Ammonium carbonate (solid) decomposes when heated to produce three gaseous products - ammonia, water, and carbon dioxide.

1. Write the balanced equation for the reaction.
2. Suppose that ammonium carbonate is heated to 500 K in a sealed vessel. At equilibrium there is still some solid in the vessel, and the partial pressure of the ammonia gas is 4.00 atm. Find both the Kp and the Kc of the reaction at 500 K.

3. It is found that the mass loss of the ammonium carbonate on being heated is 1.000 gram. What is the volume of the sealed vessel?

To answer these questions, we need to go step by step. Let's start with question 1.

1. Balanced equation for the reaction:
The reaction can be represented by the balanced equation:
(NH4)2CO3 (s) -> 2 NH3 (g) + H2O (g) + CO2 (g)

Now, let's move on to question 2.

2. Finding Kp and Kc values:
The equilibrium constant, K, can be expressed in terms of either pressures (Kp) or concentrations (Kc). To find these values, we need to use the partial pressures and concentrations at equilibrium.

Given that the partial pressure of ammonia gas (NH3) at equilibrium is 4.00 atm, we know that the equilibrium expression can be written as:

Kp = (P_NH3)^2 / (P_CO2 * P_H2O)

However, to find Kc, we need to know the molar concentrations of the gaseous species at equilibrium. Unfortunately, we don't have that information. So, we can only determine Kp at this point.

3. Finding the volume of the sealed vessel:
To determine the volume of the sealed vessel, we need to use the information provided about the mass loss of ammonium carbonate when heated. The molar mass of ammonium carbonate is approximately 96.09 g/mol.
Given that the mass loss is 1.000 gram, we can calculate the number of moles of ammonium carbonate decomposed:

moles of (NH4)2CO3 = mass loss / molar mass
= 1.000 g / 96.09 g/mol

Now, we need to use the ideal gas law to relate moles to volume. The ideal gas law equation is:

PV = nRT

Since the vessel is sealed, the total pressure (P), the number of moles (n), and the temperature (T) are constant. We can rewrite the equation as:

V = (nRT) / P

Plugging in the values, we get:

V = [(1.000 g / 96.09 g/mol) * R * 500 K] / P

Where R is the ideal gas constant. Plugging in the appropriate value, we can calculate the volume of the sealed vessel.

Please note that for thermodynamic calculations like this, you should use the actual value of the ideal gas constant (R).