Question

If 78.2 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 carbon dioxide is 15.4 atm

Explanation:

To calculate the number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

• For carbonic acid:

Given mass of carbonic acid = 78.2 g

Molar mass of carbonic acid = 62 g/mol

Putting values in above equation, we get:

$\text{Moles of carbonic acid}=\frac{78.2g}{62g/mol}=1.26mol$

For the given chemical reaction:

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

By Stoichiometry of the reaction:

1 mole of carbonic acid produces 1 mole of carbon dioxide

So, 1.26 moles of carbonic acid will produce = $\frac{1}{1}\times 1.26=1.26mol$ of carbon dioxide

To calculate the pressure, we use the equation given by ideal gas, which follows:

$PV=nRT$

where,

P = pressure of the carbon dioxide = ?

V = Volume of the container = 2.00 L

T = Temperature of the container = 298 K

R = Gas constant = $0.0821\text{ L. atm }mol^{-1}K^{-1}$

n = number of moles of carbon dioxide = 1.26 moles

Putting values in above equation, we get:

$P\times 2.00L=1.26mol\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times 298K\\\\P=\frac{1.26\times 0.0821\times 298}{2.00}=15.4atm$

Hence, the final pressure of carbon dioxide is 15.4 atm