A coffee cup calorimeter contains 100ml of .200M H2SO4 at 22.3 degrees Celsius. When 2.16g Mg is added, the temperature rises to 36.3 degrees Celsius. What is the heat of the reaction per mole Mg?

Please help and show steps. Much appreciated :)

Mg + H2SO4 ==> MgSO4 + H2

qrxn = mass H2O x specific heat H2O x (Tfinal-Tinitial)

per gram is qrxn/2.16 g Mg.
per mol Mg is (qrxn/2.16) x molar mass Mg

thank you!

To find the heat of the reaction per mole of Mg, we can use the formula for heat change:

q = mcΔT

Where:
q = heat change
m = mass
c = specific heat capacity
ΔT = change in temperature

First, let's find the heat change (q) for the solution. Since the heat is transferred from the solution to the surroundings (coffee cup calorimeter), the heat change for the solution would be equal to the heat change for the surroundings.

q(solution) = q(surroundings)

Step 1: Calculate the heat change for the solution.
q(solution) = m(solution) * c(solution) * ΔT(solution)

Given:
m(solution) = 100 ml = 0.1 L (volume of the solution)
c(solution) = specific heat capacity of the solution (water) = 4.18 J/g°C (this value is commonly used for water)
ΔT(solution) = final temperature - initial temperature = 36.3°C - 22.3°C = 14°C

q(solution) = (0.1 L) * (4.18 J/g°C) * (14°C) = 5.85 J

Now, let's find the number of moles of Mg reacted.

Step 2: Calculate the number of moles of Mg.
Given:
Mass of Mg = 2.16 g
Molar mass of Mg = 24.31 g/mol

Number of moles of Mg = Mass of Mg / Molar mass of Mg
Number of moles of Mg = 2.16 g / 24.31 g/mol = 0.089 mol

Since the reaction between Mg and H2SO4 is 1:1 (1 mole of Mg reacts with 1 mole of H2SO4), the ΔH (heat of reaction) can be calculated by dividing the heat change by the number of moles of Mg.

Step 3: Calculate the heat change per mole of Mg.
ΔH = q(solution) / Number of moles of Mg
ΔH = 5.85 J / 0.089 mol ≈ 65.84 J/mol

Therefore, the heat of the reaction per mole of Mg is approximately 65.84 J/mol.