Sure, let's determine which equation represents the combined gas law. The combined gas law is a relationship between pressure (P), volume (V), and temperature (T) of a gas. It combines three gas laws: Boyle's law, Charles's law, and Gay-Lussac's law. The combined gas law can be formulated as:
[tex]\[
\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
\][/tex]
We will now analyze each given option to see which one matches this form:
1. \( P_1V_1 = P_2 V_2 \)
- This equation is incorrect because it doesn't include temperature (T1 and T2).
2. \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)
- This equation is in an incorrect format. It seems to mix volume and temperature but fails to include both pressures (P1 and P2).
3. \( P_1 \frac{P_2V_2}{T_2} \)
- This equation is also incorrect because it does not correctly structure the combined gas law and includes a misplaced term.
4. \( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \)
- This equation is correct and accurately represents the combined gas law.
Thus, the correct equation representing the combined gas law is:
[tex]\[
\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
\][/tex]
Therefore, the correct option is:
[tex]\[
4
\][/tex]
