Bailey N-
What are 4 main properties of gases
1) They expand to fill their container (compressible)
2) their particles are constantly moving fast and randomly
3) The size of their particles is tiny compared to the volume of their container
3) there's negligible attraction between their particles and they bounce when they collide (elastic collision)
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Standard conditions for an ideal gas (SPVT)
P = 1 atm
V = 22.4L
T = 273K (0C)
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Ideal gas formula for finding initial/final amount
P1·V1 ÷ P2·V2 = n1RT1 ÷ n2RT2
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Partial pressure, partial pressure formula, and Dalton's law of partial pressure
Partial pressure is the pressure of a single gas in a mixture of gases
- Partial pressure formula: (Xa) · P(total)
- Dalton’s law: P(total) = Pa + Pb + Pc…
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Mole fraction of a single gas formula
Xa = n(a) ÷ n(total)
- Xa: mole fraction of single gas
- n: moles of the single gas and total moles of the gas mixture
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Torr/mmHg → atm
760 torr/mmHg = 1 atm
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Ideal gas law for finding volume
V = (nRT) ÷ P
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mL → L
1 mL = 0.001 L
1 L = 1000 mL
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atm x L → J
1 atm · L = 101.325 J
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Kinetic energy (KE) formula for a single molecule or when given mass/volume
KE = (1/2) · m · v2
- m in kg
- v in m/s
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KE formula for many molecules or when given temperature
KE = (3/2) · R · K
- R is 8.31 J/mol · K
- T in K
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Relationship between temperature → KE → speed
Temperature ↑ = KE ↑ = average speed ↑
(directly proportional)
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Gases that are heavier/lighter than each other can have the same KE at the same temperature because ___
They have different velocities than each other
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Lighter particles have ___ average velocity
Heavier particles have ___ average velocity
Lighter = faster average velocity
Heavier = slower average velocity
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Formula for root-mean-square speed (Urms)
Urms = √(3 · RT) ÷ M)
- M in kg/mol
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g → kg
1 kg = 1000 g
1 g = 0.001 kg
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Conversion factor for J(joules) in Urms
1 J = 1 kg · (m2 ÷ s2)
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What should you always include when calculating Urms
The conversion factors for J and kg to cancel units and make sure the final answer is in m2/s2
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Mean free path (how does pressure effect it)
The average distance a molecule travels between collisions
- Decreases ↓ as pressure increases ↑
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Diffusion
Molecules going from a higher → lower concentration
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Effusion
When molecules escape through a small hole into a vacuum
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Lighter particles have ___ diffusion/effusion rates
Heavier particles have ___ diffusion/effusion rates
Lighter = Faster diffusion/effusion
Heavier = Slower diffusion/effusion
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Ratio of effusion in 2 gases at the same temperature formula (Graham's law)
(rateA ÷ rateB) = √(MB ÷ MA)
- M in kg/mol
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Under what conditions do real gases deviate from ideal gas laws
At high pressures or low temperatures
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Ideal gas law
P · V = n · RT
- P in atm
- V in L
- R is 0.0821 · (L · atm ÷ mol · K)
- T in K
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What do a and b account for in the real gas law, what do their values indicate
a = actual intermolecular forces between gas particles
b = the finite size of gas particles
- Larger a and b values indicate less 'ideal' behaviors
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Ideal gas law for finding pressure/volume change
P1V1 = P2V2
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Ideal gas law for finding volume/temperature change
V1 ÷ T1 = V2 ÷ T2
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Ideal gas law for finding volume/amount (in moles) change
V1 ÷ n1 = V2 ÷ n2
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Ideal gas law for finding pressure/temperature change
P1 ÷ T1 = P2 ÷ T2
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Ideal gas law for finding amount (in moles) (how would you find mass g if needed)
n = PV ÷ RT · (molar mass of gas g ÷ 1 mole of gas)
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Find the (unknown) molar mass of a gas formula
n = PV ÷ RT · (given g of gas ÷ mol of gas found)
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How do you solve a gas stoichiometry problem
(Regular stoichiometry conversions) + (ideal gas law for the unknown value)
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Density of a gas formula
d = PM ÷ RT
- M is the molar mass of the gas
- R is 0.0821 · (L · atm ÷ mol · K)
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Mass g of a gas when given density formula
M = d · RT ÷ P
