Let's analyze each law and fill in the missing information based on the principles of gas laws. We know the details of each law from the given context.
### Boyle's Law
- Variables: Pressure (P) and Volume (V)
- Constants: Moles of gas and temperature
- Equation: \(P_1 V_1 = P_2 V_2\)
### Charles's Law
- Variables: Volume (V) and Temperature (T)
- Constants: Pressure and moles of gas
- Equation: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)
### Gay-Lussac's Law (or Amontons's Law)
- Variables: Temperature (T) and Pressure (P)
- Constants: Volume and moles of gas
- Equation: \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)
### Combined Gas Law
- Variables: Pressure (P), Temperature (T), and Volume (V)
- Constants: Moles of gas
- Equation: \(\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}\)
According to our understanding:
- Boyle's Law constants: 'moles of gas, temperature'
- Charles's Law constants: 'pressure, moles of gas'
- Gay-Lussac's Law constants: 'volume, moles of gas'
- Combined Gas Law constants: 'moles of gas'
Now let's fill in the missing information:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
Name & Variables & Constants & Equation \\
\hline
Boyle's law & pressure, volume & moles of gas, temperature & [tex]$P_1 V_1=P_2 V_2$[/tex] \\
\hline
Charles's law & volume, temperature & pressure, moles of gas & [tex]$\frac{V_1}{T_1} = \frac{V_2}{T_2}$[/tex] \\
\hline
Gay-Lussac's law & temperature, pressure & volume, moles of gas & [tex]$\frac{P_1}{T_1} = \frac{P_2}{T_2}$[/tex] \\
\hline
Combined gas law & pressure, temperature, volume & moles of gas & [tex]$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$[/tex] \\
\hline
\end{tabular}
\][/tex]
The fifth question: "What is assumed to be constant when using the combined gas law?" options are:
- pressure
- number of moles
- volume and moles of gas
- pressure and temperature
From the table, we see that the combined gas law assumes that the number of moles is constant.
Thus, the correct answer is number of moles.
