To calculate the partition function q and the Helmholtz free energy A of an ideal gas, we need to consider the translational, rotational, and vibrational contributions to the partition function. However, since we are not given any information about the specific gas or its molecular properties, we will only consider the translational partition function.The translational partition function for an ideal gas can be calculated using the following formula:q_trans = 2 * pi * m * k_B * T / h^2 ^3/2 * Vwhere m is the mass of a single particle, k_B is the Boltzmann constant 1.380649 10^-23 J/K , T is the temperature, h is the Planck constant 6.62607015 10^-34 Js , and V is the volume.Since we are not given the mass of the particles or the volume, we cannot calculate the exact value of the translational partition function. However, we can express the partition function in terms of the number of moles n and the molar volume V_m :q_trans = n * 2 * pi * m * k_B * T / h^2 ^3/2 * V_mNow, we can calculate the Helmholtz free energy A using the following formula:A = -k_B * T * ln q For an ideal gas, the Helmholtz free energy can be expressed as:A = -n * k_B * T * ln q_trans / n Since we do not have the exact values for the mass of the particles or the molar volume, we cannot calculate the exact value of the Helmholtz free energy. However, we can express it in terms of the given variables:A = -2 * 1.380649 10^-23 J/K * 300 K * ln 2 * pi * m * 1.380649 10^-23 J/K * 300 K / 6.62607015 10^-34 Js ^2 ^3/2 * V_m / 2 A = -2 * 1.380649 10^-23 J/K * 300 K * ln 2 * pi * m * k_B * T / h^2 ^3/2 * V_m / 2 This expression gives the Helmholtz free energy of the ideal gas in terms of the mass of the particles and the molar volume.