Question

which equation represents the combined gas law?

\\(p_1 v_1 = p_2 v_2\\)

\\(\frac{v_1}{t_1} = \frac{v_2}{t_2}\\)

\\(\frac{p_1 v_1}{t_1} = \frac{p_2 v_2}{t_2}\\)

\\(p_1 v_1 t_1 = p_2 v_2 t_2\\)

Explanation:

<pre_analysis>
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"new_concepts": [
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</pre_analysis><reasoning>

Identify the individual gas laws

\[

$$\begin{aligned} &\text{Boyle's Law: } P_1V_1 = P_2V_2 \\ &\text{Charles's Law: } \frac{V_1}{T_1} = \frac{V_2}{T_2} \\ &\text{Gay-Lussac's Law: } \frac{P_1}{T_1} = \frac{P_2}{T_2} \end{aligned}$$

\]

Combine the laws into a single relation

\[
\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
\]
</reasoning><answer>
<mcq-option>(A) \(P_1V_1 = P_2V_2\)</mcq-option>
<mcq-option>(B) \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)</mcq-option>
<mcq-correct>(C) \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)</mcq-correct>
<mcq-option>(D) \(P_1V_1T_1 = P_2V_2T_2\)</mcq-option>
</answer><post_analysis>
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"Natural Science",
"Chemistry",
"Combined Gas Law"
]
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</post_analysis>

Answer:

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"new_concepts": [
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</pre_analysis><reasoning>

Identify the individual gas laws

\[

$$\begin{aligned} &\text{Boyle's Law: } P_1V_1 = P_2V_2 \\ &\text{Charles's Law: } \frac{V_1}{T_1} = \frac{V_2}{T_2} \\ &\text{Gay-Lussac's Law: } \frac{P_1}{T_1} = \frac{P_2}{T_2} \end{aligned}$$

\]

Combine the laws into a single relation

\[
\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}
\]
</reasoning><answer>
<mcq-option>(A) \(P_1V_1 = P_2V_2\)</mcq-option>
<mcq-option>(B) \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)</mcq-option>
<mcq-correct>(C) \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)</mcq-correct>
<mcq-option>(D) \(P_1V_1T_1 = P_2V_2T_2\)</mcq-option>
</answer><post_analysis>
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"question_type": "Multiple Choice",
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"Combined Gas Law"
]
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