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(B) According to the ideal gas law,$PV = nRT$,where $n$ is the number of moles. Since the number of molecules is directly proportional to the number o

Vedclass · Accepted Answer

$2:1$

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(B) According to the ideal gas law,$PV = nRT$,where $n$ is the number of moles. Since the number of molecules is directly proportional to the number of moles $(n = \frac{N}{N_A})$,we have $n = \frac{PV}{RT}$.Given for container $A$: $P_A = 2P_B$,$V_A = 2V_B$,and $T_A = 2T_B$.The ratio of the number of molecules is equal to the ratio of the number of moles:$\frac{n_A}{n_B} = \frac{P_A V_A}{R T_A} 	imes \frac{R T_B}{P_B V_B} = \frac{P_A}{P_B} 	imes \frac{V_A}{V_B} 	imes \frac{T_B}{T_A}$.Substituting the given values:$\frac{n_A}{n_B} = (2) 	imes (2) 	imes (\frac{1}{2}) = 2$.Thus,the ratio is $2:1$.

Containers $A$ and $B$ contain the same gas. If the pressure,volume,and temperature of container $A$ are all twice those of container $B$,what is the ratio of the number of molecules in $A$ to those in $B$?

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