At 25 C, Keq = 0.90 for the reaction: H2O + Cl2O = 2HOCl (all gases)

Question

Calculate the concentrations of all species at equilibrium a) if 1.0g of H2O and 4.83 g of Cl2O are mixed in a 1-L flask. b) 1.0 mol of pure HOCl is placed in a 2.0-L flask

Answer 1

H₂O(g) + Cl₂O(g) <==> 2HOCl(g) .. balanced equation

moles H₂O = 1.0 g x 1 mol H2O / 18 g = 0.0556 mols

moles Cl₂O = 4.83 g x 1 mol / 86.9 = 0.0556 mols

H₂O(g) + Cl₂O(g) <==> 2HOCl(g)

.0556......0556...................0.............Initial

-x.............-x...................+2x.............Change

.0556-x....0.0556-x..........2x.............Equilibrium

K = 0.90 = [HOCl]² / [H₂O][Cl₂O]

0.90 = (2x)² / (0.0556-x)²

Now you'd use the quadratic equation and solve for x. Plug this value of x back into the Equilibrium line of the ICE table to find the equilibrium concentrations of all the species present. I got x = 0.018 so final equilibrium concentrations would b

[H₂O] = 0.0556 - 0.18 = 0.0376 M

[Cl₂O[ = 0.0376 M

[HOCl] = 2x0.018 = 0.036 M

b). Initial [HOCl] = 1 mol / 2 L = 0.5 M

H₂O(g) + Cl₂O(g) <==> 2HOCl(g)

.......0.............0...................0.5............Initial

.....+x............+x.................-2x............Change

.....x................x.................0.5-2x.......Equilibrium

K = [HOCl]² / [H2O][HOCl]

0.90 = (0.5-2x)² / x²

0.90x² = 4x² - 2x + 0.25

3.1x² - 2x + 0.25 = 0

x = 0.169

Equilibrium concentrations are:

[H2O] = 0.169 M

[Cl₂O] = 0.169 M

[HOCl] = 0.5 - 0.338 = 0.162 M

BE SURE TO CHECK ALL OF THE MATH

Answer 2

a) To calculate the concentrations of all species at equilibrium when 1.0 g of H2O and 4.83 g of Cl2O are mixed in a 1-L flask, we need to determine the number of moles of each substance and then use the ideal gas law to calculate the concentrations.

1. Calculate the number of moles:

Molar mass of H₂O = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol

Moles of H2O = Mass / Molar mass = 1.0 g / 18.02 g/mol

Molar mass of Cl2O = 2(35.45 g/mol) + 16.00 g/mol = 86.90 g/mol

Moles of Cl2O = Mass / Molar mass = 4.83 g / 86.90 g/mol

2. Calculate the concentrations using the ideal gas law:

Since the system is in a 1-L flask, the volume (V) is 1 L.

For H2O:

Concentration of H2O = Moles of H2O / Volume of solution = Moles of H2O / V

For Cl2O:

Concentration of Cl2O = Moles of Cl2O / Volume of solution = Moles of Cl2O / V

Now you can substitute the values you calculated in step 1 into the concentration equations to find the concentrations of H2O and Cl2O at equilibrium.

b) To calculate the concentrations of all species at equilibrium when 1.0 mol of pure HOCl is placed in a 2.0-L flask, we need to use the information given directly.

Since 1.0 mol of HOCl is placed in a 2.0-L flask, the concentration of HOCl is:

Concentration of HOCl = Moles of HOCl / Volume of solution = 1.0 mol / 2.0 L

The concentration of HOCl at equilibrium is given by the above equation.