Gas Laws Fact Sheet
| Ideal gas law | [tex]$P V=n R T$[/tex] |
Answer (2)
Use the ideal gas law: P V = n RT .
Rearrange the formula to solve for n : n = RT P V .
Substitute the given values: n = ( 8.314 mol K L kPa ) ( 295 K ) ( 21.1 kPa ) ( 3.0 L ) .
Calculate the number of moles: n ≈ 0.026 mol .
The final answer is 0.026 mol .
Explanation
Understanding the Problem We are given the volume of a human lung at maximum capacity, the partial pressure of oxygen in the air, and the air temperature. We are asked to find the number of moles of oxygen in the lung. We can use the ideal gas law to solve this problem. The ideal gas law is given by the equation P V = n RT , where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Listing Given Information We are given:
V = 3.0 L (Volume of the lung) P = 21.1 kPa (Partial pressure of oxygen) T = 295 K (Air temperature) R = 8.314 mol K L kPa (Ideal gas constant)
We want to find n , the number of moles of oxygen.
Rearranging the Ideal Gas Law We can rearrange the ideal gas law equation to solve for n :
P V = n RT ⟹ n = RT P V
Substituting Values Now, we can substitute the given values into the equation:
n = ( 8.314 mol K L kPa ) ( 295 K ) ( 21.1 kPa ) ( 3.0 L )
Calculating the Number of Moles Calculating the value of n :
n = 8.314 × 295 21.1 × 3.0 = 2452.63 63.3 ≈ 0.0258 mol
Final Answer The number of moles of oxygen in the lung is approximately 0.0258 mol. Looking at the answer choices, the closest value is 0.026 mol.
Examples
The ideal gas law is useful in many real-world applications. For example, it can be used to calculate the amount of gas in a container, such as an oxygen tank used in hospitals or by scuba divers. It can also be used to predict how the volume of a gas will change with changes in temperature or pressure, which is important in designing engines and other mechanical systems. Understanding the relationship between pressure, volume, temperature, and the number of moles of a gas is crucial in many scientific and engineering fields.
The ideal gas law is expressed as P V = n RT , allowing us to calculate the number of moles of a gas based on its pressure, volume, and temperature. By substituting values into the rearranged formula n = RT P V , we find that approximately 0.026 moles of oxygen can be present in the lung under the given conditions. This law is essential for understanding gas behavior and has various practical applications in science and engineering fields.
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