The final temperature change (ΔT) in the reaction of magnesium with hydrochloric acid is approximately -7.18 °C. Consequently, the final temperature of the solution is approximately 18.42 °C.
To find the final temperature change (ΔT), we can use the equation:
q = mcΔT
where:
q is the heat absorbed or released,
m is the mass of the solution,
c is the specific heat of the solution, and
ΔT is the change in temperature.
First, let's find the moles of magnesium (n) reacting using its molar mass (M):
n = mass / M
The molar mass of magnesium (Mg) is approximately 24.31 g/mol.
n = 0.158 g / 24.31 g/mol ≈ 0.0065 mol
Now, we know that the enthalpy change (ΔH) for the reaction is given as -4.62 × 10^5 J/mol.
The heat (q) released or absorbed by the reaction is given by:
q = ΔH × n
q = (-4.62 × 10^5 J/mol) × (0.0065 mol) ≈ -3003 J
This heat is absorbed by the solution, so q in the q = mcΔT equation is positive.
Now, we need to find the mass (m) of the solution. The mass of water is the sum of the mass of the solvent (water) and the solute (magnesium):
m = mass of water + mass of Mg
The volume of the solution is given as 100.0 mL, and the density of water is 1.00 g/mL.
mass of water = volume × density = (100.0 mL) × (1.00 g/mL) = 100.0 g
Now, the total mass of the solution is:
m = 100.0 g + 0.158 g = 100.158 g
Now, we can rearrange the q = mcΔT equation to solve for ΔT:
ΔT = q / mc
ΔT = -3003 J / (100.158 g × 4.18 J/g°C)
ΔT ≈ -7.18 °C
Finally, we can find the final temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 25.6 °C - 7.18 °C ≈ 18.42 °C
Therefore, the final temperature is approximately 18.42 °C.