Question

Dr. Russell keeps a desk in the chemical storeroom where he eats his lunch. During an earthquake, two chemicals spill inside a locked chemical cabinet in the storeroom. A large tub containing 17.2kg of sodium carbonate reacts with 4.00L of 12.0M hydrochloric acid when they completely mix after the spill. The cabinet is airtight and has dimensions of 1.00m tall by .500 meters wide, and .500 meters deep. The ambient temperature of the room is 23.5 C. The air pressure inside the cabinet was 758mmHg before the chemicals spilled. The chemical cabinet is designed to handle internal pressures up to 3.00 atm. Unfortunately, due to the poor design of this cabinet, at any pressure above 3.00 atm the cabinet shatters into metal pieces. Dr. Russell is safely outside the building, but realizes he left his bologna sandwich at his desk next to the cabinet.

Besides it not being very wise for Dr. Russell to eat in a chemical storeroom, is it safe for him to eat his lunch at his desk or will the cabinet explode? What is the pressure inside the cabinet after the two chemicals completely react? Assume the volume occupied by the bottles is negligible. (4pts) Explode? Y/N_____________ Answer_______________

Answer 1

Ans. Step 1.

Moles od Na2CO3 = Mass (in grams) / molar mass

                                    = 17200 g/ (105.988736 g/mol)                     ; [1 kg =1000 g]

                                    = 162.28 mol

Moles of HCl = Molarity x Volume (in L) of solution

                        = 12.0 M x 4.0 L

                        = (12.0 mol/L) x 4.0 L                                                  ; [1 M = 1mol/L]

                        = 48 mol

Reaction between HCl and Sodium carbonate-

            Na2CO3(s) + 2 HCl(aq) -------> 2 NaCl(aq) + H2O(l) + CO_2(g)

The only gaseous product of the reaction is CO₂. It’s assumed that the pressure developed inside the desk is solely due to CO₂.

Stoichiometry: 1 mol Na2CO3 reacts with 2 mol HCl produces to produce 1 mol CO2.

Liming reactant: Na2CO3: HCl in balanced reaction = 1: 2 by mol

Na2CO3: HCl as available amounts in desk = 162.28 : 48 = 1: 0.29 by mol.

Note, the (162.28 : 48) ratio is divided by 162.28 to get a ratio comparable to that of balanced reaction. Also note that, dividing a ratio by any factor does affect the ratio.

Compare the two ratio- balanced and in desk, moles of HCl is lesser than 2.0 whereas Na2CO3 is the same. Thus, HCl is the limiting reactant.

From stoichiometry: 2 mol HCl produces 1 mol CO2.

So,

            Moles of CO2 produced = (1/2) x mol of HCl

                                                = (1/2) x 48 mol

                                                = 24 mol.

Thus, total moles of CO2 produced during reaction = 24 mol.

Step 2: Volume of desk = l x b x h

                                    = 1.0 m x 0.5 m x 0.5m

                                    = 0.25m³

                                    = 250 L                                                ; [1 m³ = 1000 L]

Step 3: Using Ideal gas equation:     PV = nRT        - equation 1

            Where, P = pressure in atm

            V = volume in L                     

            n = number of moles

            R = universal gas constant= 0.0821 atm L mol^-1K^-1

            T = absolute temperature (in K)

Putting the values in above equation (for pressure generated by CO2 gas)-

            p x 250 L = 24 mol x (0.0821 atm L mol^-1K^-1) x 296.65 K

            or, p = 2.338 atm

Thus, pressure created by CO₂ = 2.338 atm.

Step 4. Conclusion:

Total pressure in the desk = Initial pressure + Pressure generated by CO2 formation

                                    = 0.99 atm + 2.338 atm                      ; [760 mm Hg = 1atm]

                                    = 3.328 atm

Since the total pressure (3.33 atm) inside the desk increase above threshold 3.0 atm, the desk will explode.