Question

brenda fills in the table below to organize information about the gas laws.

gas law	constant	changing
boyle’s	3	4
charles’s	5	6

in which numbered cells should she place volume?

• 2, 3, and 6
• 1, 4, and 6
• 1, 3, and 5
• 2, 4, and 5

Explanation:

Step1: Recall Gas Laws

- Gay - Lussac’s Law: Relates pressure and temperature, with volume constant. So in Gay - Lussac’s row, "Constant" (cell 1) has volume? No, "Changing" (cell 2) has pressure and temperature changing, volume is constant (so volume is not in cell 2). Wait, correction: Gay - Lussac’s Law: \( \frac{P_1}{T_1}=\frac{P_2}{T_2} \) (constant volume, \( V \) constant). So constant: volume (cell 1? No, wait the table: Gas law, Constant, Changing. So for Gay - Lussac’s, constant is volume (so cell 1? No, wait Boyle's Law: \( P_1V_1 = P_2V_2 \) (constant temperature, \( T \) constant). Charles’s Law: \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \) (constant pressure, \( P \) constant).

Step2: Analyze Each Law

- Gay - Lussac’s Law: Constant is volume (so volume in cell 1? No, wait no: Gay - Lussac's is \( P \propto T \) at constant \( V \). So "Constant" column (cell 1) is volume? No, "Changing" column (cell 2) has \( P \) and \( T \), "Constant" is \( V \). Wait no, the table: Gas law, Constant (what's constant), Changing (what's changing). So:
- Gay - Lussac’s: Constant = Volume (so volume in cell 1? No, wait no, let's re - express:
- Boyle's Law: \( P_1V_1 = P_2V_2 \), constant is Temperature (\( T \)). So "Constant" column (cell 3) is Temperature, "Changing" (cell 4) is \( P \) and \( V \).
- Charles’s Law: \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \), constant is Pressure (\( P \)). So "Constant" column (cell 5) is Pressure, "Changing" (cell 6) is \( V \) and \( T \).
- Gay - Lussac’s Law: \( \frac{P_1}{T_1}=\frac{P_2}{T_2} \), constant is Volume (\( V \)). So "Constant" column (cell 1) is Volume? No, this is confusing. Wait, let's list the variables:
- Boyle's Law: Variables: \( P \) (changing), \( V \) (changing), \( T \) (constant). So "Constant" (cell 3) is \( T \), "Changing" (cell 4) is \( P \) and \( V \). So volume is in cell 4.
- Charles’s Law: Variables: \( V \) (changing), \( T \) (changing), \( P \) (constant). So "Constant" (cell 5) is \( P \), "Changing" (cell 6) is \( V \) and \( T \). So volume is in cell 6.
- Gay - Lussac’s Law: Variables: \( P \) (changing), \( T \) (changing), \( V \) (constant). So "Constant" (cell 1) is \( V \), "Changing" (cell 2) is \( P \) and \( T \). Wait, no, this is wrong. Wait, no:
- Correct analysis:
- Boyle's Law: Constant = Temperature (\( T \)), Changing = Pressure (\( P \)) and Volume (\( V \)). So "Changing" column (cell 4) has \( V \).
- Charles’s Law: Constant = Pressure (\( P \)), Changing = Volume (\( V \)) and Temperature (\( T \)). So "Changing" column (cell 6) has \( V \).
- Gay - Lussac’s Law: Constant = Volume (\( V \)), Changing = Pressure (\( P \)) and Temperature (\( T \)). Wait, no, that can't be. Wait, no:
- Boyle's Law: \( P \) and \( V \) change, \( T \) constant. So "Constant" (cell 3) is \( T \), "Changing" (cell 4) is \( P \) and \( V \) (so \( V \) in cell 4).
- Charles’s Law: \( V \) and \( T \) change, \( P \) constant. So "Constant" (cell 5) is \( P \), "Changing" (cell 6) is \( V \) and \( T \) (so \( V \) in cell 6).
- Gay - Lussac’s Law: \( P \) and \( T \) change, \( V \) constant. So "Constant" (cell 1) is \( V \)? No, that's the mistake. Wait, no: Gay - Lussac's is \( P \propto T \) at constant \( V \). So "Constant" is \( V \) (cell 1), "Changing" is \( P \) and \( T \) (cell 2). But we need to find where volume is placed. So volume is in:
- Boyle's "Changing" (cell 4), Charles's "Changing" (cell 6), and Gay - Lussac's "Constant" (cell 1)? No, that's not matching options. Wait, the options are:
- Option 1: 2, 3, and 6
- Option 2: 1, 4, and 6
- Option 3: 1, 3, and 5
- Option 4: 2, 4, and 5

Wait, let's re - do:

- Boyle's Law: \( P_1V_1 = P_2V_2 \) (constant \( T \)). So "Constant" (cell 3) is \( T \), "Changing" (cell 4) is \( P \) and \( V \) (so \( V \) in cell 4).
- Charles’s Law: \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \) (constant \( P \)). So "Constant" (cell 5) is \( P \), "Changing" (cell 6) is \( V \) and \( T \) (so \( V \) in cell 6).
- Gay - Lussac’s Law: \( \frac{P_1}{T_1}=\frac{P_2}{T_2} \) (constant \( V \)). So "Constant" (cell 1) is \( V \) (so \( V \) in cell 1).

So volume is in cell 1 (Gay - Lussac's constant), cell 4 (Boyle's changing), and cell 6 (Charles's changing). So the cells are 1, 4, and 6.

Answer:

1, 4, and 6 (the option with 1, 4, and 6)