Let's analyze the question and provide a detailed step-by-step solution.
The table provided lists the gas laws, their variables, constants, and equations. We want to identify what remains constant for each of these gas laws, including the Combined Gas Law.
1. Boyle's Law states that the product of pressure and volume is a constant, as long as the temperature is held constant.
- Variables: pressure ([tex]\(P\)[/tex]), volume ([tex]\(V\)[/tex])
- Constant: temperature
- Equation: [tex]\(P_1 V_1 = P_2 V_2\)[/tex]
2. Charles's Law states that the volume of a gas is directly proportional to its temperature, as long as the pressure remains constant.
- Variables: volume ([tex]\(V\)[/tex]), temperature ([tex]\(T\)[/tex])
- Constant: pressure
- Equation: [tex]\(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)[/tex]
3. Gay-Lussac's Law states that the pressure of a gas is directly proportional to its temperature when the volume is held constant. By looking at the equation and the variables, we can determine the constant.
- Variables: pressure ([tex]\(P\)[/tex]), temperature ([tex]\(T\)[/tex])
- Constant: volume
- Equation: [tex]\(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)[/tex]
4. Combined Gas Law combines Boyle's, Charles's, and Gay-Lussac's laws. It describes the relationship between pressure, volume, and temperature of a fixed quantity of gas.
- Variables: pressure ([tex]\(P\)[/tex]), volume ([tex]\(V\)[/tex]), temperature ([tex]\(T\)[/tex])
- Constant: moles of gas
- Equation: [tex]\(\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}\)[/tex]
Based on the provided information, the constant for each law is identified as follows:
- Boyle's Law: temperature
- Charles's Law: pressure
- Gay-Lussac's Law: volume
- Combined Gas Law: moles of gas
Therefore, when using the combined gas law, it is assumed that the moles of gas remain constant.
