An important formula in chemistry is 𝑃𝑉=𝑛𝑅𝑇PV=nRT. Solve the formula for the variable R.

1. Break Down the Problem

To solve the formula $PV = nRT$ for the variable $R$, we need to isolate $R$ on one side of the equation.

2. Relevant Concepts

The ideal gas law is expressed by the equation $PV = nRT$, where:

• $P$ = Pressure
• $V$ = Volume
• $n$ = Amount of substance (in moles)
• $R$ = Ideal gas constant
• $T$ = Temperature (in Kelvin)

3. Analysis and Detail

To isolate $R$, we can rearrange the equation $PV = nRT$ as follows:

1. Divide both sides by $nT$: $R = \frac{PV}{nT}$

4. Verify and Summarize

The equation $R = \frac{PV}{nT}$ simplifies our original formula to express $R$ in terms of pressure, volume, the amount of substance, and temperature.

Final Answer

The isolated variable $R$ can be expressed as: $R = \frac{PV}{nT}$