Answer:
20075.35 J
Explanation:
We'll begin by calculating the number of mole in 89.9 g of CH₃OH. This can be obtained as follow:
Mass of CH₃OH = 89.9 g
Molar mass of CH₃OH = 12 + (3×1) + 16 + 1
= 12 + 3 + 16 + 1
= 32 g/mol
Mole of CH₃OH =?
Mole = mass / molar mass
Mole of CH₃OH = 89.9 / 32
Mole of CH₃OH = 2.81 moles
Next, we shall determine the heat required to melt the solid methanol (CH₃OH). This can be obtained as follow:
Mole of CH₃OH (n) = 2.81 moles
Heat of fusion (Hբ) = 3.17 KJ/mol
Heat required to melt CH₃OH (Q₁) = ?
Q₁ = n × Hբ
Q₁ = 2.81 × 3.17
Q₁ = 8.9077 KJ
Converting to J
Q₁ = 8.9077 × 1000
Q₁ = 8907.7 J
Next, we shall determine the heat required to change the temperature of methanol to 49.1 °C. This can be obtained as follow:
Mass of CH₃OH (M) = 89.9 g
Initial temperature (T₁) = 0 °C
Final temperature (T₂) = 49.1 °C.
Specific heat capacity of CH₃OH (C) = 2.53 J/gºC
Heat required to change the temperature (Q₂) =?
Q₂ = MC(T₂ – T₁)
Q₂ = 89.9 × 2.53 × (49.1 – 0)
Q₂ = 89.9 × 2.53 × 49.1
Q₂ = 11167.65 J
Finally, we shall determine the total heat. This can be obtained as follow:
Heat required to melt CH₃OH (Q₁) = 8907.7 J
Heat required to change the temperature (Q₂) = 11167.65 J
Total heat required (Q) =?
Q = Q₁ + Q₂
Q = 8907.7 + 11167.65
Q = 20075.35 J
Therefore, the total heat required to melt the methanol and bring it to a temperature of 49.1 °C is 20075.35 J
