A 0.1219-g sample of solid magnesium is burned in a bomb calorimeter that has a heat capacity of 1769 J/°C. The calorimeter contains exactly 271 g of water, and the temperature increases by 1.126°C. Calculate the heat given off by the burning Mg, in kJ/g and in kJ/mol.
q = [mass H2O x specific heat H2O x (delta T)] + (Ccal*delta T)
q = (271)(1)(1.126)+(1769)(1.126)
= 2297.04
q/.1219 = 18,843.64 J/g = 18.8436 kJ/g
this isnt right
To calculate the heat given off by the burning magnesium, we first need to determine the amount of heat absorbed by the water and bomb calorimeter. We can then subtract this from the total heat generated to find the heat given off by the Mg.
Step 1: Calculate the heat absorbed by the water and calorimeter:
To do this, we can use the equation:
q = m × c × ΔT
Where:
q is the heat absorbed by the water and calorimeter (in J),
m is the mass of water and calorimeter (in g),
c is the specific heat capacity of water (4.18 J/g°C),
ΔT is the change in temperature (in °C).
In this case, the mass of the water and calorimeter (m) is 271 g, the specific heat capacity of water (c) is 4.18 J/g°C, and the change in temperature (ΔT) is 1.126 °C.
So, we have:
q = 271 g × 4.18 J/g°C × 1.126 °C
= 1220.84 J
Step 2: Convert the heat absorbed by the water and calorimeter to kJ:
To convert from J to kJ, we divide by 1000.
q(kJ) = 1220.84 J / 1000
= 1.22084 kJ
Step 3: Calculate the total heat generated by the burning Mg:
Since the heat absorbed by the water and calorimeter represents the total heat generated, we can calculate the total heat as:
Total heat = q(kJ) + Heat released by Mg
Total heat = 1.22084 kJ + Heat released by Mg
Step 4: Calculate the heat released by the Mg:
We can use the heat capacity of the calorimeter to find the heat released by the Mg using the equation:
Heat released by Mg = q × C
Where:
q is the heat absorbed by the water and calorimeter (in kJ),
C is the heat capacity of the bomb calorimeter (1769 J/°C).
The heat absorbed by the water and calorimeter (q) is 1.22084 kJ.
So, we have:
Heat released by Mg = 1.22084 kJ × 1769 J/°C
Step 5: Convert the heat released by the Mg to kJ/g and kJ/mol:
To convert the heat released by the Mg to kJ/g, we divide by the mass of the Mg sample (0.1219 g). To convert to kJ/mol, we divide by the molar mass of Mg (24.31 g/mol).
Heat released by Mg (kJ/g) = Heat released by Mg / mass of Mg
Heat released by Mg (kJ/mol) = Heat released by Mg / molar mass of Mg
The molar mass of Mg is 24.31 g/mol.
By substituting the given values:
Heat released by Mg (kJ/g) = (1.22084 kJ × 1769 J/°C) / 0.1219 g
= 17.78 kJ/g (rounded to two decimal places)
Heat released by Mg (kJ/mol) = (1.22084 kJ × 1769 J/°C) / 24.31 g/mol
= 84.47 kJ/mol (rounded to two decimal places)
Therefore, the heat given off by the burning Mg is approximately 17.78 kJ/g and 84.47 kJ/mol.