molecule directly proportional to?

Answer 27

The KE of a molecule, directly proportional to its absolute temp.

Question 28

Explain how to derive the equation: Ek = 3/2 kT

Answer 28

pV = ⅓ Nm x (mean c^2)

Note: pV = nRT = NkT

⅓ Nm x (mean c^2) = NkT

⅓ m x (mean c^2) = kT

½ m x (mean c^2) = 3/2 kT

Ek = 3/2 kT

Question 29

For an ideal gas containing N identical molecules, each of mass, m in a container of volume, V, the pressure, p of the gas is given by:

Answer 29

pV = ⅓ Nm x (mean c^2)

Question 30

RMS (Root Mean Square) molecular Speed, Crms:
(Derive equation)

Answer 30

If a gas contains N molecules each having speeds c1 + c2 + c3 + … + cN, then root mean square speed, Crms given:

c,rms = square root of the mean of c^2

mean c^2 (mean square speed) = c,rms^2