From the given condition, the temperature and pressure of a container filled with 175g argon should be determined. Concept introduction: By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law . According to ideal gas law, PV = nRT Where, P = pressure in atmospheres V= volumes in liters n = number of moles R =universal gas constant ( 0.08206 L ⋅ a t m / K ⋅ m o l ) T = temperature in kelvins By knowing any three of these properties, the state of a gas can be simply identified with applying the ideal gas equation.

Question

16. Consider the probability distribution p(x) = ax", 0 ≤ x ≤ 1 for a positive integer n. A. Derive an expression for the constant a, to normalize p(x). B. Compute the average (x) as a function of n. C. Compute σ2 = (x²) - (x)², the variance of x, as a function of n.

Answer 1

Question

Chapter 8, Problem 53E

a)

Interpretation Introduction

Interpretation: From the given condition, the temperature and pressure of a container filled with 175g argon should be determined.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

                                             PV = nRT

Where,

          P = pressure in atmospheres

          V= volumes in liters

          n = number of moles

          R =universal gas constant ( 0.08206L⋅atm/K⋅mol )

          T = temperature in kelvins

By knowing any three of these properties, the state of a gas can be simply identified with applying the ideal gas equation.

(b)

Interpretation Introduction

Interpretation: From the given condition, the temperature and pressure of a container filled with 175g argon should be determined.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

                                             PV = nRT

Where,

          P = pressure in atmospheres

          V= volumes in liters

          n = number of moles

          R =universal gas constant ( 0.08206L⋅atm/K⋅mol )

          T = temperature in kelvins

By knowing any three of these properties, the state of a gas can be simply identified with applying the ideal gas equation.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Students have asked these similar questions

16. Consider the probability distribution p(x) = ax", 0 ≤ x ≤ 1 for a positive integer n. A. Derive an expression for the constant a, to normalize p(x). B. Compute the average (x) as a function of n. C. Compute σ2 = (x²) - (x)², the variance of x, as a function of n.

451. Use the diffusion model from lecture that showed the likelihood of mixing occurring in a lattice model with eight lattice sites: Case Left Right A B C Permeable Barrier → and show that with 2V lattice sites on each side of the permeable barrier and a total of 2V white particles and 2V black particles, that perfect de-mixing (all one color on each side of the barrier) becomes increasingly unlikely as V increases.

46. Consider an ideal gas that occupies 2.50 dm³ at a pressure of 3.00 bar. If the gas is compressed isothermally at a constant external pressure so that the final volume is 0.500 dm³, calculate the smallest value Rest can have. Calculate the work involved using this value of Rext.