Which statement would be the most useful for deriving the ideal gas law?
A. Volume is directly proportional to the number of moles.
B. Volume is inversely proportional to the temperature.
C. Pressure is directly proportional to the volume.
D. Pressure is inversely proportional to the number of moles.
Answer (2)
The ideal gas law is P V = n RT .
Analyze each statement to see which aligns with the ideal gas law.
Volume is directly proportional to the number of moles ( V ∝ n ) is consistent with the ideal gas law.
The most useful statement is: Volume is directly proportional to the number of moles. V o l u m e i s d i rec tl y p ro p or t i o na lt o t h e n u mb ero f m o l es .
Explanation
Understanding the Ideal Gas Law The question asks which statement is most useful for deriving the ideal gas law. The ideal gas law is represented by the equation P V = n RT , where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. We need to determine which of the given relationships aligns with this law.
Analyzing the Statements Let's analyze each statement:
Volume is directly proportional to the number of moles: This means V ∝ n . If we keep pressure ( P ) and temperature ( T ) constant, then V = P RT n , which is consistent with the ideal gas law.
Volume is inversely proportional to the temperature: This means V ∝ T 1 . This contradicts the ideal gas law, which states that volume is directly proportional to temperature.
Pressure is directly proportional to the volume: This means P ∝ V . This contradicts the ideal gas law, as pressure and volume are inversely proportional when the number of moles and temperature are constant.
Pressure is inversely proportional to the number of moles: This means P ∝ n 1 . This contradicts the ideal gas law, which implies that pressure is directly proportional to the number of moles when volume and temperature are constant.
Determining the Most Useful Statement From the analysis, we can see that the statement "Volume is directly proportional to the number of moles" is the most useful for deriving the ideal gas law because it directly reflects the relationship in the ideal gas law equation when pressure and temperature are held constant.
Conclusion Therefore, the most useful statement for deriving the ideal gas law is that volume is directly proportional to the number of moles.
Examples
The ideal gas law is used in various real-world applications, such as predicting the behavior of gases in weather forecasting, designing airbags in cars, and optimizing industrial processes involving gases. For instance, understanding the relationship between volume and the number of moles helps engineers determine the amount of gas needed to inflate an airbag to a specific volume, ensuring passenger safety during a collision. The direct proportionality between volume and the number of moles, as described by the ideal gas law, is crucial in these calculations.
The most useful statement for deriving the ideal gas law is that volume is directly proportional to the number of moles. This is consistent with the ideal gas law, which describes the behavior of gases. Therefore, the correct answer is the first statement: Volume is directly proportional to the number of moles.
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