to entertain children between the ages of 2 and 90, I enjoy popping corks from b

Question

to entertain children between the ages of 2 and 90, I enjoy popping corks from bottles of vinegar and baking soda. I pour about 50mL of vinegar into a 500mL plastic bottle. Then I wrap about 5g of baking soda (NaHCO3)in one layer of tissue and drop the tissue into the bottle. I place a cork tightly in the mout of the bottle and step back. The chemical reaction generates CO2(g) that pressurizes the bottle and eventually bursts the cork into the air.

CH3CO2H + NaHCO3 --> CH3CO2- + Na+ +CO2(g) + H2O

Use the ideal gas law to calculate how many L of CO2(g) are generated if P=1bar and T=300K. If there is 0.5L of air space in the bottle, what pressure can be generated to pop the cork?

Explanation / Answer

From the reaction we know,

1 mole of Vinegar or 1 mole of NaHCO3 will react to form 1 mole of CO2

moles of NaHCO3 = g/molar mass = 5 g / 84.007 g/mol = 0.06 mols = moles of CO2

density of vinegar = 1 g/ml

g of vinegar = 50 ml x 1 g/ml = 50 g

Generally vinegar is 5wt% acetic acid solution

Thus, 50 g will have 2.5 g acetic acid

moles of acetic acid = 2.5 g / 60.05 g/mol = 0.04 mols = moles of CO2

So acetic acid (vinegar) is the limiting reagent

Now using the formula,

PV = nRT and feeding the given values

V = nRT/P [R = gas constant]

    = 0.04 x 0.08206 x 300 / 1

    = 0.985 L of CO2 generated

Pressure generated with 0.5 L open space = nRT/V = 0.04 x 0.08206 x 300 / 0.5 = 1.97 atm

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