Question

calculate the standard entropy change for the industrial synthesis of urea, a common fertilizer.
co₂(g) + 2nh₃(g) → co(nh₂)₂(s) + h₂o(l)
compound | s°(j/mol·k)
co₂(g) | 213.74
nh₃(g) | 192.45
co(nh₂)₂(s) | 104.60
h₂o(l) | 69.91
δs° = ? j/k
enter either a + or - sign and the magnitude in your answer.

Explanation:

Step1: Recall the formula for standard entropy change

The formula for the standard entropy change (\(\Delta S^\circ\)) of a reaction is \(\Delta S^\circ=\sum S^\circ(\text{products})-\sum S^\circ(\text{reactants})\).

Step2: Identify products and reactants with their stoichiometric coefficients

For the reaction \(\ce{CO2(g) + 2NH3(g) -> CO(NH2)2(s) + H2O(l)}\):

• Products: \(\ce{CO(NH2)2(s)}\) (coefficient 1) and \(\ce{H2O(l)}\) (coefficient 1)
• Reactants: \(\ce{CO2(g)}\) (coefficient 1) and \(\ce{NH3(g)}\) (coefficient 2)

Step3: Calculate \(\sum S^\circ(\text{products})\)

\(\sum S^\circ(\text{products}) = S^\circ(\ce{CO(NH2)2(s)})+S^\circ(\ce{H2O(l)})\)
Substitute the values: \(104.60 + 69.91 = 174.51\space J/mol\cdot K\)

Step4: Calculate \(\sum S^\circ(\text{reactants})\)

\(\sum S^\circ(\text{reactants}) = S^\circ(\ce{CO2(g)})+2\times S^\circ(\ce{NH3(g)})\)
Substitute the values: \(213.74+2\times192.45 = 213.74 + 384.9 = 598.64\space J/mol\cdot K\)

Step5: Calculate \(\Delta S^\circ\)

\(\Delta S^\circ=\sum S^\circ(\text{products})-\sum S^\circ(\text{reactants})\)
Substitute the values: \(174.51 - 598.64=-424.13\space J/K\)

Answer:

-424.13