Final answer:
The correct units for the ideal gas law constant, R, given the volume in liters, pressure in atmospheres, temperature in kelvins, and amount in moles, are L·atm/mol·K and J/mol·K.
Step-by-step explanation:
The ideal gas law constant, R, has different values depending on the units used for pressure, volume, temperature, and amount of substance in the ideal gas equation. When volume is expressed in liters (L), pressure in atmospheres (atm), temperature in kelvins (K), and amount in moles (mol), the correct value for R is 0.0821 L atm/mol K. Therefore, among the options provided, Option 1: L·atm/mol·K and Option 2: J/mol·K are correct because R also has an equivalent value in energy per mole per kelvin (J/mol K). Option 3: g·cm^2/ s^2.K.mol and Option 4: kg·m^2/ s^2 ·mol·K are not correct units for R. It is important to use the value of R that corresponds to the units of the other variables in the equation.