The Dieterici equation of state is

Pe^{a/Vm RT} (V_m − b) = RT,

where P is the pressure, T is the temperature, V_m is the molar volume, and R is the ideal gas constant. The constant parameters a and b have different values for different gases. For carbon dioxide, a = 0.468 Pa m⁶ mol⁻², b = 4.63 × 10⁻⁵ m³ mol⁻¹. Without linearization, find the molar volume of carbon dioxide if T = 298.15 K and P = 10.000 atm = 1.01325 × 10⁶ Pa. Use Mathematica, Excel, or trial and error.