9/23/2015

Objective:
Determine the percent of NaHCO3 in a mixture by
Gasometry
Concepts:

Gasometric Determination
of NaHCO3
in a
Mixture

Stoichiometry
Gas Non-ideality
Henrys Law

Techniques:
Capture Gaseous Product
Determine Dissolved Gas

Vapor Pressure of Water

60

Vapor Pressure (mm Hg)

Limiting Reagents
Partial Pressure

50
40
30
20
10

Ideal Gas Law

Vapor Pressure

Determine System Volume

10

15

20

25

30

35

Temperature ( C)

(P+a/v2)(v b) = RT

40

Apparatus:
Gas Syringe
Balance

Thermometer
Cylinder

Barometer

Gasometry: An analytical technique which

depends on measuring an evolved gas.

The Exercise is Conceptually Simple

The unknowns, again, consist of a uniform
solid mixture of NaHCO3 and NaCl
1. Weigh Sample
2. Do Chemistry

Virtual Lab 1 Visible Spectroscopy

is due on the day that you perform this
exercise.

NaHCO3 reacts with HCl (aq) to liberate CO2(g)

NaCl does not react with HCl (aq)
So, the moles of CO2 should relate to NaHCO3 moles
3. Determine volume of liberated gaseous CO2
Measure gas volume to get moles of CO2
2

? QUESTIONS ?

The Basic Experimental Arrangement

Syringe

Can we determine the composition of a mixture by

measuring the amount of gas evolved when that
mixture undergoes a chemical reaction?

Patm
v

What principles and concerns do we use in

measuring the total amount of gas liberated?

nCO2 = P v / RT

What will limit the accuracy and precision of our

determination?
HCl
3

NaHCO3 / NaCl

9/23/2015

Accuracy and Reproducibility 2

Our Tentative Model

1. Weigh unknown sample

Capacity of syringe limits maximum weight of NaHCO3/unknown

< 60 mL means < 2.5 mmol CO2 max at Room Temp and 1 atm
That means 2.5 mmol NaHCO3 max
max weight of unknown @ 100% NaHCO3 = 2.5 X 84 = 168 mg
(can weigh up to 335 mg if unknown is 50% NaHCO3)

NaHCO3 reacts with,

HCl to liberate CO2

2. React unknown with HCl (aq)

a) NaHCO3 (s) + H+ (aq) Na+ (aq) + H2O (l) + CO2 (g)

b) NaCl(s)

Na+ (aq) + Cl- (aq)

NaCl dissolves, but does

not react with, HCl

For 50 mL of CO2, the weight range of unknown is 140 280 mg

Everyone does a trial run (< 200 mg) to determine weight
of unknown required to produce 40 10 mL of CO2

But, CO2 (g) + H2O (l) CO2 (aq) Some CO2 dissolves in water.
(HCl is mostly water.)

3. Capture and measure the volume of liberated gaseous CO2

Procedure requires unknown to be the limiting reagent

Unknown weight of ~200 mg determines analytical balance must be
used to weigh unknown if we want ~1 % accuracy.

DoMeasure
we need
to account
the dissolved
amount?
4.
Temperature
andfor
Atmospheric
Pressure
5. Use Ideal Gas Law, Patmv = nCO2RT, to calculate moles of CO2

This also determines minimum amount of 1.0 M HCl required

To insure that NaHCO3 is limiting for any unknown we must add
at least 2.5 mmol of HCl. For 1.0 M HCl, this means 2.5 mL

But, the Ideal Gas Law as written applies to one pure gas. We
have a mixture (there is air in our system).
PCO2v = nCO2RT

How do we measure PCO2?

10

How Much CO2 Dissolves in the HCl (aq)?

Some Questions
Intrinsic limitations of apparatus

Henrys Law: the partial pressure of a gas, Px, in equilibrium with

a solution of the gas at a given temperature, is proportional
to the concentration of the gas in the solution, Cx.

a. Balance, syringe, thermometer, barometer other apparatus?

Henrys Law

What could affect the accuracy & precision of our results?

1.

+ (aq)
NaHCO
(s) + H+add
(aq)10
H2O excess!
(l) + CO2 (g)
We3 actually
mLNa
which
is a+ large

2. Limitations due to our model

a.

And,

Can CO2 be treated as an ideal gas to adequate precision?

PCO2 = Patm ?

For CO2 and water at

room temperature,
KH = 3.2 X 10-2 mol/L-atm

PCO2 = nCO2 RT/vftot = 2.0 * 0.0821 * 298/140 ~ 0.35 atm

3. Limitations due to procedure/techniques

From Henrys Law, the concentration of CO2 in the water/HCl is

a. How do we insure that all of the NaHCO3 has reacted?

CCO2 = 3.2 X 10-2 * 0.35 = 0.011 M

b. How accurately do we need to know the sample weight?

10 mL of solution contains 0.011 * 10 = 0.1 mmol of CO2 which is

c. How do we insure that all of the CO2 has been captured?

8

Accuracy and Reproducibility 1

100 * 0.1 / 2 = 5% of the moles in the gas phase.

11

Accuracy and Reproducibility 3

Syringe:
Maximum capacity is 60 mL
Syringe can be read to 0.5 mL ( 1% precision at ~50 mL )

Can CO2 be treated as an Ideal Gas?

We can estimate the deviation from ideality by examining the van
der Waals constants.

Balance:
Which balance shall we use?
Depends on how much unknown we will weigh.

( P + n2a / v2 ) ( v nb ) = nRT

Top Loading Balance can be read to 0.01 g ( 10% at 0.1 g )

Analytical Balance can be read to 0.0001 g ( 0.1% at 0.1 g )

For CO2 at Room Temperature, the corrections to P and v are:

Barometer:
Can be read to 0.1 Torr ( 0.15% at 1 atm = 760 Torr )

CO2

( 0.8% at 25 oC ) ( 0.07% at 298 K )

Thermometer:
Can be read to 0.2 oC

a / v2

b / v

0.5%

0.2%

How does this compare with other corrections?

Tube Volume:
Assume 0.5 mL ( 0.6% at ~80 mL )
The Volume measurements have the least precision ~ 1%

KH is called the Henrys Law constant

nCO2l = CCO2 vl = KH PCO2 vl

In the typical lab setup, the total gas volume after the CO2 is
generated, vftot is ~ 140 mL. If we generate 2.0 mmol of CO2,
the partial pressure of CO2 at Room Temperature will be

b. Can we ignore the dissolved CO2?

c. Is

CCO2 = KH PCO2

12

9/23/2015

Accuracy and Reproducibility 4

NaHCO3 (s) +

H+

(aq)

Na+

Gas Mixtures Partial Pressure

Reaction is conducted in a closed system
at constant external pressure
- atmospheric ( P ~ 1 atm )
at constant temperature
- room temperature ( T ~ 25oC)

(aq) + H2O (l) + CO2 (g)

Reaction produces water.

1 mol NaHCO3 1 mol H2O
Still, considering pure NaHCO3,
(200 mg NaHCO3 = 2.4 mmol)
We produce at most 2.4 mmol of liquid H2O
Is this volume significant compared to the
~ 10 mL of HCl?
1 drop = 0.05 mL
2.4 mmol X 18 mg/mmol = 43 mg; Volume = 0.043 mL

Initially:
System contains air & water (HCl)
Pressure in system is potentially due to:
water (from HCl)
PH2O
the air in the system
Pair*
After reaction,
the liberated CO2

About 1 drop of water is produced ( 0.5% )

13

Patm

PH2O + Pair = Patm

PH2O, Pair*

and

PCO2

PH2O + Pair + PCO2 = Patm

* Pair includes the partial pressure of any HCl in the gas phase

16

What is the Magnitude of PH2O ?

The Apparatus More Detail

Vapor Pressure of Water

RIGHT
ANGLE
ELBOW

60
Vapor Pressure (mm Hg)

EXTENSION
CLAMP

PH2O is a
function of
Temperature

SYRINGE
LARGE
TEST
TUBE

20
10

10

15

20

25

30

35

40

Temperature (oC)

w mmol

w mmol

H2O (l)

556 mmol

556 + x mmol

HCl (aq)

10 mmol

10 x mmol

NaHCO3 (s)

x mmol

0 mmol

NaCl (s)

y mmol

0 mmol

NaCl (aq)

0 mmol

x + y mmol

CO2 (g)

0 mmol

x - z mmol

CO2 (aq)

0 mmol

z mmol

Over the range 20oC 30oC, PH2O increases from:

(0.023 to 0.042 atm)
17.5 to 31.8 mm Hg
2.3% to 4.2% for P ~1 atm

tot
PiH2O
H2O ,T, vi , nair
Piair

Final (mmol)

Air (g)

H2O/HCl (l)
Initially, we have
P = Piair + PH2O

17

PH2O, T, vftot, nair

nCO2g
Pfair, PfCO2
l
nCO2 H2O/HCl (l)
Finally, we have
P = Pfair + PH2O + PfCO2

Piair + PH2O = Pfair + PH2O + PfCO2

Pf

10 mL of 1.0 M HCl contains:

103 X
= +10
mmol
NaHCO
(s)1.0
+H
(aq)
+ Cl-HCl
(aq) Na+ (aq) + H2O (l) + CO2 (g) + Cl- (aq)
10 mL H2O = 10 g H2O
10 g = 10,000 mg / 18.0 mg/mmol
= 556 mmol H2O

30

What Substances are in the System?

Initial (mmol)

40

SMALL
TEST
14
TUBE

Species

50

CO2

= Piair Pfair = nair RT (1/vitot 1vftot)

But,

Piair = nair RT/vitot = P PH2O

So,

nair = (P - PH2O) vitot / RT

PfCO2g = [(P - PH2O) vitot / RT] (1/vitot 1/vftot) RT

15

PfCO2g = (P - PH2O) (1 vitot/vftot)

18

9/23/2015

Our Final Procedure

PfCO2g = (P - PH2O) (1 vitot/vftot)

nCO2g = PfCO2 vftot/RT = (P - PH2O) (1 vitot/vftot) vftot/RT

1. Measure volume of tube assembly, vtube

2. Weigh unknown sample, wsample (By difference!)

= (P - PH2O) (vftot vitot) /RT

Equation 3

nCO2g = (P - PH2O) (vfsyr - visyr) / RT

We have determined nCO2g

3. Measure Temperature and convert to Absolute, T

4. Look up Vapor Pressure of water, PH2O

We need nCO2l

5. Record Atmospheric Pressure, P

From the partial pressure of CO2, we can calculate nCO2l

using Henrys Law

6. Measure Initial Syringe Reading, visyr

7. React Unknown with 10.0 mL 1 M HCl (aq), vl

nCO2l = KH PfCO2 vl

8. Measure Final Syringe Reading, vfsyr

19

What are the various volumes in the exercise?

22

Our Final Model

1. Use ideal gas law to calculate moles of CO2 in gas phase
nCO2g = ( P PH2O ) ( vfsyr visyr ) / RT
2. From ideal gas law, Calculate PCO2

vitot & vftot: The gas phase* volumes

of the entire closed system before
& after the reaction.

PCO2 = nCO2g RT / ( vfsyr + vtube vl )

3. Use Henrys Law to calculate moles of CO2 in liquid phase
nCO2l = PCO2 KH vl
4. Calculate weight of NaHCO3 in sample

vitot = vtube + visyr vHCl

wNaHCO3 = ( nCO2g + nCO2l ) 84.01

vftot = vtube + vfsyr vHCl

5. Calculate % NaHCO3 in unknown

% NaHCO3 = 100 * wNaHCO3 / wsample

*We must exclude the volume of the liquid HCl ( 10 mL )

but we can ignore the initial solid unknown ( ~ 0.1 mL)

20

23

Calculations

Review
Assuming P and T do not change during a run.
Issue
Volume of H2O Produced

Affected
Variable

Effect
%

vl

~ 0.5

Volume Change of Unknown

vCO2g

~ 0.1

Non -Ideality of CO2

PCO2

~ 0.5

Vapor Pressure of Water

PCO2

~ 3.0

nCO2tot

~ 5.0

Solubility of CO2

If we seek accuracy to within 1%

in the % NaHCO3

Final Small Test Tube

15.7488 g
Initial Small Test Tube
15.5341 g
Weight of Sample
0.2147 g
Volume of HCl
10.0 mL
100.0 mL
Tube Volume, Vtube
Initial Syringe
5.0 mL
Final Syringe
50.7 mL
Volume of gaseous CO2, v
45.7 mL
Pressure,
P = 752 mm Hg =
0.989 atm
296.4 K
Temperature, T = 23.3 oC =
PH2O@ 23.3oC (from Table) 21.9 mm Hg 0.028 atm

21

mmol CO2 (gas)

= (P - PH2O) v / RT
mmol CO2 (liquid) (Henrys Law)
0.10 mmo1 mmol

1.81 mmol
???

24

9/23/2015

To calculate the Henrys Law correction, we need the

partial pressure of CO2 & the final total gas volume, vftot
The final gas volume is,
vftot = 100.0 - 10.0 + 50.7
= 140.7 mL
PCO2 = nCO2g R T / vftot
= ( 1.81 * 0.0821 * 296 ) / 140.7)
= 0.312 atm
Henrys Law gives us the CO2 concentration:
cCO2 = 3.2 X 10-2 mol/L-atm * 0.312 atm = 0.010 M
which in 10.0 mL of water/HCl contains
nCO2l = 10.0 mL * 0.010 mmol/mL = 0.10 mmol

25

Calculations
Weight of Sample
0.2147 g
Volume of gaseous CO2 v
45.7 mL
Pressure,
P = 752 mm Hg =
0.989 atm
296 K
Temperature, T = 23oC =
PH2O@ 23oC (from Table) 21 mm Hg 0.028 atm
mmol CO2 (gas) = (P - PH2O) v / RT
mmol CO2 (liquid) (Henrys Law)

1.81 mmol
0.10 mmol

Total CO2

1.91 mmol

mmol NaHCO3 (from stoichiometry)

Weight of NaHCO3 1.91 X 84.0

1.91 mmol
0.160 g

% NaHCO3 = 100 X 0.160 / 0.2147 = 74.5 %

26

Procedure - Notes
Everyone should weigh ~ 200 mg = 0.2 g
ACCURATELY for their trial run
Depending on your sample, you must adjust the
weight in subsequent runs to insure that you get
between 35 and 50 mL of CO2, but not more than
50 mL. (Check before doing the run!)
Test that system is air-tight before using
Set syringe at 5.0 mL initially read to 0.5 mL
remember to subtract initial from final volume
Do test run - then up to 4 which you report.
27