Question

Alka-Seltzer is an over-the-counter medicine used to treat acid indigestion and heartburn. The active pharmaceutical ingredients (API) in each Alka-Seltzer tablet are aspirin (325mg), citric acid 1:000 103 mg, and sodium bicarbonate 1:916 103 mg. For a single dose, two Alka-Seltzer tablets are dissolved in 4.0 fluid ounces of water (1.0 fluid ounce 29:57 mL), causing the following reaction:

C6H8O7aq 3NaHCO3aq ! 3H2Ol 3CO2g Na3C6H5O7aq |fflfflfflffl{zfflfflfflffl} |fflfflfflfflfflffl{zfflfflfflfflfflffl} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} citric acid sodium sodium citrate

bicarbonate

(a) What volume of CO2 gas (mL) at 25°C and 1 atm would be produced by a normal dose of Alka-Seltzer? Assume ideal-gas behavior and that the reaction goes to completion.

(b) Youwakeupfeelingmiserablebeforeyourmaterial-and-energy-balancesfinalexam,butyouknow you can’t miss it. You grab some Alka-Seltzer and an 11-ounce bottle of water. You drink just enough water to leave 4.0 fluid ounces in the bottle (you’ve had lots 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°C and neglecting the volume of the tablets.

(c) How reasonable are the assumptions of ideal-gas behavior in Parts (a) and (b)?

Answer 1

The reaction is

Molecular weight of citric acid=192.124 g/mol

Number of moles of C6H8O7 in 1000mg = / tablet

Molecular weight of sodium bicarbonate= 84g/mol

Number of moles of NaHCO3 in 1916mg=

In a single dose, two tablets are dissolved therefore total moles of C6H8O7are=

Total moles of NaHCO3 in single dose =

According to the reaction 1 moles of citric acid reacts with 3 moles of sodium bicarbonate to produce 3 moles of CO2.

Here according to the quantity citric aid is limiting reagent thus 0.01 moles of citric acid will react with 0.03 moles of sodium bicarbonate to produce 0.03 moles of CO2.

The volume of 0.03 moles CO2 at 25^o C and 1atm=

from the ideal gas formula PV=nRT

(b) To calculate the pressure inside of the sealed bottle, the total number of moles present in bottle are =

Moles of air in air portion + Moles of CO2 in water portion

To calculate n_{air} based on the volume of air present before the tablets are added when

V =7 fl oz and P = 1 atm.  

n_{air}= 0.0085 moles

Therefore

From the ideal gas law

Here n =

(Volume of gas)

Therefore

(c)

Assuming ideal gas behavior for part (a) is reasonable as the gas is at a temperature of 25 ^oC which above 0^oC and at atmospheric pressure 1 atm.

If the gas has ideal behave then the volume per mole for gas should be around 22.4 L/mol. For cross check, the volume of 0.03 mole is 0.7336 L then volume of 1 mole =

This indicates an error in ideal gas behaviour of gas.

For part (b) the pressure inside the bottle is 4.548 atm which is almost 5 times greater than atmospheric pressure. At a higher pressure, the ideal gas behaviour is less accurate.