Gases Chemistry Worksheet - Chapter 13, An Introduction To Chemistry Page 21
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13.2 Equation Stoichiometry and Ideal Gases
There are several ways to convert between moles of a gaseous substance and its
volume. One approach is to use as a conversion factor the molar volume at STP. STP
stands for “standard temperature and pressure.” Standard temperature is 0 °C, or 273.15
K, and standard pressure is 1 atm, or 101.325 kPa, or 760 mmHg. The molar volume,
or liters per mole of an ideal gas, at STP can be calculated from the ideal gas equation.
PV = nRT
8.3145 L kPa
(273.15 K)
V
RT
22.414 L
K mol
=
=
=
n
P
101.325 kPa
1 mol
STP
Because the ideal gas equation applies to all ideal gases, the molar volume at STP
applies to all gases that exhibit the characteristics of the ideal gas model. In equation
stoichiometry, the molar volume at STP is used in much the way we use molar mass.
Molar mass converts between moles and the measurable property of mass; molar
volume at STP converts between moles and the measurable property of volume of gas.
Note that while every substance has a different molar mass, all ideal gases have the same
molar volume at STP. Example 13.5 provides a demonstration.
e
13.5 - Gas Stoichiometry
xample
How many liters of carbon dioxide at STP will be formed from the complete combustion
O
19
bjeCtive
of 82.60 g of ethanol, C
H
OH(l )?
2
5
Solution
Because we are converting from units of one substance to units of another substance,
both involved in a chemical reaction, we recognize this problem as an equation
stoichiometry problem. We can therefore use unit analysis for our calculation.
Equation stoichiometry problems have at their core the conversion of moles of one
substance to moles of another substance. The conversion factor that accomplishes this
part of the calculation comes from the coefficients in the balanced equation. Although
we have not been given the balanced equation for the combustion of ethanol, we
can supply it ourselves by remembering that when a hydrocarbon compound burns
completely, all its carbon forms carbon dioxide, and all its hydrogen forms water.
OH(l ) + 3O
(g) → 2CO
(g) + 3H
C
H
O(l )
2
5
2
2
2
First, however, we convert from mass of C
H
OH to moles, using the compound’s
2
5
molar mass. Then we set up the mole-to-mole conversion, using the molar ratio of
ethanol to carbon dioxide derived from the coefficients in the balanced equation. The
next step is the new one; we use the molar volume at STP to convert from moles of
CO
to volume of CO
at STP. The sequence as a whole is
2
2
OH → moles C
OH → moles CO
→ volume of CO
Mass C
H
H
at STP
2
5
2
5
2
2
1 mol C
H
OH
2 mol CO
22.414 L CO
2
5
2
2
= 82.60 g C
H
OH
? L CO
2
5
2
46.0692 g C
H
OH
1 mol C
H
OH
1 mol CO
2
5
2
5
2
STP
= 80.37 L CO
2
The molar volume at STP—22.414 L/mol—is useful for conversions as long as the
gases are at 0 °C and 1 atm of pressure. When the temperature or pressure changes,
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