Sodium carbonate, Na₂CO₃(s), may be prepared by heating sodium bicarbonate, NaHCO₃(s). 2NaHCO₃(s) Na₂CO₃(s) + CO₂(g) + H₂O(g) K_P = 0.23 at 100ºC If a sample of NaHCO₃ is placed in an evacuated flask and allowed to achieve equilibrium at 100ºC, what will the total gas pressure be?

Question

Quizplus · Accepted Answer

The balanced equation for the reaction is: 2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(g) The equilibrium constant, K, is given as 0.23. This means that at equilibrium, the concentration of the products will be 0.23 times higher than the concentration of the reactants. We can use this information to set up an ICE table: | | NaHCO₃(s) | CO₂(g) | H₂O(g) | |--------|-------------------|------------------|------------------| | Initial | 1 | 0 | 0 | | Change | -2 | +1 | +1 | | Equil. | 0 | 1 | 1 | From the ICE table, we can see that at equilibrium, the pressure of CO₂(g) and H₂O(g) will both be equal to 1 atm. Therefore, the total gas pressure will be 2 atm. However, we need to take into account that the question asks for the pressure at 100ºC, which is not at standard temperature and pressure (STP, 0ºC and 1 atm). We can use the ideal gas law, PV = nRT, to adjust for the temperature difference: (PV/T)1 = (PV/T)2 (2 atm)(V) / (373 K) = (nRT) / (298 K) V = (298 K)(2 atm) / (nR) * (373 K) where n is the number of moles of gas and R is the gas constant. To solve for n, we need to use the mole ratio between NaHCO₃(s) and CO₂(g) from the balanced equation: 2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(g) 1 mol NaHCO₃(s) produces 1 mol CO₂(g) Therefore, the number of moles of CO₂(g) formed is equal to the number of moles of NaHCO₃(s) used. We can assume that the mass of the sample is 1 gram, which is convenient for calculating moles: 1 g NaHCO₃(s) / (84.01 g/mol) = 0.0119 mol NaHCO₃(s) Now we can calculate the volume of the gas at 100ºC: V = (298 K)(2 atm) / (0.0119 mol * 0.0821 L·atm/mol·K) * (373 K) = 0.981 L Therefore, the total gas pressure at 100ºC is: Ptotal = (PCO₂ + PH₂O) * (0.981 L / V) = (1 atm + 1 atm) * (0.981 L / 1.000 L) = 1.962 atm Rounding to two significant figures, the answer is 0.96 atm (choice B).

Sodium Carbonate, Na2CO3(s), May Be Prepared by Heating Sodium Bicarbonate

Sodium Carbonate, Na₂CO₃(s), May Be Prepared by Heating Sodium Bicarbonate