Ammonium carbonate decomposes upon heating according to the balanced equation: (NH4)2CO3(s) -> 2NH3(g)+CO2(g)+H2O(g)
Calculate the total volume of gas produced at 27.0 degrees C and 2.03 atm from the reaction of 1.4kg of (NH4)2CO3. What is the pressure of each of the gases produced?
I don't know where to start...
To solve this problem, we need to follow a few steps:
Step 1: Convert the mass of (NH4)2CO3 to moles.
To do this, we'll use the molar mass of (NH4)2CO3. The molar mass of (NH4)2CO3 is calculated by adding up the atomic masses of each element in the compound:
(NH4)2CO3:
(NH4) = 2 * 14.01 g/mol = 28.02 g/mol
C = 12.01 g/mol
O3 = 3 * 16.00 g/mol = 48.00 g/mol
Total molar mass of (NH4)2CO3 = 28.02 + 12.01 + 48.00 = 88.03 g/mol
Now, we can convert the mass of (NH4)2CO3 to moles using the formula:
moles = mass (g) / molar mass (g/mol)
moles = 1.4 kg * 1000 g/kg / 88.03 g/mol
moles = 15.90 mol
Step 2: Calculate the volume of gas produced at 27.0 degrees Celsius and 2.03 atm.
To calculate the volume of gas, we'll use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (K)
First, convert the temperature from Celsius to Kelvin:
T (K) = T (°C) + 273.15
T (K) = 27.0 + 273.15
T (K) = 300.15 K
Now we can rearrange the ideal gas law equation to solve for the volume:
V = nRT / P
V = (15.90 mol) * (0.0821 L·atm/(mol·K)) * (300.15 K) / 2.03 atm
V ≈ 359.05 L
So, the total volume of gas produced is approximately 359.05 liters.
Step 3: Calculate the pressure of each gas produced.
From the balanced equation, we can see that for every 1 mole of (NH4)2CO3, 2 moles of NH3, CO2, and H2O are produced.
Therefore, the number of moles of NH3, CO2, and H2O are also 15.90 mol each.
To calculate the partial pressure of each gas, we'll use the formula:
Partial pressure = (moles of gas / total moles) * total pressure
For NH3:
Partial pressure of NH3 = (15.90 mol / 15.90 mol) * 2.03 atm
Partial pressure of NH3 = 2.03 atm
For CO2:
Partial pressure of CO2 = (15.90 mol / 15.90 mol) * 2.03 atm
Partial pressure of CO2 = 2.03 atm
For H2O:
Partial pressure of H2O = (15.90 mol / 15.90 mol) * 2.03 atm
Partial pressure of H2O = 2.03 atm
So, the pressure of each gas produced is 2.03 atm for NH3, CO2, and H2O.