In this exercise, weighed samples of a solid unknown containing NaCl and NaHCO 3

Question

In this exercise, weighed samples of a solid unknown containing NaCl and NaHCO3react 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 CO2will 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 entire system gas volume in addition to the initial and final syringe readings.   

The entire system gas volume is the sum of the quantities labeled Vtube and Vsyr in the diagram below, corrected for the liquid volume (the aqueous HCl).

The table below contains the data collected in one run of the reaction between an unknown and hydrochloric acid:

Initial Weight of container and unknown

Torr

The following questions deal with the above data. The appropriate units are specified in the questions. Pay close attention to the number of significant figures in your answers.

1). What is the volume of CO2 captured in the gas phase (in mL)?

2).What is the number of mmols of CO2 captured in the gas phase? (Remember to account for the vapor pressure of water.)

3). What is the weight of the sample in grams?

Value Units Gas Constant 0.0821 L-atm/mol K Absolute Zero (0 K) -273.15 oC Atmosphere 760.0 Torr Molar Mass of NaHCO3 84.01 g/mol Henry's Law Constant for CO2in water 3.2 X 10-2 mol/L-atm

Explanation / Answer

Part 1 : Volume of CO2 captured in the gas phase.

This can be calculated using initial and final volume of syringe.

The volume of syringe changes, because the gas that gets liberated during the reaction gets captured in it.

Volume of CO2 captured in gas phase : Final volume of syring - Initial volume of syringe

Volume of CO2 captured in gas phase = 50.7 mL = 5.0 mL = 45.7 mL

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Part 2

mmols of CO2 in gas phase.

For this we will use ideal gas law, PV = nRT

Because the gas is getting evolved in presence of aqueous medium,

the total pressure P(t) is the partial pressure of CO2 gas and the vapor pressure of water

P(t) = P (CO2) + P (H2O)

764.4 torr = P(CO2) + 25.8 torr

P(CO2) = 738.6 torr

Let's convert this to atm

738.6 torr * 1 atm/760 torr = 0.9718 atm

PV = nRT , where we have

P = 0.9718 atm

V = 45.7 mL ( we want mmol , so we will keep unit of volume as mL)

R, Gas constant = 0.0821 L-atm/mol K

T = 26.5 C = 26.5 + 273.5 = 299.65 K .

Let's plug in the values

0.9718 atm * 45.7 mL = n * 0.0821 L-atm/mol K * 299.65 K

n = 0.9718 * 45.7 / 0.0821 * 299.65

n = 1.805 mmol

mmol of CO2 captured in gas phase = 1.805 mmol

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Part 3

We need to find total mmols of CO2 which would be mmol in gas phase and mmol in dissolved aqueous medium

To find mmol in dissolved aq. medium, we will be using Henry's law

At this point we have to consider the total volume that the gas will occupy which will include the volume of syringe and the empty volume inside the tube.

Let's find V(t) total volume occupied by the gas

V(t) = volume occupied in syringe + volume of glass tube

V(t) = 45.7 mL + 92.3 mL

V(t) = 138 mL

Since the total volume occupied by gas is changed, it will also change partial pressure of CO2

New partial pressure of CO2 for V(t) can be calculated using ideal gas equation again.

We have V(t) = 138 mL

n = 1.805 mmol

T = 299.65 K

R = 0.0821 L-atm/mol K

P = nRT/V(t)

P = 1.805 mmol * 0.0821 L-atm/mol K * 299.65 K/ 138 mL

P(CO2) = 0.322 atm

Concentration of CO2 in dissolved state can be calculated as

C (CO2) = P (CO2) * H .................... H is Henry's constant for CO2

C (CO2) = 0.322 atm * 3.2 x 10^-2 mol/L-atm

C (CO2) = 0.0103 mol/L

But the volume HCl we have is 10 mL

mol of CO2 in dissolved state = 0.0103 mol/L * 1 L/1000 mL * 10 mL = 1.03 x 0^-4 mol

1.03 x 10^-4 mol * 1000 mmol/ 1 mol = 0.103 mmol

mmol of CO2 in dissolved state = 0.103 mmol

Total mmols of CO2 = mmol of CO2 in dissolved state + mmol of CO2 captured as gas

Total mmols of CO2 = 0.103 mmol + 1.805 mmol

Total mmols of CO2 = 1.908 mmol

1.908 mmol * 1 mol/1000 mmol = 0.001908 mol

Let's write the reaction that is responsible for formation of CO2

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

Using mol ratio, we can find moles of NaHCO3

0.001908 mol CO2 * 1 mol NaHCO3/ 1 mol CO2 = 0.001908 mol NaHCO3

0.001908 mol NaHCO3 * 84.01 g/mol = 0.1603 g

Mass of NaHCO3 in the sample is 0.1603

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