Question

If 60.0 grams of carbonic acid are sealed in a 2.00 L soda bottle at room temperature (298 K) and decompose completely via the equation below, what would be the final pressure of carbon dioxide assuming it had the full 2.00 L in which to expand? H₂CO₃(aq) → H₂O(l) + CO₂(g)

Answer 1

Answer:

The final pressure of the carbon dioxide gas will 11.84 atm.

Explanation:

Moles of carbonic acid = $\frac{60.0 g}{62 g/mol}=0.9677 mol$

$H_2CO_3(aq)\rightarrow H_2O(l) + CO_2(g)$

According to reaction, 1 mol of carbonic acid gives 1 mole of carbon dioxide gas.

Then 0.9677 moles of carbonic acid will give :

$\frac{1}{1}\times 0.9677 mol=0.09677 mol$ of carbon dioxide

Moles of carbon dioxide gas = n = 0.09677 mol

Volume of soda bottle = $V_1=2 L$

Pressure of the carbon dioxide gas = P

Temperature of the carbon dioxide gas = T = 298 K

$PV=nRT$ (ideal gas law)

$P=\frac{nRT}{V}=\frac{0.9677 mol\times 0.0821 atm L/mol K\times 298 K}{2 L}=11.84 atm$

The final pressure of the carbon dioxide gas will 11.84 atm.