Question

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=\frac{nrt}{v} )
b ( v=\frac{nrt}{p} )
c ( n=\frac{pv}{rt} )
d ( r=\frac{pv}{nt} )
ef ( t=\frac{pv}{nr} )

Explanation:

Step1: Analyze each option

• Option A: \(P = \frac{nkT}{V}\) is not the standard form of the ideal gas law \(PV = nRT\).
• Option B: \(V=\frac{nRT}{P}\) is derived from \(PV = nRT\) by dividing both sides by \(P\).
• Option C: \(n=\frac{PV}{RT}\) is derived from \(PV = nRT\) by dividing both sides by \(RT\).
• Option D: \(R=\frac{PV}{nT}\) is derived from \(PV = nRT\) by dividing both sides by \(nT\).
• Option E: \(T=\frac{PV}{nR}\) is derived from \(PV = nRT\) by dividing both sides by \(nR\).

Answer:

B. \(V=\frac{nRT}{P}\), C. \(n=\frac{PV}{RT}\), D. \(R=\frac{PV}{nT}\), E. \(T=\frac{PV}{nR}\)