methanol and aluminum are reacted. how many moles of methanol must burn to raise the temperature of 100g of aluminum by 80 degrees Celsius?
To determine the number of moles of methanol required to raise the temperature of aluminum, we need to use the equation:
Q = mcΔT
Where:
Q is the amount of heat transferred in joules (J)
m is the mass of the aluminum in grams (g)
c is the specific heat capacity of aluminum (J/g°C)
ΔT is the change in temperature of aluminum in °C
First, let's calculate the amount of heat (Q) needed to raise the temperature of aluminum:
Q = mcΔT
Q = 100g * c * 80°C
The specific heat capacity of aluminum is approximately 0.897 J/g°C. Therefore:
Q = 100g * 0.897 J/g°C * 80°C
Q ≈ 7176 J
Now, we need to convert the amount of heat required to moles of methanol by using the enthalpy of combustion for methanol:
ΔH = n * ΔHf
Where:
ΔH is the enthalpy change in kilojoules (kJ)
n is the number of moles of methanol
ΔHf is the standard enthalpy of formation for methanol, which is -238.7 kJ/mol
First, let's convert the heat transfer value (Q) to kilojoules:
Q = 7176 J = 7.176 kJ
Now, rearrange the equation to solve for the number of moles of methanol (n):
n = Q / ΔHf
n = 7.176 kJ / -238.7 kJ/mol
After performing the calculation, we find:
n ≈ -0.03 mol
Since we cannot have a negative number of moles, we can conclude that the reaction between methanol and aluminum is exothermic (releasing heat) and that approximately 0.03 moles of methanol needs to burn to raise the temperature of 100g of aluminum by 80 degrees Celsius.