Answered

The incomplete table below shows selected characteristics of gas laws.




Name		VariablesConstantsEquation

?		??$P_1 V_1=P_2 V_2$

Charles's law		??$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

?		temperature, pressure?$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

Combined gas law		pressure, temperature, volume??






Which constants would most likely be filled in the first row of the table?


Atemperature and moles of gas
Bvolume and temperature
Cpressure and volume
Dpressure and moles of gas

Verified Answer :

  • The equation \(P_1 V_1 = P_2 V_2\) represents Boyle's Law.
  • Boyle's Law describes the inverse relationship between pressure and volume for a gas.
  • This relationship holds true only when temperature (\(T\)) and the amount of gas (\(n\)) remain constant.
  • The correct choice is temperature and moles of gas.
  • Final Answer: \(\boxed{\text{temperature and moles of gas}}\)

Explanation

  1. Analyzing the Gas Law Equation

The first row of the table provides the equation \(P_1 V_1 = P_2 V_2\). This equation is a fundamental expression in thermodynamics known as Boyle's Law. It describes the relationship between the pressure (\(P\)) and the volume (\(V\)) of a gas. According to the kinetic theory of gases and the ideal gas law, \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles of gas, \(R\) is the gas constant, and \(T\) is temperature. For the product of pressure and volume to remain constant across two different states (i.e., \(P_1 V_1 = P_2 V_2\)), the other factors in the ideal gas law equation, \(n\) and \(T\), must remain constant. Therefore, Boyle's Law assumes that the temperature and the amount of gas (measured in moles) do not change during the process.

  1. Selecting the Correct Constants

Comparing our conclusion—that temperature and the amount of gas (moles) are the constants—with the given multiple-choice options:

  • temperature and moles of gas
  • volume and temperature
  • pressure and volume
  • pressure and moles of gas

The first option matches our derivation. Consequently, the constants for the equation \(P_1 V_1 = P_2 V_2\) are temperature and moles of gas.

Examples

Understanding gas laws is essential in fields like meteorology and scuba diving. For example, a scuba diver must understand that as the pressure increases with depth, the volume of air in their lungs and equipment changes according to these laws. Maintaining a constant temperature and ensuring the amount of gas remains controlled is critical for safety and calculating the remaining oxygen supply. These principles serve as the foundation for modern engineering of breathing apparatus and environmental control systems.