Question

Chemistry - Gas Laws:

A 1.00 liter vessel contains 5.00 grams of nitrogen (N2) and 1.50 grams of water at 25°C.

a)Determine the RMS speed of nitrogen molecules and water molecules in the vapor phase at 25°C.

b)Calculate the average kinetic energyper moleculeof nitrogen and of water vapor at 25°C.

(Show all work and calculations, include units in answer. If calculations must be used in several parts, rounding should be made to 6 decimal points to ensure accuracy. Final Answers can be rounded to 3 decimal points. Molar Mass N = 14.01 g/mol. Molar Mass H₂O = 18.016 g/mol, Vapor Pressure of Water at 25 C is 23.76 torr)

Answer 1

a)

RMS speed -->

T = 298K

Apply the RMS equation

RMS =sqrt(3*RT/MW)

where, R = ideal gas constant, T = temperature, MW moalr mas in kg/mol

MW of N2= 28 g/mol --> change to kg --> 28*10^-3 kg/mol

RMS= sqrt(3*8.314*298/ (28*10^-3))

RMS = 515.22 m/s for N2

Now, for water

mass = 18 g/mol --> 18*10^-3 kg/mol

RMS= sqrt(3*8.314*298/ (18*10^-3))

RMS = 642.59 m/s for H2O

b)

AVG. kinetic energy per molecule of N2

Ekavg = 3/2*k*T

where k = boltzmann constant = 1.38066 x 10-23 J/K

T = Temperature

Ekavg = 3/2*k*T = 3/2*(1.38066 *10^-23)(298) = 6.171*10^-21 J/molecule

for both cases