Im confused how do i solve? 4.70. Can equation 4.62 be used to calculate ☀ for an idealgas? Why or why not? 4.62. Like the entropy of mixing, a Gibbs energy of mixing forgases can be derived:no of gasesAmix G = RT Σ n₁ Inx;i=1where n, is the number of moles and x; is the mole fractionof the ith gas. (a) Derive this equation. Hint: assume AmixH = 0and use equation 3.25. (b) Show that mixing is always spon-taneous by demonstrating that AmixG is always less than zerofor a mixture of gases. (c) Calculate AmixG when 1.0 mol Ne,2.0 mol He, and 3.0 mol Ar are mixed at 35.0°C.

“Since you have posted a question with multiple sub parts, we will provide the solution only to the first three sub parts as per our Q&A guidelines. Please repost the remaining sub parts separately.”Given:Gibbs energy of mixing for gases derived:1 mol Ne gas2.0 mol He gas3.0 mol Ar gasT= 35.0oCDerive the above equation.The Gibbs free energy change () is a thermodynamic variable that determines a reaction's spontaneity. If is negative, .a) Derivation of the Equation:The spontaneity of a reaction can be determined by the Gibbs free energy change (). ....(1)Where: = Gibbs free energy change = Enthalpy changeT = Temperature in Kelvin = Entropy changeGiven that the Now simplify the equation (1):...(2)Now, we know that entropy ((S)) is related to mole fraction by:Now substitute this value in the equation and we get: ...(3)(b) Show that Mixing is Spontaneous:For a spontaneous process, should be negative. Using the derived equation:Since (R) and (T) are positive, and the natural logarithm of any number between 0 and 1 is negative, is always negative, indicating that mixing is spontaneous.c) Calculate :First convert temperature to kelvin by using the unit conversion factor:Now, calculate the mole fractions using this equation:Now substitute these values in the equation and we get:Therefore, the Gibbs energy of mixing for the given mixture of gases is approximately indicating that the mixing is spontaneous.The answer to the question is explained in steps 2,3,4 and 5.