Alka-Seltzer^TM is an OTC medicine used to treat acid indigestion and heartburn.

Question

Alka-Seltzer^TM is an OTC medicine used to treat acid indigestion and heartburn. The active pharmaceutical ingredients (API) in each Alka-Seltzer^TM tablet are aspirin (325 mg), citric acid r (1916 mg), and sodium bicarbonate (1000 mg). For a single dose two Alka-Seltzer^TM tablets are dissolved m 4.0 fluid ounces of water (1 fluid ounce = 29.57 mL) causing the following reaction: What volume of CO_2 gas (mL) at 25 degree C and 1 atm would be produced by a single dose of Alka-Seltzer^TM ? Assume ideal gas behavior and that the reaction goes to completion. You wake up feeling miserable before the Chem Pro exam but you know you can't miss it. You grab some Alka-Seltzer^TM and an 11 ounce bottle of water. You drink just enough water to leave 4 fluid ounces in the bottle (you have had a lot of practice with this). Then you drop in the two tablets, screw the cap tightly onto the bottle and rush out the door. Calculate the pressure inside the bottle assuming the temperature remains constant at 25 and neglecting the volume of the tablets. Are the assumptions of ideal gas behavior is pans (a) and (b) reasonable Explain.

Explanation / Answer

(a) The reaction taking place is given:

C6H8O7 (aq) + 3 NaHCO3 (aq) --------> 3 H2O (l) + 3 CO2 (g) + Na3C6H5O7 (aq)

As per the balanced stoichiometric reaction,

1 mole citric acid = 3 moles sodium bicarbonate = 3 moles CO2.

We need to find out the limiting reactant. The limiting reactant will produce the CO2 required for the calculations.

Find the moles of citric acid and sodium bicarbonate present in Alka-Seltez tablets by noting the molar masses of citric acid and sodium bicarbonate.

Molar mass of citric acid, C6H8O7 = (6*12 + 8*1 + 7*16) g/mol = 192 g/mol.

Molar mass of sodium bicarbonate, NaHCO3 = (23 + 1 + 12 + 3*16) g/mol = 84 g/mol.

Molar mass of CO2 = (12 + 2*16) g/mol = 44 g/mol.

Find the moles of citric acid and sodium bicarbonate present as below:

Moles of citric acid = (mass of citric acid in g)/(molar mass of citric acid) = (1916 mg)*(1 g/1000 mg)/(192 g/mol) = 9.979*10-3 mole.

Moles of sodium bicarbonate = (mass of sodium bicarbonate in g)/(molar mass of sodium bicarbonate) = (1000 mg)*(1 g/1000 mg)/(84 g/mol) = 0.0119 mole.

Find out the limiting reactant as below:

Citric acid: (9.979*10-3 mole citric acid)*(3 moles sodium bicarbonate/1 mole citric acid) = 0.0299 mole sodium bicarbonate

Sodium bicarbonate: (0.0119 mole sodium bicarbonate)*(1 mole citric acid/3 moles sodium bicarbonate) = 3.967*10-3 mole citric acid.

Offcourse, we have a fewer moles of sodium bicarbonate in Alka-seltex tablet than required by 1 mole of citric acid for complete conversion. Therefore, sodium bicarbonate is the limiting reactant and the volume of CO2 produced at 1 atm and 25C (this is called STP = standard temperature and pressure) is decided by the moles of sodium bicarbonate present.

Moles of CO2 generated = (0.0119 mole sodium bicarbonate)*(3 moles CO2/3 moles sodium bicarbonate) = 0.0119 mole CO2.

We know that 1 mole of an ideal gas occupies 22.4 L at STP. Therefore,

0.0119 mole CO2 = (0.0119 mole)*(22.4 L/1 mole) = 0.26656 L 0.27 L = (0.27 L)*(1000 mL/1 L) = 270 mL (ans).

(b) In this part of the problem, we need to evaluate the pressure exerted by 270 mL of CO2 at 25C = (25 + 273) K = 298 K.

Moles of CO2 gas produced, n = 0.0119 mole.

Use the ideal gas law:

P*V = n*R*T

Plug in values and obtain

P*(0.27 L) = (0.0119 mole)*(0.082 L-atm/mol.K)*(298 K)

====> P = 1.0769 atm 1.08 atm (ans).

(c) CO2 is a real gas and hence the ideal gas law is only an approximation of the behavior of the gas. Moreover, in part (b), we assumed that there was no loss of CO2 to the atmosphere, but we cannot be doubly sure that there was no loss indeed. Infact, a small amount of CO2 may have leaked to the atmosphere and in that event, the pressure inside the bottle will be different from the one calculated here. Moreover, CO2, being a real gas, is sparingly soluble in water and ideal gas laws warrant that gases do not dissolve in water to form solutions.

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