Boyle's Law
V  1/P
P₁V₁ = P₂V₂ (n,T constant)
PV = constant
1 atm = 760 mm Hg = 760 torr

Volume-Pressure Data:

V(mL)	100	50	25	20	10	5.0	2.0	1.0
P(atm)	1.0	2.0	4.0	5.0	10	20	50	100

Boyle's Law Example
If 75.0mL at 2.50 atm, calculate volume at 2550 torr.
P₁ = 2.50 atm
V₁ = 75.0 mL
P₂ = 2550 torr = 2550/760 atm = 3.36 atm
V₂ = ?

V₂ = (P₁V₁)/P₂
     = (2.50atm)(75.0mL)/3.36atm) = 55.8 mL
 
 

Charles' Law
V  T
V₁T₂ = V₂T₁ (n,P constant)
Temperature convenient way to measure kinetic energy.
Absolute zero (0 K) when all KE removed.
Must use Kelvin temperature scale (K = ºC + 273)
0 K = 273ºC  (absolute zero)

Charles' Law Example
If 250 mL of gas at 50ºC, calculate volume at -50ºC.
V₁ = 250 mL
T₁= 50ºC =323K
T₂ = -50ºC =223K
V₂ = ?
V₂ = (V₁T₂)/T₁ = (250mL)(223K)/323K) = 173 mL
 
 

Amontons' Law
P  T
P₁T₂ = P₂T₁ (n,V constant)
Must use Kelvin temperature scale

Amonton's Law Example
If pressure 1.75atm at 25ºC, calculate temperature (ºC) when pressure 3.25atm.
P₁ = 1.75 atm
T₁= 25ºC =298K
P₂ = 3.25 atm
T₂ = ?ºC

T₂ = (P₂T₁)/P₁ = (3.25atm)(298K)/1.75atm) = 553K = 280ºC
 

Avogadro's Law
V n
V₁n₂ = V₂n₁ (T,P constant)
Gases at same P,V,T contain same number of molecules
1.0 mol of any gas at STP (273K & 1.00 atm) occupies 22.4L

Avogadro's Law Example
If 3.50 mol of gas occupy 125mL, calculate volume for 4.85 mol.
n₁ = 3.50 mol
V₁= 125 mL
n₂ = 4.85 mol
V₂ = ?
V₂ = (V₁n₂)/n₁ = (125 mL)(4.85 mol)/3.50 mol) = 173 mL
 
 

General Gas Law
[P₁V₁/n₁T₁] = [P₂V₂/n₂T₂]

At constant n & T, General Gas Law becomes Boyle's Law.
At constant n & P, General Gas Law becomes Charles' Law.
At constant V & n, General Gas Law becomes Amonton's Law.
At constant P & T, General Gas Law becomes Avogadro's Law.

General Gas Law Example
If 250 mL of gas at 35ºC and 1.55 atm, calculate volume at STP (273K & 1.00 atm).
V₁ = 250 mL
T₁= 35ºC = 308K
P₁ = 1.55 atm
T₂= 273K
P₂ = 1.00 atm
V₂ = ?

P₁V₁/n₁T₁ = P₂V₂/n₂T₂      (n₁ = n₂)

V₂ = P₁V₁T₂ / P₂T₁
     = (1.55atm)(250mL)(273K)/(1.00atm)(308K) = 343mL
 
 

Ideal Gas Law
V  T
V  1/P
V n

V  nT/P
V = nRT/P
PV = nRT     R = 0.0821 atm-L/mol-K

Ideal Gas Example 1
Calculate volume 7.00g of nitrogen (N₂) occupies at 127º C and 4.10 atm.
n = 7/28 = 0.25 mol
T = 127 + 273 = 400K
P = 4.10 atm
V = nRT/P
      = (0.25 mol)(0.0821 atm-L/mol-K)(400K)/(4.10atm)
    = 2.0L
 

Ideal Gas Example 2
Calculate molar mass (M) if 10.4g of gas occupies 2.00L at 300K and 1.50atm.
PV = nRT = mRT/M         n = m/M    n=mass   M=molar mass
M = mRT/PV
    = (10.4g)(0.0821 atm-L/mol-K)(300K)/(2.00L)(1.50atm)
      = 85g/mol
 
 

Ideal Gas Example 3
Calculate density for CH₄ gas at STP.
PV = mRT/M         d = m/V   m=mass  M=molar mass
   d = MP/RT
     = [(16.0g/mol)(1.00atm)] / [(0.0821 atm-L/mol-K)(273K)]
    = 0.714 g/L
 
 

Stoichiometry
To express mol for pure substance, solution, gas:
   n = m/mm      n = M^.L      n = PV/RT
 ^{pure substance         solution                 gas}

Stoichiometry Example #1
2KClO_3(s)    2KCl_(s)  +  3O_2(g)
Calculate volume of O₂ produced at STP if 25.0g KClO₃ react.
3 mol KClO₃ = 2 mol O₂
(3)(m/mm) = PV/RT         m=mass  mm=molar mass
(3)(25/122) = (2)(1.00)(V)/(.0821)(273)
V = 6.89L

Stoichiometry Example #2
2HCl_(aq)  +  Na₂CO_3(s)   2NaCl_(aq)  +  H₂O_(l)  +  CO_2(g)
Calculate volume of CO₂ produced at 300K and 2.50atm if
45.0 mL of 3.00M HCl allowed to react with excess Na₂CO₃.
mol HCl = 2 mol CO₂
M L = 2PV/RT
(3.00)(.0450) = 2(2.50)(V)/(.0821)(300)
V = 0.665L

Stoichiometry Example #3
CaSO_3(s)   CaO_(s) + SO_2(g)
Calculate mass CaSO₃ needed to produce 5.00L SO₂ at 350K and 1.50atm.
mol CaSO₃ = mol SO₂
(m/mm) = PV/RT
(m/120) = (1.50)(5.00)/(.0821)(350)
m = 31.3g
 

Partial Pressure
 P_A = n_ART/V     P_A = X_AP_T      X_A = n_A/[n_A + n_B]

Partial Pressure Example #1
Container with total pressure of 6.00atm possesses
1.00 mol A
2.00 mol B
3.00 mol C
What is partial pressure of each gas?

P_A = X_AP_T = (1/6)(6.00atm) = 1.00atm
P_B = X_BP_T = (2/6)(6.00atm) = 2.00atm
P_C = X_CP_T = (3/6)(6.00atm) = 3.00atm

Partial Pressure Example #2
Container with total pressure of 10.0atm possesses:
64.0g O₂= 2.00 mol O₂
20.0g He = 5.00 mol He
44.0g CO₂ = 1.00 mol CO₂
What is partial pressure of each gas?
P_O2 = X_O2P_T = (2/8)(10.0atm) = 2.50 atm
P_He = X_HeP_T = (5/8)(10.0atm) = 6.25 atm
P_CO2 = X_CO2P_T = (1/8)(10.0atm) = 1.25 atm