Answer :
The given question deals with the identification of constants for different gas laws. Based on Boyle's Law, let's carefully fill in the table and answer the query about its constants.
Let's first recognize the gas laws and their respective forms:
1. Boyle's Law:
- Variables: Pressure ([tex]\( P \)[/tex]) and Volume ([tex]\( V \)[/tex])
- Equation: [tex]\( P_1 V_1 = P_2 V_2 \)[/tex]
- Constants: Temperature and moles of gas
2. Charles's Law:
- Variables: Volume ([tex]\( V \)[/tex]) and Temperature ([tex]\( T \)[/tex])
- Equation: [tex]\( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)[/tex]
- Constants: Pressure and moles of gas
3. Gay-Lussac's Law:
- Variables: Pressure ([tex]\( P \)[/tex]) and Temperature ([tex]\( T \)[/tex])
- Equation: [tex]\( \frac{P_1}{T_1} = \frac{P_2}{T_2} \)[/tex]
- Constants: Volume and moles of gas
4. Combined Gas Law:
- Variables: Pressure ([tex]\( P \)[/tex]), Volume ([tex]\( V \)[/tex]), and Temperature ([tex]\( T \)[/tex])
- Equation: [tex]\( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \)[/tex]
- Constants: Moles of gas
Given that [tex]\( P_1 V_1 = P_2 V_2 \)[/tex] is Boyle's Law, the constants in the first row of the table must be temperature and moles of gas, since these are the parameters that remain unchanged according to Boyle’s Law.
Therefore, the most likely constants to be filled in the first row of the table are temperature and moles of gas.
Let's first recognize the gas laws and their respective forms:
1. Boyle's Law:
- Variables: Pressure ([tex]\( P \)[/tex]) and Volume ([tex]\( V \)[/tex])
- Equation: [tex]\( P_1 V_1 = P_2 V_2 \)[/tex]
- Constants: Temperature and moles of gas
2. Charles's Law:
- Variables: Volume ([tex]\( V \)[/tex]) and Temperature ([tex]\( T \)[/tex])
- Equation: [tex]\( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)[/tex]
- Constants: Pressure and moles of gas
3. Gay-Lussac's Law:
- Variables: Pressure ([tex]\( P \)[/tex]) and Temperature ([tex]\( T \)[/tex])
- Equation: [tex]\( \frac{P_1}{T_1} = \frac{P_2}{T_2} \)[/tex]
- Constants: Volume and moles of gas
4. Combined Gas Law:
- Variables: Pressure ([tex]\( P \)[/tex]), Volume ([tex]\( V \)[/tex]), and Temperature ([tex]\( T \)[/tex])
- Equation: [tex]\( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \)[/tex]
- Constants: Moles of gas
Given that [tex]\( P_1 V_1 = P_2 V_2 \)[/tex] is Boyle's Law, the constants in the first row of the table must be temperature and moles of gas, since these are the parameters that remain unchanged according to Boyle’s Law.
Therefore, the most likely constants to be filled in the first row of the table are temperature and moles of gas.
