Question

25ml of liquid nitrogen (density = .807 g/ml) is poured into a cylindrical container with a radius of 10cm and a length of 20cm. The container initially contains only air at a pressure of 760mmHg (atm pressure) and a temp of 298K. If the liquid N completely vaporizes, what is the total force (in lbs) on the interior of the container at 298K?

Answer 1

Answer:

16311 lbs

Explanation:

Volume of the cylinder = πr²l

                                       = π (10 cm)² x 20cm

                                        =3.14 x 100 x 20 cm³

                                         = 6283 cm³

                                          =6283 ml  

                          6283 ml - 25 ml = 6258 ml

                                                       = 6.258 l     ( since 1 l = 1000 ml )

                    PV  = nRT

  n = $\frac{PV}{RT}$

P = 760 mm

V = 6.258 l

R = 0.082057 l. atm/mol.K

n=?

 n = $\frac{PV}{RT}$

     =  0.2559 mol/air

T = 298 K

mass of Nitrogen = 25ml

density = 0.807 g/ml

mol mass of nitrogen =28.0134 g/mol

 = (25ml x 0.807 g/ml) ÷  (28.0134 g/mol)

 = 0.72019 mol N₂

Total mol = 0.2559 +0.72019 = 0.9761 mol

P=( n ×R × T) ÷ V

V = 6.283l ; R = 0.082057 l ; T = 298K ;n = 0.9761

∴ P = 3.799 atm

F = P × SA ( Force = pressure × surface Area )

P = 3.799atm

SA  = 2πr² + 2πrl

       = 2π ( 0.0010m) + 2π (0.0010m) (0.020m)

       = 0.188496 m²

∴ Force F = 384934 × 0.1884

                 =  72558 N = 16311 lbs