Transcript Gases and the Mole

Gases and the Mole
Gay-Lussac’s Observations
“Under constant conditions, the volumes of
reacting gases and gaseous products are in
the ratio of small whole numbers.”
5 L of H2 react with 2.5 L of O2 to produce
5 L of H2O
Ratio = ?
2:1:2
Avogadro’s Hypothesis
“Under the same conditions of temperature
and pressure, equal volumes of all gases
contain equal numbers of particles.”
H-H
XX
H-H
XX
H-H
XX
2H2
H-H
XX
H-H
XX
H-H
XX
+
+
O-O
X
X
O-O
X
X
O-O
X
X
O2


H 2O
H 2O
H 2O
H 2O
H 2O
H 2O
2H2O
Molar Volume of Gases
Gas densities measured at STP:
CO2 = 1.96 g/dm3
D = M / V V = M / D
CO2
V = 44 g/mol = 22.4 L/mol
1.96 g/L
You calculate the molar volume of H2 and O2
H2 = 0.0893 g/dm3
O2 = 1.429 g/dm3
The Molar Volume Concept
One mole of any gas measured at STP will
occupy a volume of 22.4 L
11.2 L x 1mol / 22.4 L = 0.5 mol
3 mol x 22.4 L / 1mol = 67.2 L
What is the density of neon gas at STP?
D = m/V
D = 20 g/mol ÷ 22.4 L/mol
D = 0.893 g/L
The Ideal Gas Equation
The combined gas law:
PV = KT
The value of the constant (K) depends on the
number of mols (n) of gas in the sample.
Kn
 PV  nT
Adding a proportionality constant (R)…
PV = nRT
The Gas Constant (R)
R is the “universal” gas constant
PV = nRT
Solve the equation for the gas constant (R)
R = PV
nT
To determine the value of R, we need a situation where
all of the other values are known. ???
The molar volume concept!!!
The Value of R
The molar volume concept:
1 mol of any gas measured at STP will occupy a
volume of 22.4 L
R = PV / nT
P=
V=
n=
T=
101.3 kPa
22.4 L
1 mol
273 K
R = (101.3 kPa) (22.4 L)
(1 mol) (273 K)
R=
8.31 kPa L
mol K
An Equation of “State”
Boyle’s Law, Charles’s Law, etc. all involve
changing conditions.
No conditions are changing in the Ideal Gas
Law.
The Ideal Gas Law describes the state of the
system.
If 3 of the conditions are known, the other
condition may be calculated.
Solve the Ideal Gas equation for each of the
variables
PV = nRT
P=
nRT/V
V=
nRT/P
n=
(PV)/(RT)
T=
(PV)/(nR)
Equations you need to know
Combined gas law:
P1V1 / T1 = P2V2 / T2
Graham’s law:
VA / VB = √mB / mA
Dalton’s law:
Pt = P1 + P2 + …. Pn
Ideal gas equation:
PV = nRT
Calculating Moles
63 grams of H2O contains how many moles of
water?
63 g x 1 mol = 3.5 mol H2O
18 g
If:
n = mols
m = mass
M = molecular mass
Then: n = m/M
Calculating Molecular Mass
In the Ideal Gas equation (PV = nRT), n is
equal to the number mols of gas.
The number of mols can be found by dividing
the sample mass by the molecular mass.
n = m/M
PV = mRT
M
M=?
M = (mRT) / PV
Calculating Gas Density
PV = nRT
PV = mRT
M
D = m
V
D = m = PM
V RT
Gas Stoichiometry
What volume of hydrogen at STP can be produced
when 8.37 g of zinc reacts with hydrochloric acid?
a. Write the balanced equation.
b. Calculate the number of moles of Zn
c. Determine the moles of hydrogen produced
d. Calculate the volume of hydrogen
The Solution
a. Write the equation
8.37g ?dm3
2 HCl + Zn  H2 + ZnCl2
b. Convert grams to moles
8.37 g Zn x 1mol / 65.5 g = 0.128 mol Zn
c. Determine the moles of hydrogen
0.128 mol Zn x 1mol H2/1mol Zn = 0.128 mol H2
d1. Calculate the volume of H2 gas
PV = nRT
 V = nRT / P
V = (0.128)(8.31)(273) / 101.3
V = 2.87 dm3
d2. 0.128 mol x 22.4 dm3 / 1 mol
V = 2.87 dm3
Your Turn
Ammonium nitrite decomposes when heated to form nitrogen
gas and water vapor. When a sample of ammonium nitrite is
decomposed, 511 cm3 of nitrogen is collected over water at
26oC and 745 torr total pressure. How many grams of
ammonium nitrite were decomposed? The vapor pressure of
water at 26oC is 3.4 kPa.
a.
b.
c.
d.
Write the balanced equation.
Calculate the number of moles of N2
Determine the moles of NH4NO2 produced
Calculate the mass of NH4NO2
Cubic Conversions
1m
10 dm
1m
1m
10 dm
10 dm
1 m3 =
1000 dm3