When 10.00 g of phosphorus is burned in O₂(g) to form P₄O₁₀(s), enough heat is generated to raise the temperature of 2950 g of water from 18.0 °C to 38.0 °C. Calculate the enthalpy of formation of P₄O₁₀(s) under these conditions.

Verified step by step guidance

1. Identify the chemical reaction: \( 4P(s) + 5O_2(g) \rightarrow P_4O_{10}(s) \).
2. Calculate the heat absorbed by the water using the formula: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of water, \( c \) is the specific heat capacity of water (4.18 J/g°C), and \( \Delta T \) is the change in temperature.
3. Convert the heat absorbed by the water from joules to kilojoules, since enthalpy is typically expressed in kJ.
4. Determine the moles of phosphorus used by dividing the mass of phosphorus by its molar mass (30.97 g/mol).
5. Calculate the enthalpy change per mole of \( P_4O_{10} \) formed by dividing the total heat change by the moles of \( P_4O_{10} \) produced.

Key Concepts

Enthalpy of Formation

The enthalpy of formation is the heat change that occurs when one mole of a compound is formed from its elements in their standard states. It is a crucial concept in thermodynamics and is typically expressed in kilojoules per mole (kJ/mol). Understanding this concept is essential for calculating the energy changes associated with chemical reactions, such as the combustion of phosphorus to form P4O10.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this context, it involves calculating the heat absorbed by water when phosphorus is burned, using the formula q = mcΔT, where q is the heat absorbed, m is the mass of the water, c is the specific heat capacity, and ΔT is the change in temperature. This measurement is vital for determining the enthalpy change of the reaction.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to relate the amount of phosphorus burned to the amount of P4O10 produced. In this problem, stoichiometry is necessary to convert the heat calculated from the calorimetry into the enthalpy of formation per mole of P4O10, ensuring accurate results.