![Page 1: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/1.jpg)
Aula #04
![Page 2: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/2.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
![Page 3: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/3.jpg)
Gases…
V a TCharles’ & Gay-Lussac’s Law
FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds for O2.
![Page 4: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/4.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
![Page 5: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/5.jpg)
Gases…
Ideal Gas Equation
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
Boyle’s law: V a (at constant n and T)1
P
V anTP
V = constant x = RnT
P
nT
P
R is the gas constant
PV = n RT
![Page 6: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/6.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
0.082057338(47) L atm K−1 mol−1
![Page 7: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/7.jpg)
Gases…
R is the gas constantPV = n RT
The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).
Pressão e temperatura normais (PTN)
R = PV
nT=
(1 atm)(22.414L)
(1 mol)(273.15 K)
R = 0.082057 (L .atm) / (mol • K)
Experiments show that at STP,
1 mole of an ideal gas occupies 22.414 L.
R = 8.314 L JK-1mol -1)
![Page 8: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/8.jpg)
Gases…
A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?
V1 = 3.20 L
T1 = 398.15 K
V2 = 1.54 L
T2 = ?
T2 = V2 x T1
V1
1.54 L x 398.15 K3.20 L
= = 192 K
V1 /T1 = V2 /T2
T1 = 125 (0C) + 273.15 (K) = 398.15 K
T2 = 192 (K) - 273.15 (K) = - 81 0C
![Page 9: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/9.jpg)
Gases…
R is the gas constantPV = n RTSI ... 8.3144598(48) J⋅mol−1⋅K−1
What is the volume (in liters) occupied by 49.8 g of HCl at 1.00 bar and T=0 oC ?
PV = nRT
T = 0 0C = 273.15 K
P = 1.00 bar = 1.00x105 Pa n = 49.8 g x 1 mol HCl
36.45 g HCl= 1.37 mol
V =1.00x105 (Pa)
1.37 (mol) x 8.31446 (J.mol-1K-1) x 273.15 (K)= 0.0311 m3 = 31.1 L
![Page 10: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/10.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume.
What is the final pressure of argon in the lightbulb (in atm)?
PV = nRT n, V and R are constant
nR
V=
P
T= constant
P1
T1
P2
T2=
P1 = 1.20 bar
T1 = 291 K
P2 = ?
T2 = 358 K
P2 = P1 x T2
T1
= 1.20 bar x 358 K291 K
= 1.48 bar
![Page 11: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/11.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
Density (d) Calculations
d = mV
=PMRT
m is the mass of the gas in g
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
dRT
PM = d is the density of the gas in g/L
n = m/M
![Page 12: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/12.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
Molar Mass (M ) of a Gaseous Substance
dRT
PM = d is the density of the gas in g/L
A 2.10 L vessel contains 4.65 g of a gas at 1.00 bar and 27.0 0C. What is the molar mass of the gas?
d = mV
4.65 g
2.10 L= = 2.21 g/L
M =
2.21g
L
1 bar
x 8.3145 x 300.15 K= 55.2 g/mol
![Page 13: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/13.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
He (g) Ar (g)
![Page 14: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/14.jpg)
Gases…
T= 290 K, V= 5 dm3
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
T= 290 K, V= 5 dm3T= 70 K, V= 1 dm3
Lets ask the nature !!
![Page 15: Aula #04 - moodle.up.pt · Gases… Charles’ & Gay-Lussac’s Law V aT FIGURE Distribution of molecular speeds for different gases at 25°C. FIGURE Distribution of molecular speeds](https://reader034.vdocuments.us/reader034/viewer/2022042303/5ecef3de20b7c35e7901842a/html5/thumbnails/15.jpg)
Gases…
R is the gas constant
PV = n RT
SI ... 8.3144598(48) J⋅mol−1⋅K−1
PVT…equation of state
PV = n RT Ideal Gas Lawvan der Waals …equation of stateReal behaviour