What is the absolute entropy of 1.9 mol of gaseous ammonia at 2.8 bar and 298 K?
To calculate the absolute entropy of a substance, we need to know the molar entropy of the substance at a standard state (usually at 1 bar and 298 K) and use the ideal gas law.
To find the molar entropy of gaseous ammonia at a standard state, we consult a reference source such as a textbook or a database. Let's assume that the molar entropy is given as 192.77 J/(mol·K).
The ideal gas law is given by:
PV = nRT
Where:
P = Pressure (in this case, 2.8 bar)
V = Volume (the volume of 1.9 mol of ammonia is not given, but it's not necessary for this calculation)
n = Number of moles (in this case, 1.9 mol)
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature (298 K)
From the ideal gas law, we can rearrange the equation to calculate the volume (V):
V = (nRT) / P
Using the given values, we can plug them into the equation and calculate the volume:
V = (1.9 mol * 8.314 J/(mol·K) * 298 K) / (2.8 bar * 10^5 Pa/bar)
Once you have calculated the volume, you can use the formula for entropy:
S = n * Smolar
Where:
S = Absolute entropy
n = Number of moles (in this case, 1.9 mol)
Smolar = Molar entropy (192.77 J/(mol·K))
Finally, you can calculate the absolute entropy:
S = 1.9 mol * 192.77 J/(mol·K)