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Match List-I with List-II regarding the missing term ' x ' in various forms of the ideal gas equation. List-I List-II (A) P = x RT M₀ (I) Number density (B) P = x k_B T (II) Mass density (C) PV = x RT (III) Molar mass (D) PV = ( m x )RT (IV) Number of moles Choose the correct answer from the options given below:

Options

  1. A(A)-(I), (B)-(II), (C)-(IV), (D)-(III)
  2. B(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
  3. C(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
  4. D(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

Correct answer

D. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

Step-by-step solution

The ideal gas equation can be expressed in various forms. In the macroscopic form involving mass density , the equation is P = RT M₀ . Thus, in (A), x represents mass density (II). In the microscopic form, the equation is P = n_v k_B T , where n_v is the number density (number of molecules per unit volume). Thus, in (B), x represents number density (I). The standard molar form is PV = nRT , where n is the number of moles. Thus, in (C), x represents the number of moles (IV). The number of moles n can be written as t

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