Question

calculate the standard entropy change for the industrial synthesis of urea, a common fertilizer.\\(\ce{co2(g) + 2nh3(g) \
ightarrow co(nh2)2(s) + h2o(l)}\\)\

compound	\\(s^\circ\\)(j/mol·k)	\
---	---	\
\\(\ce{co2(g)}\\)	213.74	\
\\(\ce{nh3(g)}\\)	192.45	\
\\(\ce{co(nh2)2(s)}\\)	104.60	\
\\(\ce{h2o(l)}\\)	69.91	\

\\(\delta s^\circ = ?\\) 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: \(\ce{CO(NH2)2(s)}\) (1 mole) and \(\ce{H2O(l)}\) (1 mole)
• Reactants: \(\ce{CO2(g)}\) (1 mole) and \(\ce{NH3(g)}\) (2 moles)

Step3: Calculate the sum of standard entropies of products

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

Step4: Calculate the sum of standard entropies of reactants

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

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

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

Answer:

\(-424.13\)