Ammonia will decompose into nitrogen and hydrogen at high temperature. An industrial chemist studying this reaction fills a 200. mL flask with 3.4 atm of ammonia gas, and when the mixture has come to equilibrium measures the amount of nitrogen gas to be 1.5 atm. Calculate the pressure equilibrium constant for the decomposition of ammonia at the final temperature of the mixture. Round your answer to 2 significant digits.

See explanation below

Explanation:

In this case, let's write the reaction first:

2NH₃ <> N₂ + 3H₂   Kp = ?

The problem states that we have 3.4 atm initially of ammonia. When the reaction reaches the equilibrium, the concentration of the nitrogen gas (one of the products) is 1.5 atm. All we need to know is the other values of the rest of species there, and then, we can calculate the equilibrium constant (Kp) for the reaction. To do that, we need to write the ICE chart for this reaction:

      2NH₃ <> N₂ + 3H₂

i)      3.4                 0       0

c)    -2x                +x     +3x

e)    3.4-2x             x      3x

The problem is already giving us the equilibrium pressure of the nitrogen, which is 1.5 atm. This would be the value of "x", so replacing in the rest of the species:

PpNH₃ = 3.4 - (2*1.5) = 0.4 atm

PpH₂ = 3*1.5 = 4.5 atm

Now that we have the values of the pressure, we can calculate Kp:

Kp = [H₂]³ [N₂] / [NH₃]²

Replacing the values:

Kp = (4.5)³ (1.5) / (0.4)²

Kp = 854.3

This would be the equilibrium constant value

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3