The reaction of cyanamide, NH2CN (s), with dioxygen was carried out in a bomb calorimeter, and ?U was found to be –742.7 kJ mol–1 at 298 K. Calculate enthalpy change for the reaction at 298 K. ?

To determine the enthalpy change (ΔH) for the reaction of cyanamide (NH2CN) with dioxygen (O2) at 298 K, we can use the relationship between internal energy change (ΔU) and enthalpy change (ΔH). The equation that connects these two thermodynamic quantities is given by:

Understanding the Relationship

The relationship is expressed as:

ΔH = ΔU + ΔnRT

Where:

• ΔH = Enthalpy change
• ΔU = Internal energy change (which is given as –742.7 kJ mol–1)
• Δn = Change in the number of moles of gas during the reaction
• R = Universal gas constant (approximately 8.314 J mol–1 K–1)
• T = Temperature in Kelvin (298 K in this case)

Calculating Δn

To find Δn, we need to look at the balanced chemical equation for the reaction. Let's assume the reaction can be represented as:

2 NH2CN (s) + O2 (g) → Products

In this hypothetical reaction, if we assume that the products are gaseous, we can calculate Δn as follows:

• Reactants: 1 mole of O2 (g) + 2 moles of NH2CN (s) contributes 0 moles of gas.
• Products: Let's say we produce 2 moles of gaseous products.

Thus, Δn = moles of gaseous products - moles of gaseous reactants = 2 - 1 = 1.

Substituting Values

Now that we have Δn, we can substitute the values into the equation:

ΔH = ΔU + ΔnRT

ΔH = –742.7 kJ mol–1 + (1 mol)(8.314 J mol–1 K–1)(298 K)

First, convert the gas constant R from J to kJ:

R = 8.314 J mol–1 K–1 = 0.008314 kJ mol–1 K–1

Now, calculate the second term:

ΔnRT = (1 mol)(0.008314 kJ mol–1 K–1)(298 K) = 2.478 kJ

Final Calculation

Now, plug this value back into the equation:

ΔH = –742.7 kJ mol–1 + 2.478 kJ = –740.222 kJ mol–1

Result

Therefore, the enthalpy change for the reaction at 298 K is approximately:

ΔH ≈ –740.2 kJ mol–1

This indicates that the reaction is exothermic, releasing energy in the form of heat. Understanding these thermodynamic principles is crucial for predicting how reactions will behave under different conditions.