Question

n this exercise, weighed samples of a solid unknown containing NaCl and NaHCO3 react with hydrochloric acid. The volume of the CO2 liberated by the reaction in the gas phase is measured with a gas collection syringe. From the volume we can calculate the number of moles of CO2 in the gas phase using the ideal gas approximation.

Since the CO2 is generated in an aqueous environment (aqueous HCl), some CO2 will dissolve in the liquid phase. The amount of CO2 dissolved in the liquid phase is computed using Henry's Law which requires knowing the partial pressure of CO2. As described in the exercise, this requires knowing the volume of the entire gas system ( VfTOT)

To insure that your answers agree with Mr. OSCER's, use the values in the below table for the basic constants required. .

	Value	Units
Ideal Gas Constant	0.0821	L-atm/mol K
Convert Celsius temperture to Kelvin	273.15	K
Atmospheric Pressure	760.0	Torr
Molar Mass of NaHCO3	84.01	g/mol
Henry's Law Constant for CO2 in water	3.2 X 10-2	mmol/mL-atm

The figure below illustrates the volumes that are designated by Vtube and Vsyr .

Note also that Vsyr = Vf – Vi .

The table below contains data collected for one run of the required reaction, where an unknown sample mixture containing some NaHCO3 is mixed with hydrochloric acid:

	Value	Units
Initial Weight of container (empty)	18.4395	g
Final Weight of container and unknown	18.6185	g
Volume of hydrochloric acid	10.0	mL
Volume of tube, Vtube (see Figure above)	92.3	mL
Initial volume of syringe   (Vi)	5.0	mL
Final volume of syringe (Vf)	50.7	mL
Temperature	26.5	oC
Atmospheric Pressure	764.4	Torr
Vapor Pressure of Water at 26.5 oC	25.8	Torr

Use this data to answer the following questions. The appropriate units are specified in the each question. Pay close attention to the number of significant figures in your answers.

weight of sample (g) mixture before the start of the reaction = .179 g. Volume of CO2 gas (mL) that is produced by the reaction and is now contained in the syringe= 45.7 mL

1.

What mass (g) of NaHCO₃ was contained in the sample mixture that was mixed with HCl ?

Enter a numeric answer only, to the correct number of significant figures. Do not include units with your answer.

Answer 1

First write the balanced chemical reaction of NaHCO₃ reacting with HCl to give CO₂ and NaCl

NaHCO₃ + HCl ------------> CO₂ + NaCl + H₂O

So, 1 mole of NaHCO₃ will give 1 mole of  CO₂ .

Now, we have to convert the pressure from Torr to atm as units are in atm

1 atm =760 Torr

Now 45.7 mL of CO₂ is contained in syringe. So, we have to convert this to number of moles of CO₂

Using gas law, we have to convert gas produced at 26.5 degree to 25 degree (STP)

V₁/T₁ =V2/T2

So, we have

45.7/(273.15+26.5)= x/ (273.15+25)

X= 45.47 mL

Now, 1 mole of gas at STP occupies 22.4 L

Therefore number of moles of CO₂ = 45.47*10^-3/22.4 moles

=0.002 moles

Using Henry's law we get

S= K_H p

where p is the pressure of CO₂, K_H is Henry's constant and s is the solubility of the gas

From ideal gas law,

PV=nRT

P= nRT/V = .002*0.0821* 299.65/ 45.7*10^-3

P= 1.07 atm

Applying Henry's law

s=1.07 *3.2*10^-2

s= 0.034 moles / L Volume of liquid =10 ml= 0.001 L

So, amount of gas dissolved =0.001* 0.034 =0.000034 moles

Total number of moles of CO₂ = 0.002+ 0.000034 = 0.002034 moles

So 1 mole of CO₂ gives 1 mole NaHCO₃.

Number of moles of NaHCO₃ = 0.002034

weight of NaHCO₃. = 0.002034*84 = 0.170856 = 0.171g

So answer is 0.171