Answer:
-3.10 × 10⁶ J/mol
Explanation:
The heat (Qw) required to raise the temperature of the water can be calculated using the following expression.
Qw = c . m . ΔT
where,
c: specific heat capacity
m: mass
ΔT: change in the temperature
Qw = (4.186 J/g.°C) . 2990 g . (38.0°C - 18.0°C) = 2.50 × 10⁵ J
According to the law of conservation of energy, the sum of the heat released from the formation of P₄O₁₀ and the heat absorbed by the water is zero.
Qw + Qf = 0
Qf = -Qw = -2.50 × 10⁵ J
Let's consider the formation of P₄O₁₀.
4 P(s) + 5 O₂(g) → P₄O₁₀(s)
The heat of formation must be expressed per mole of P₄O₁₀. -2.50 × 10⁵ J is the heat released when 10.00 g of P react. Let's consider the following conversion factors:
The heat of formation of P₄O₁₀ is:
[tex]\frac{-2.50 \times 10^{5}J}{10.00gP} .\frac{30.97gP}{1molP} .\frac{4molP}{1molP_{4}O_{10}} =-3.10 \times 10^{6}J/mol[/tex]
