Alka-Seltzer ® is an over-the-counter medicine used to treat acid indigestion an

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 (325 mg), 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:

C6H8O7(aq)citric acid+3NaHCO3(aq)sodium bicarbonate3H2O(l)+3CO2(g)+Na3C6H5O7(aq)sodium citrate

(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)  

You wake up feeling miserable before your material-and-energy-balances final exam, but you know 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}?

Explanation / Answer

a)

find V of CO2 in T = 25°C , P = 1 atm

by normal dose

6H8O7(aq)+3NaHCO3(aq)3H2O(l)+3CO2(g)+Na3C6H5O7(aq)

mol of acid = 1/192.124 = 0.005204

mol of baking soda = 1.916/84.007 = 0.02280

ratio is 1:3 so

0.005204 mol of acid --> 0.005204*3 = 0.015612 mol of baking soda, so Acid is limitin greaction

0.005204 mol of acid --> 0.015612 mol of CO2

PV = nRT

V = nRT/P

V = (0.005204)(0.082)(298)/(1) = 0.1271 L = 127.1 mL of CO2 per tablet

n = 2 tablets

V = 2*127.1 = 254.2 mL

b)

V = 11-4 = 7 mL left = 29.57*7 = 206.99 mL = 0.20699 L

find P inside bottle:

PV = nRT

P = nRT/V

P = (0.005204*2)(0.082)(298)/0.20699 = 1.2287 atm

c)

they are pretty reasonable since:

- P arent that high, i.e. P < 10 atm

- T arent that low, i.e. T > 150 K

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