which equation agrees with the ideal gas law?\n$\frac{v_1}{t_1}=\frac{v_2}{t_2}$\n$v_1n_1=v_2n_2$\n$p_1n_1=p_…

: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Explanation:

Step1: Recall ideal gas law

The ideal gas law is $PV = nRT$, where $P$=pressure, $V$=volume, $n$=moles, $R$=gas constant, $T$=temperature.

Step2: Analyze each option

For $\frac{V_1}{T_1} = \frac{V_2}{T_2}$: Rearrange ideal gas law to $\frac{V}{T} = \frac{nR}{P}$. If $n$ and $P$ are constant, $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (Charles's Law, a special case of ideal gas law). For $V_1n_1 = V_2n_2$: From ideal gas law, $V \propto n$ (at constant $P,T$), so $\frac{V_1}{n_1} = \frac{V_2}{n_2}$, not $V_1n_1=V_2n_2$. For $P_1n_1 = P_2n_2$: From ideal gas law, $P \propto n$ (at constant $V,T$), so $\frac{P_1}{n_1} = \frac{P_2}{n_2}$, not $P_1n_1=P_2n_2$. For $\frac{P_1}{P_2} = \frac{T_2}{T_1}$: From ideal gas law, $P \propto T$ (at constant $V,n$), so $\frac{P_1}{T_1} = \frac{P_2}{T_2}$, which rearranges to $\frac{P_1}{P_2} = \frac{T_1}{T_2}$, not $\frac{P_1}{P_2} = \frac{T_2}{T_1}$.