If it takes three "breaths" to blow up a balloon to 1.2 L, and each breath supplies the balloon with 0.060 moles of exhaled air, how many moles of air are in a 3.0 L balloon? Express your answer to two decimal places and include the appropriate units.
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 Statement
If it takes three "breaths" to blow up a balloon to 1.2 L, and each breath supplies the balloon with 0.060 moles of exhaled air, how many moles of air are in a 3.0 L balloon?
**Express your answer to two decimal places and include the appropriate units.**
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### Solution
To find the number of moles of air in a 3.0 L balloon, use the given data and follow these steps:
1. **Determine the volume of air supplied per breath:**
- It takes 3 breaths to fill a balloon to 1.2 L.
- Therefore, each breath supplies:
\[
\frac{1.2\text{ L}}{3} = 0.4\text{ L per breath}
\]
2. **Calculate moles per liter:**
- Each breath supplies 0.060 moles.
- Hence moles per liter (moles/L) is:
\[
\frac{0.060\text{ moles}}{0.4\text{ L}} = 0.15\text{ moles per liter (moles/L)}
\]
3. **Find total moles in 3.0 L:**
- Multiply the moles per liter by the volume of the balloon:
\[
0.15\text{ moles/L} \times 3.0\text{ L} = 0.45\text{ moles}
\]
**Final Answer:**
0.45 moles (to two decimal places)
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