A piece of aluminum with mass of 5.0 g is immersed in 30.0 g of water. This system is heated electrically from 20.8 to 42.6°C. How many joules of energy are absorbed by the aluminum? (Cpaluminum = 24.4 J/mol-K; 1 mole of aluminum has a mass of 27.0 g)
And How many joules of energy are absorbed by the water?
q Al = mass Al x specific heat Al x (Tfinal-Tinitial)
q H2O = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Note: If you use specific heats in J/mol*K then you must use mass in mols and not grams.
To calculate the amount of energy absorbed by the aluminum, we can use the formula:
q = m × Cp × ΔT
where:
q is the energy absorbed (in joules)
m is the mass of the aluminum (in grams)
Cp is the specific heat capacity of aluminum (in J/mol-K)
ΔT is the change in temperature (in °C)
First, let's convert the mass of the aluminum to moles:
moles of aluminum = mass of aluminum / molar mass of aluminum
moles of aluminum = 5.0 g / 27.0 g/mol = 0.185 moles
Now we can calculate the energy absorbed by the aluminum:
q = m × Cp × ΔT
q = 0.185 moles × 24.4 J/mol-K × (42.6°C - 20.8°C)
Let's calculate the value:
q ≈ 0.185 × 24.4 × 21.8
q ≈ 89.84 joules
Therefore, approximately 89.84 joules of energy are absorbed by the aluminum.
To calculate the energy absorbed by the aluminum, we need to use the formula:
Q = mcΔT
Where:
Q = energy absorbed (in joules)
m = mass of the aluminum (in grams)
c = specific heat capacity of aluminum (in J/mol-K)
ΔT = change in temperature (in Kelvin)
First, we need to convert the mass of aluminum from grams to moles using its molar mass:
n = m/M
Where:
n = moles of aluminum
m = mass of aluminum (in grams)
M = molar mass of aluminum
Given that the molar mass of aluminum is 27.0 g/mol, we can calculate:
n = 5.0 g / 27.0 g/mol
n ≈ 0.185 moles
Now, we can calculate the energy absorbed using the formula:
Q = mcΔT
Where:
m = number of moles of aluminum
c = specific heat capacity of aluminum (in J/mol-K)
ΔT = change in temperature (in Kelvin)
Given that the specific heat capacity of aluminum is 24.4 J/mol-K, and the change in temperature is ΔT = 42.6°C - 20.8°C = 21.8°C, we need to convert ΔT to Kelvin:
ΔT = 21.8°C + 273.15 K
ΔT ≈ 295.95 K
Now we can substitute the values into the formula:
Q = (0.185 mol)(24.4 J/mol-K)(295.95 K)
Q ≈ 1264.34 J
Therefore, approximately 1264.34 joules of energy are absorbed by the aluminum.