If 67.0 grams of carbonic acid are sealed in a 2.00 L soda bottle at room temperature (298.15 K) and decompose completely via the equation below, what would be the final pressure of carbon dioxide (in atm) assuming it had the full 2.00 L in which to expand? H2CO3(aq) → H2O(1) + CO2(g)
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![**Problem:**
If 67.0 grams of carbonic acid are sealed in a 2.00 L soda bottle at room temperature (298.15 K) and decompose completely via the equation below, what would be the final pressure of carbon dioxide (in atm) assuming it had the full 2.00 L in which to expand?
\[ \text{H}_2\text{CO}_3(\text{aq}) \rightarrow \text{H}_2\text{O}(\text{l}) + \text{CO}_2(\text{g}) \]
**Explanation:**
This problem involves decomposing carbonic acid in a soda bottle to find the final pressure exerted by the carbon dioxide gas produced. Here's a step-by-step guide to solving it:
1. **Calculate the number of moles of carbonic acid (H₂CO₃):**
- Use the molar mass of carbonic acid, which is approximately 62.03 g/mol.
- Number of moles \( n \) = \(\frac{\text{Mass}}{\text{Molar mass}} = \frac{67.0 \ \text{g}}{62.03 \ \text{g/mol}} \).
2. **Determine the moles of carbon dioxide (CO₂) produced:**
- The balanced chemical equation shows a 1:1 molar ratio between carbonic acid and carbon dioxide.
- Therefore, the moles of CO₂ will be the same as the moles of H₂CO₃.
3. **Use the Ideal Gas Law to find the final pressure:**
- Ideal Gas Law: \( PV = nRT \), where:
- \( P \) = pressure,
- \( V \) = volume (2.00 L),
- \( n \) = number of moles of CO₂,
- \( R \) = gas constant (0.0821 L atm / K mol),
- \( T \) = temperature (298.15 K).
4. **Solve for \( P \):**
- Rearrange the Ideal Gas Law to \( P = \frac{nRT}{V} \).
5. **Substitute the values and calculate:**
- Calculate the number of moles of CO₂.
- Plug the values into the appropriate places and solve for the pressure in atm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44982666-d339-4885-b9e9-36706f6e8dd1%2F7f17e691-cf17-4539-b76e-52482d879da6%2Fngv4pdg_processed.png&w=3840&q=75)
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