I need help with answering this question.
Thanks!
What is the absolute entropy of 1.9 mol of gaseous ammonia at 2.8 bar and 298 K?
To find the absolute entropy of gaseous ammonia at the given conditions, we will follow a few steps:
Step 1: Find the molar entropy of ammonia at standard conditions.
Step 2: Apply the ideal gas law to find the molar volume of ammonia at the given conditions.
Step 3: Calculate the absolute entropy using the molar entropy and molar volume obtained.
Let's break down each step:
Step 1: Find the molar entropy of ammonia at standard conditions.
The molar entropy (S°) at standard conditions (298 K and 1 bar) can be found using reliable reference sources or tables. For ammonia (NH3), the molar entropy under standard conditions is approximately 193.6 J/(mol·K).
Step 2: Apply the ideal gas law to find the molar volume of ammonia at the given conditions.
The ideal gas law is given by: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Rearranging the equation gives: V = (nRT) / P.
In this case, we have:
P = 2.8 bar (convert to Pa by multiplying by 10^5: 2.8 * 10^5 Pa)
n = 1.9 mol
R = 8.314 J/(mol·K)
T = 298 K
Calculating the molar volume V:
V = (1.9 * 8.314 * 298) / (2.8 * 10^5)
Step 3: Calculate the absolute entropy using the molar entropy and molar volume obtained.
The absolute entropy (S) is given by the equation: S = S° + R * ln(V / V°), where V° is the standard molar volume (22.414 L/mol).
Since we know S°, V°, and V, we can substitute these values into the equation and solve for the absolute entropy S.
S = 193.6 + 8.314 * ln(V / 22.414)
Now, you can plug in the calculated value of V from Step 2 and solve the equation to find the absolute entropy of gaseous ammonia at the given conditions (2.8 bar and 298 K).