Question

in physics, the ideal gas law describes the relationship among the pressure, volume, and temperature of a gas sample. this law is represented by the formula ( pv = nrt ), where ( p ) is the pressure, ( v ) is the volume, ( t ) is the temperature, ( n ) is the amount of gas, and ( r ) is a physical constant. select all the equations that are equivalent to the formula ( pv = nrt ).
a ( p = v/nrt )
b ( v = \frac{nrt}{p} )
c ( n = \frac{pv}{rt} )
d ( r = pv/nt )
e ( t = \frac{nr}{pv} )

Explanation:

Step1: Analyze Option A

Given \(PV = nRT\), if we solve for \(P\), we get \(P=\frac{nRT}{V}\), not \(P = V/nRT\). So option A is incorrect.

Step2: Analyze Option B

Starting with \(PV=nRT\), divide both sides by \(P\) to solve for \(V\). We have \(V=\frac{nRT}{P}\). So option B is correct.

Step3: Analyze Option C

From \(PV = nRT\), solving for \(n\), we divide both sides by \(RT\) to get \(n=\frac{PV}{RT}\), not \(n=\frac{PV}{RT}\) (typo in original analysis, correct is \(n=\frac{PV}{RT}\)). So option C is correct.

Step4: Analyze Option D

From \(PV=nRT\), solving for \(R\), we get \(R=\frac{PV}{nT}\), not \(R = PVnT\). So option D is incorrect.

Step5: Analyze Option E

From \(PV=nRT\), solving for \(T\), we divide both sides by \(nR\) to get \(T=\frac{PV}{nR}\), not \(T=\frac{nR}{PV}\). So option E is incorrect.

Answer:

B. \(V=\frac{nRT}{p}\), C. \(n = \frac{PV}{RT}\)