Question

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. What is the volume of CO_2 captured in the gas phase (in mL)? What is the number of mmols of CO_2 captured in the gas phase? (Remember to account for the vapor pressure of water.) What is the weight of the sample in grams? What weight of sample (in grams) would be required to produce 35. mL CO_2 (g)? What weight of sample (in grams) that would be required to produce 55. mL CO_2 (g)? When the CO_2 has been completely collected, what is the partial pressure (in atm) of CO_2 (P_CO2) in the system? Assuming the liquid phase (aqueous HCl) is primarily water, what is the concentration (in mol/L) of CO_2 in the liquid phase assuming Henry's Law (concentration is proportional to partial pressure)? What is the number of mmol of CO_2 in the liquid phase?

The set up:

In 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 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 V_tube and V_syr in the diagram below, corrected for the liquid volume (the aqueous HCl).

Answer 1

Considering that water is in equilibrium, its partial pressure in the gas phase is 13.2 Torr. Since the total pressure is the sum of the partial pressures, The CO₂ pressure can be calculated as the difference:

p_CO2 = 760 Torr - 13.2 Torr = 746.8 Torr

Now, using the ideal gas approximation, the number of moles is given by:

746.8T orr * Atm * 0.1226L -= 0.00509 = 5.09mmoles 0.082 Atm * 288.6K

Torr have been converted to Atm and mL to L (total volume = syringe + tube - solution).

The weight of the sample is given by the difference between the final mass of container + unknown and its initial mass:

18.8279 g - 18.6239 g = 0.204 g

Considering the stoichiometry of the reaction is a fixed relation, we can use cross multiplication to calculate the mass needed to produce 35 mL of CO₂, since we know the mass we needed to produce 47.4 mL:

0.2049 m = 35mL* = 0.1519 47.4mL

Same idea for calculating the needed mass for 55 mL:

0.2049 m = 55mL * = 0.2379 47.4mL

The partial pressure of CO₂ was already calculated: 746.8 Torr. In Atm:

1 Atm 746.8T orr * - = 0.983 Atm 760Torr

To calculate the amount of dissolved CO₂ we need the value of Henry's constant at 15.6 °C. If this value is provided to you, the calculation would be simply.

C = K_H * p

If we consider K_H at that temperature with a value of 4.55x10^-4 mol/m³Pa (approximate value):

C = 4.55x10^-4 mol/m³Pa * 0.983 Atm * 101350 Pa/1 Atm * 1 m³/1000 L = 0.045 M

And the number of mmoles can be calculate taking into account the total liquid volume:

0.04549 *0.01L = 0.00045moles = 0.45mmoles