A 0.1589 g sample of solid magnesium is burned in a bomb calorimeter that has a heat capacity of 1769 J/°C. The calorimeter contains exactly 251 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 water x specific heat water x delta T] + [calorimeter constant x delta T]

This give you q.
Then q/0.1589 g gives J/g. Convert that to kJ/g and to kJ/mol.

To calculate the heat given off by the burning Mg, we need to use the formula:

q = m × C × ΔT

where:
q is the heat given off
m is the mass of the substance burned (in this case, the mass of magnesium)
C is the heat capacity of the calorimeter
ΔT is the change in temperature

First, let's calculate the heat given off in J using the given values:

m = 0.1589 g
C = 1769 J/°C
ΔT = 1.126°C

Plugging these values into the formula:

q = 0.1589 g × 1769 J/°C × 1.126°C
q = 38.428 J

To convert the heat from J to kJ, divide by 1000:

q = 38.428 J ÷ 1000
q ≈ 0.038 kJ

Therefore, the heat given off by burning 0.1589 g of magnesium is approximately 0.038 kJ.

To calculate the heat given off in kJ/mol, we need to know the molar mass (atomic weight) of magnesium. The atomic weight of magnesium is 24.305 g/mol.

To find the number of moles of magnesium:
moles = mass / molar mass
moles = 0.1589 g / 24.305 g/mol
moles ≈ 0.006533 mol

Now, we can calculate the heat given off per mole:

q/mol = q / moles
q/mol = 0.038 kJ / 0.006533 mol
q/mol ≈ 5.811 kJ/mol

Therefore, the heat given off by burning magnesium is approximately 5.811 kJ/mol.