Question

-3.39. 600 L of a gas mixture (containing hydrogen, carbon dioxide and nitrogen; t = 20 °C, p = 101 325 Pa) was introduced into 3 L of a 20 % NaOH solution (p = 1.43 g/mL). The carbon dioxide was absorbed whereas hydrogen and nitrogen bubbled through without any reaction. The produced sodium hydrogen carbonate was filtered out and a remaining NaOH solution was titrated with a 10 % H2SO4 solution (p = 1.07 g/mL, M=98 g/mol). Calculate the mole fraction of CO2 in the gaseous mixture when 5.25 mL of the H2SO4 solution were used for the titration. CO2 + NaOH — NaHCO3 2 NaOH+H2SO4 + Na2SO4 + 2H2O

Answer 1

The main answer to the question is to calculate the mole fraction of CO2 in the gaseous mixture.

Here's a step-by-step explanation to solve the problem:

1. Calculate the number of moles of NaOH used in the reaction:
- Given that the density of the NaOH solution is 1.43 g/mL and you used 3 L, you can calculate the mass of NaOH used: mass = volume * density = 3 L * 1.43 g/mL = 4.29 g
- The molar mass of NaOH is 40 g/mol, so the number of moles of NaOH used is: moles = mass / molar mass = 4.29 g / 40 g/mol = 0.10725 mol

2. From the balanced equation, you can see that 1 mole of CO2 reacts with 2 moles of NaOH. Therefore, the number of moles of CO2 produced is half of the moles of NaOH used: moles of CO2 = 0.10725 mol / 2 = 0.05363 mol

3. Now, calculate the volume of the H2SO4 solution used in the titration:
- Given that the density of the H2SO4 solution is 1.07 g/mL and you used 5.25 mL, you can calculate the mass of H2SO4 used: mass = volume * density = 5.25 mL * 1.07 g/mL = 5.6175 g
- The molar mass of H2SO4 is 98 g/mol, so the number of moles of H2SO4 used is: moles = mass / molar mass = 5.6175 g / 98 g/mol = 0.05728 mol

4. From the balanced equation, you can see that 1 mole of H2SO4 reacts with 1 mole of NaOH. Therefore, the number of moles of NaOH remaining after the reaction is equal to the moles of H2SO4 used: moles of NaOH remaining = 0.05728 mol

5. The mole fraction of CO2 in the gaseous mixture can be calculated using the following formula:
Mole fraction of CO2 = moles of CO2 / total moles of gases in the mixture
- To find the total moles of gases in the mixture, we need to know the moles of hydrogen and nitrogen that bubbled through without any reaction. Unfortunately, the question does not provide this information, so we cannot calculate the exact mole fraction of CO2.

In conclusion, the mole fraction of CO2 in the gaseous mixture cannot be calculated without knowing the moles of hydrogen and nitrogen.